OC2 V2 final01.docozcoasts.org.au/wp-content/uploads/pdf/CRC/OC2_V2_Investigation_… ·...

CONTENTS Contents......................................................................................................................0

List of Figures ............................................................................................................3

List of Tables ..............................................................................................................4

Glossary......................................................................................................................5

1 Introduction ........................................................................................................7

1.1 Project Overview ..........................................................................................7

1.2 Overview of Delft3D .....................................................................................7

2 Numerical ModelSet-Up.....................................................................................9

2.1 Introduction...................................................................................................9

2.2 Numerical domain ........................................................................................9

2.2.1 Boundaries conditions ..........................................................................9

2.2.2 Computational Grid (CG)....................................................................10

2.2.3 Input Grid............................................................................................11

2.2.4 Obstacles............................................................................................11

2.2.5 Output Grid .........................................................................................12

3 Waves Data input .............................................................................................14

3.1 Grid parameters .........................................................................................14

3.2 Specification of Boundaries........................................................................14

3.3 Tidal Information.........................................................................................15

3.4 Physical parameters...................................................................................16

3.5 Numerical parameters ................................................................................18

3.6 Output Curves ............................................................................................19

3.7 Output Parameters .....................................................................................20

4 Flow Data Input.................................................................................................21

4.1 Grid Parameters .........................................................................................21

4.2 Bathymetry .................................................................................................22

4.3 Dry Points / Thin dams ...............................................................................22

4.4 Time Frame ................................................................................................22

4.5 Processes...................................................................................................24

4.6 Initial Conditions .........................................................................................24

4.7 Boundaries .................................................................................................24

4.8 Physical Parameters ..................................................................................27

4.9 Discharges .................................................................................................30

4.10 Monitoring...................................................................................................30

4.11 Output parameters .....................................................................................32

5 MOR DATA INPUT ............................................................................................34

Investigation of Ebb Tidal Deltas 1

5.1 Introduction.................................................................................................34

5.2 Process Tree � Morphodynamic simulations under a tidal regime.............34

5.3 Time management for coastal applications................................................36

5.4 Description of the modules within Delft3D-MOR ........................................37

5.5 Description of Input file for Transport module.............................................39

5.5.1 Module Options ..................................................................................39

5.5.2 Time parameters ................................................................................40

5.5.3 Spiral Motion and gravity (bed) slope effects .....................................40

5.5.4 Bed Characteristics ............................................................................40

5.5.5 Initial Distribution of sediment concentration ......................................40

5.5.6 Boundary conditions ...........................................................................41

5.5.7 General sediment parameters ............................................................41

5.5.8 Sediment transport relation � Bijker with wave effects ...........................41

5.5.9 Slope effect on magnitude of sediment transport ...............................41

5.5.10 Stability options ..................................................................................41

5.5.11 Output options ....................................................................................43

5.6 Description of Input file for Bottom Module.................................................43

5.6.1 General Input Data .............................................................................43

5.6.2 Output Options ...................................................................................43

5.6.3 Boundary conditions ...........................................................................44

5.6.4 Dredging option ..................................................................................44

6 Model Calibration .............................................................................................46

6.1 Instrument repositioning .............................................................................46

6.2 Calibration of the FLOW module ................................................................47

6.2.1 Water levels........................................................................................47

6.2.2 Flow Velocities....................................................................................50

6.2.3 Conclusion on Flow calibration...........................................................51

6.3 Calibration of the WAVE module ................................................................51

6.4 Calibration of the MORPHOLOGICAL module...........................................53

6.4.1 Bijker Formula (1971) with wave effects: basic formulation................53

6.4.2 Influence of roughness and friction coefficients..................................55

6.4.3 Calibration of the longshore transport ................................................55

Grain size ...............................................................................................................59

Bottom shear stress due to the waves: Bijker or Fredsoe?....................................59

6.4.4 Calibration of the inlet bed load transport ...........................................60

7 Results ..............................................................................................................67

7.1 Summary table of the simulations ..............................................................67


7.2 Description of morphological changes........................................................67

7.2.1 Comparison between current-dominated simulations T1 and T2 .......67

7.2.2 Comparison between wave-dominated simulations T3 and T4..........70

7.3 Ebb delta Growth curves ............................................................................73

7.3.1 Why are the simulations periods of the physical model extended in the numerical model? ...............................................................................................73

7.3.2 Why is the volume of delta greater in the numerical model than in the physical model?..................................................................................................73

7.3.4 Deposition rate of the delta.................................................................75

7.3.5 Impact of sediment bypassing around the entrance...........................76

7.4 Cross-sections............................................................................................77

7.4.1 Ruling depth and evolution of the ebb delta profile ............................78

T3 � Wave dom. Unbypassed............................................................................78

7.4.2 Scouring of the inlet............................................................................78

7.4.3 Ebb delta cross-shore profiles ............................................................79

7.5 Channel cross-section................................................................................81

8 Discussion ........................................................................................................83

8.1 Accuracy of the 2DH approximation...........................................................83

8.2 Overall assessment of morphological changes between the Physical and Numerical simulations. ...........................................................................................84

8.3 Choosing the right calibration?...................................................................87

8.3.1 Acting on the sediment grain size to reduce the inlet sediment transport? ...........................................................................................................87

8.3.2 Acting on the transport mode .............................................................88

8.3.4 Acting on the stability correction option? ............................................89

9 Conclusions......................................................................................................90

9.1 1st objective: reproduce the physical model outcomes..............................90

9.2 2nd objective: Validate the outcomes related to the sand bypassing systems 91

References................................................................................................................93

Appendix A*..............................................................................................................96

Appendix B .............................................................................................................129

Appendix C .............................................................................................................132

Appendix D .............................................................................................................138

Appendix E .............................................................................................................143

Appendix F..............................................................................................................146

Appendix G .............................................................................................................148

Appendix H .............................................................................................................151

Appendix I* .............................................................................................................159


LIST OF FIGURES Figure 2.1 � Disturbed regions in the computational grid...........................................10 Figure 2.2 � Numerical domain (blue boundaries) vs. Physical domain (green

boundaries) ........................................................................................................10 Figure 2.3 � WAVE-grid (green) overlapping the FLOW-grid (red)............................13 Figure 3.2 - Indication of Waves over tidal cycles (from Delft3D-WAVE user manual)

...........................................................................................................................16 Figure 4.1 � Staggered grid of Delft3D-FLOW (from Delft3D-Flow manual)..............21 Figure 4.3 - Location of the numerical Boudaries ......................................................25 Figure 4.4 � Discharge distribution through the River Boundary ...............................27 Figure 4.5 � Observation Points at the entrance........................................................31 Figure 4.6 � Observation Points within the domain area ...........................................31 Figure 4.7 � Example of current velocities extracted from ADV data (cm/s)..............32 Figure 4.8 � Output Specification window..................................................................34 Figure 5.1 - Schematic overview of a morphodynamic simulation (Extracted from the

Delft3D-MOR Manual)........................................................................................35 Figure 5.2 - Process tree for a morphodynamic simulation under a tidal regime

(Extracted from the Delft3D-MOR Manual) ........................................................36 Figure 5.3 - Time progress for Coastal Approach (from Delft-MOR manual).............37 Figure 5.4 - Morphological Tree processes................................................................39 Figure 6.3 � Position of the monitoring points within the numerical domain in

reference to the T1 case (26/10/2002 physical model simulations). ..................47 Figure 6.23 � Influence of Wave height in measured transport .................................57 Figure 6.24 � Influence of Wave angle in measured longshore transport..................57 Figure 6.25 � Influence of Roughness height for current rc in measured longshore

transport .............................................................................................................58 Figure 6.26 � Influence of Bed roughness ks in measured longshore transport ........59 Figure 6.27 � Influence of Grain size in measured longshore transport ....................59 Figure 6.28 � Influence of Wave height in measured inlet transport..........................62 Figure 6.29 � Influence of Bed roughness ks in measured inlet transport..................62 Figure 6.30 � Influence of Roughness height for current rc in measured inlet transport

...........................................................................................................................63 Figure 6.31 � Influence of Grain size in measured inlet transport..............................64 Figure 6.32 � Influence of the current velocity in measured inlet transport................64 Figure 6.33 � Influence of the bed shear stress formulae in measured inlet transport

...........................................................................................................................65 Figure 7.2 � Ebb delta growth for T3 and T4 (Physical and Numerical model)..........75 Figure 7.3 � Deposition rate of the ebb delta for all test cases ..................................75 Figure 7.4 � Representation of the delta longitudinal cross-section (AA�) .................77 Figure 7.6 - Evolution of ebb delta cross-section for all test cases ............................79 Figure 7.7 � Evolution of ebb delta cross-section for T3............................................80 Figure 7.8 � Evolution of ebb delta cross-section for T1............................................80 Figure 7.9 � Evolution of ebb delta cross-section for T4............................................81 Figure 7.10 � Evolution of ebb delta cross-section for T2..........................................81


Figure 7.11 � Representation of the channel cross-section BB� ................................82 Figure 7.12 � Evolution of the Channel cross-section for T2 simulation. ...................82 Figure 8.1: Morphological changes between physical (left) after 2280 minutes and

numerical (right) after 2500 minutes - T1 simulations ........................................85 Figure 8.2: Morphological changes between physical (left) and numerical (right) after

2000 minutes - T2 simulations ...........................................................................86 Figure 8.3: Morphological changes between physical (left) after 3120 minutes and

numerical (right) after 3000 minutes - T3 simulations ........................................86 Figure 8.4: Morphological changes between physical (left) and numerical (right) after

2500 minutes - T4 simulations ...........................................................................87 Figure 8.5 �Ebb delta Growth curves for Physical and Numerical simulations (T1 &

T2) with coarser sediment size within the inlet...................................................87 Figure 8.6 �Ebb delta Growth curves in Physical and Numerical simulations (T3 &

T4) with coarser sediment size within the inlet...................................................88 Figure 8.8 Morphological changes for T1 simulations with suspended transport (after

1500 minutes).....................................................................................................89

LIST OF TABLES Table 2.0 - Obstacles coefficient (Seelig, 1979) .......................................................12 Table 3.0 � Physical processes involved in the Generation modes of SWAN ...........17 Table 4.0 � Type of Numerical Boundaries................................................................25 Table 4.1 � Flow Boundary condition input (Delft3D-Flow)........................................26 Table 6.0 � Water level variations within the inlet ......................................................49 Table 7.1 � Review of the simulated test cases.........................................................67 Table 7.2 � Ruling depth and ebb flat position for all test cases................................78 Table 6.1 � Influence of bed roughness and grain size on lonsghore transport ......149 Table 6.2 � Influence of bed roughness and grain size on inlet transport................150


Glossary In any discussion on coastal engineering an agreement of the meaning of terms is necessary. Provided here are definitions of terms used in this report. Although the terms came from many sources, the Shore Protection Manual was of particular value.

Artificial Bypassing - A mechanical action where sediment is transport past a tidal inlet prior to it infilling the channel.

Bar - A submerged or emerged embankment of sand, gravel, or other unconsolidated material built on the sea floor in shallow water by waves and currents.

Channel - A natural or artificial waterway of perceptible extent which either periodically or continuously contains moving water, or which forms a connecting link between two bodies of water.

Coastline - The line that forms the boundary between the land and the water.

Cross-shore transport - The transport of sediment onshore and offshore via current.

Current - A flow of water.

Current, Ebb - The tidal current away from shore or down a tidal stream. Usually associated with the decrease in the height of the tide.

Current, Flood - The tidal current toward shore or up a tidal stream. Usually associated in the increase in the height of the tide.

Current, Tidal - The alternating horizontal movement of water associated with the rise and fall of the tide caused by the astronomical tide producing forces.

Downdrift - The directing of predominant movement of littoral materials.

Ebb Delta - A mass of sand that accumulates on the ocean side of a tidal inlet as a result of ebb tidal flow.

EPA - Environmental Protection Agency

Fall Velocity - The speed that a sediment particle falls in a fluid

Flood Delta - A mass of sand that accumulates on the protected side of a tidal inlet as a result of flood tidal flow.

GCCM - Griffith Centre for Coastal Management

Geomorphology - That branch of both physiography and geology which deals with the form of the earth, the general configuration of it's surface, and the changes that take place in the evolution of landform.

High-energy wave event - Significant waves over 2.5 metres measured continuously over several wave records.

Inlet - A short, narrow waterway connecting a bay, lagoon, or similar body of water with a large parent body of water.

Jonswap Spectrum Waves - A random train based on a wave energy spectrum defined from wave measurements in the North Sea.

Littoral drift - The sedimentary material moved in the littoral zone under the influence of waves and currents.

Littoral Transport - movement of littoral drift in the nearshore zone by waves and currents. Movement can be perpendicular (onshore-offshore) or parallel (longshore) to the shore.

Littoral zone - zone of water extending from the shoreline to just beyond the seaward most breakers.

Longshore transport - littoral transport in the direction parallel to the shore.


Longshore transport -The transport of sediment alongshore via the action of wave generated currents.

Nearshore zone - region where the forces of the sea react against the land.

Offshore - The comparatively flat zone of variable width, extending from the breaker zone to the seaward edge of the continental shelf. The direction seaward from the shore.

Prototype - The real world structure/process that is under investigation. In the case of this study a tidal inlet like the Tweed River Entrance.

Sand bypassing - Hydraulic or mechanical movement of sand from the accreting updrift side to the eroding downdrift side of an inlet. Natural or man made.

Scour - Removal of underwater material by waves and currents, especially at the base or toe of a shore structure.

Seas - Waves caused by wind at the place and time of observation.

Setup, Wave � Super elevation of the water surface over normal surge elevation due to onshore mass transport of the water by wave action alone.

Shoal: Verb - To become shallow gradually.

Shoal or Delta: Noun - A detached elevation of the sea bottom, comprised of any material except rock or coral, which may endanger surface navigation.

Significant wave height - Average of the highest one-third waves in the record.

Spit - A small point of land or a narrow shoal projecting into a body of water from the shore.

Surge - The name applied to wave motion with a period intermediate between that of the ordinary wind wave and that of the tide.

Swell - Wind generated waves that have travelled out of their generating area. Swell characteristically exhibits a more regular and longer period and has flatter crests than waves within their fetch.

Tidal Inlet - A location where an embayment or river joins the open ocean.

Tidal inlet - A natural inlet maintained by tidal flow.

Updrift - The direction opposite that of the predominant movement of littoral materials.

Wave - A ridge, deformation, or undulation of the surface or a liquid.

Wave height - The vertical distance between a crest and the proceeding trough.

Wind setup - The vertical rise in the still water level on the leeward side of a body of water caused by wind stresses on the surface of the water.


1 INTRODUCTION Tidal entrances are key components of the overall character of tidal waterway ecosystems. The physical changes which occur at these entrances due to natural variability in coastal processes need to be assessed in order to identify the significance of tidal exchange mechanisms on bay water quality. Equally, tidal entrances are often the site of major urban development and the dynamic interactions between the tidal entrance channel, shoals and the adjacent beaches are very significant factors in the management of the coastline in their vicinity. Sedimentary processes in the vicinity of an inlet are governed by complex interactions of tidal currents, waves and sediment. In spite of recent advances in the description of flow field near the inlet, and in the understanding of sediment transport by waves and currents, it is still not possible to accurately predict the changes which will occur at an inlet in response to an event, such as storms, and in response to longer term climate variability and changes in tidal dynamics. A major aspect of the ability to predict the overall behaviour of these environments is the need to understand the development of the ebb-tidal delta. This geomorphic feature provides the link between the wave dominated open coast processes and the tide dominated entrance channel behaviour. 1.1 Project Overview The background to the Planning and Management for Natural Variability on Open Coastlines Project is given in Volume 1 of this report. The objective of the work reported herein was to develop a numerical simulation of the physical model in order to extend the predictive capability of the model of the idealised inlet conditions and ultimately to numerically model real inlets and undertake scenario testing. Only the former objective has been met and the results of the numerical modelling are presented below. The numerical model software used in the work is the Delft3D modelling suite developed by the Delft Hydraulics laboratory in the Netherlands. The use of the model is covered by a research licence held by CRC partner � Griffith University. Delft3D has been used extensively world-wide for coastal process studies and is well suited to tidal inlet processes. The model suite comprises a number of modules for wave transformations, hydrodynamics, sediment transport and morphological change. A brief description follows. 1.2 Overview of Delft3D

• MOR Module

The MOR module of Delft3D integrates the effects of waves, currents and sediment transport on morphological developments. It has been designed to simulate the morphodynamic behaviour of rivers, estuaries and coastal areas on time scales of days to years due to the complex interactions between waves, currents, sediment transport and bathymetry. Each of these processes are dealt with in separate modules. The module simulates the processes on the curvilinear grid system as it is used in the FLOW module, which allows a very efficient and accurate representation of complex areas. Sediment transport computes the bedload and (the equilibrium) suspended load on the curvilinear model grid as a local function of wave and flow properties and the bed characteristics. It has the following features:


Total transport (equilibrium) mode: bedload and equilibrium suspended load transports are added.

Suspended load mode: the entrainment, deposition, advection and diffusion of the suspended sediment is computed by a transport solver. Here, a quasi-3D approach is followed, where the vertical profiles of sediment concentration and velocity are given by shape functions.

Numerous options for the bedload and equilibrium suspended load transport formulations are listed below:

• Engelund-Hansen (1967) • Meyer-Peter-Muller (1948) • Bijker (1968) • Bailard (1981) • Van Rijn (1984)

for sand, and a separate formulation for silt transport, with the ability to take into account effects of bed slope on magnitude and direction of transport, and effects of unerodible layers for all formulations. The bed change update module contains several explicit schemes of the Lax-Wendroff type. Options on fixed or automatic time-stepping, fixed layers and various boundary conditions. Delft3D-MOR has a facility to include a dredging scenario. This dredging option concerns automatic dredging, which is active during the whole morphodynamic simulation and will be used to model the bypassed cases T2 and T4. A dredging scenario involves the specification of a reference dredging bed level and a dredging allowance.

• WAVE Module The SWAN wave module of Delft3D is used to simulate the wave generation and wave propagation into the model, computing the wave conditions in the offshore and nearshore area. The time variation is implemented in a quasi-stationary mode, which sequences of conditions (input waves, water level and flow field) specified in one single run.

• FLOW Module The FLOW module is a multi-dimensional (2D or 3D) hydrodynamics (and transport) simulation program, which calculates non-steady flow and transport phenomena resulting from wave, tidal and meteorological forcing on a curvilinear, boundary fitted grid. For this study, the model was run in 2DH.


2 NUMERICAL MODELSET-UP 2.1 Introduction Morphological changes in coastal areas with a river outflow are driven by many factors, such as winds, tides and waves. These processes interact with each other to produce bathymetric changes, at time scales varying from hours to centuries. This time scale is obviously decreased for prototype and scaled down models. Physical model of idealised cases might help to outline a conceptual model of the real world prototype, but at extensive costs and project duration. The increasing computation capabilities reduce the need for costly physical modelling and promote the use of numerical modelling as predictive tools. However, there still exists a need for calibration data, which can only be provided by hydrographical campaign or physical modelling data. A physical model usually provides a more complete set of data in any wave, tide and wind conditions, which proves to be adequate for calibration of numerical tool. The datasets that were generated with the physical model will be used to calibrate the numerical simulations. If this technique proves to be reliable, the numerical model will be use as predictive tools on a prototype scale. Because numerical models are quicker to implement and flexible in parameter variation, it will greatly reduce the costly simulation times. The aim of this task is to reproduce the T1 (Current-dominated, unbypassed), T2 (Current-dominated, bypassed), T3 (Wave-dominated, unbypassed) and T4 (Wave-dominated, bypassed) simulations cases undertaken in the Basin of QGHL (EPA), with the numerical model Delft3D, coupling FLOW, WAVE and MOR modules. 2.2 Numerical domain All Ti cases have been carried out within the same physical model boundaries. The layout of the model is shown in Figure 2.2. The model domain is approximately 85 m long and 29 wide. 2.2.1 Boundaries conditions Due to numerical constraints, the numerical model uses an extension of the physical domain, replicating and extending the bathymetry further offshore and on each side. Offshore boundary is moved away further offshore to smooth out the numerical disturbances that propagate into the model. Offshore boundary is parallel to the shoreline, while in the physical model it makes a 20 degrees angle with the shoreline. Wave angle is corrected at boundary input. The offshore boundary is the up-wave boundary as well. It must be chosen in water so deep that refraction effects have not (yet) influenced the wave field. However, a deep-water up-wave is not a strict requirement for Delft3D-wave. Offshore boundary has been extended to a 0.8m depth. It cannot be considered in deep water, but this maximum depth has been chosen to save computational grid cells. Wave height and directions input has been modified to fit the original input at the location of the physical model up-wave boundary.


Side boundaries are spaced out, because along each lateral side of the grid (if there is an open boundary along that side) a region exits where the wave field is disturbed by an import of zero energy from the lateral boundaries (refer to Figure 2.1 below)

Figure 2.1 � Disturbed regions in the computational grid

The angle of the line dividing the disturbed area from the up-wave corner point (of the computational grid) is approximately equal to the half power width of the directional energy distribution of the waves (this half power is typically 5o to 10o for swell). 2.2.2 Computational Grid (CG) The computational grid is in three dimensions: x-, y- and θ-space, on which Delft3D performs the computations. During the computations (on the computational grid), bottom and current information is obtained by bilinear interpolation from the input grid (see following Section 2.2.3). It is larger than the area where we need to know the wave parameters. The length (in x-direction) needs to be no longer than the up-wave boundary to the most down-wave point of interest, which is located inside the tidal channel. The width (in y-direction) must be larger than the area of interest, as explained above.

Figure 2.2 � Numerical domain (blue boundaries) vs. Physical domain (green

boundaries)

The origin of the Computational grid with respect to the problem coordinate system is located a (Xo,Yo)=(50.05, 94.7). In x-direction the grid extends to approximately 24m and in y-direction to 86m.

Region of Interest

10o Disturbed

10o Disturbed

Y

X


• Spatial resolution:

The spatial resolution of the computational grid has been chosen to resolve relevant details of the wave field. Grid size ranges from 0.15m to 0.3m, with a grid aspect ratio ∆x/∆y ranging from 1.25 up to 3.5, which accounts for constraints of numerical stability. From the left term, we demand:

(2.2.a)

In a �no-current� situation c0y/c0x is equal to tan (θ) in which θ is the discrete spectral wave propagation direction. So (2.2.a) becomes:

(2.2.b)

If instability occurs, the ration ∆x/∆y must be chosen even smaller. This implies that the directional sector of wave propagation must be reduced.

• Directional resolution The directional resolution has been chosen to resolve accurately the directional distribution of energy density and mean frequency. A typical directional resolution for swell should be much less than 10o, perhaps as little as 2o or 3o. 2.2.3 Input Grid Input grid is used to input the bottom, current field, friction coefficient and wind field (if present). Input grid is chosen identical to the Computational grid, with identical spatial resolution, such that details in the bottom and current pattern are resolved. A replication of the bathymetry from the Physical model has been implemented. Samples (xyz) from model surveys were imported in Delft3D, through the Grid and Depth generators (respectively RGFGRID and QUICKIN). These samples were interpolated onto the Input grid, to create depth contours, which are the exact replica of the model itself. The resolution of the grid is sufficient to avoid sharp depth discontinuities between adjacent grid cells in the direction of wave and flow propagation. 2.2.4 Obstacles Training walls are modelled as sub-grid obstacles, which interrupt the propagation of the waves from one grid to the next wherever this obstacle line is located between two neighbouring points (of the computational grid; the resolution of transmission or blockage is therefore equal to the computational grid spacing). The model grid was set-up to enable the training walls or breakwaters to take an equivalent grid cell width (∆y) and few grid cells in length (x-direction).

21

.

.

0

0 ≤∆∆

x

y

cycx

θ)cot(21=

∆∆

yx


• Type of obstacle: Dam

The transmission coefficient depends on the incident wave conditions at the obstacle and on the obstacle height (which may be submerged).

• Height The elevation of the top of the obstacle is above the reference level, which is the same as the one used for the bottom (MWL). The obstacle height has been chosen as 2.5 times the significant wave height to prevent wave overtopping the structure. Height = 0.15 m

• Transmission coefficients alpha and beta The transmissions coefficient depend on the shape of the dam (Refer to Table 2.0 below). Alpha = 2.6 Beta = 0.15

Table 2.0 - Obstacles coefficient (Seelig, 1979) Case α β Vertical thin wall 1.8 0.1 Caisson 2.2 0.4 Dam with slope 1:3/2 2.6 0.15

The above coefficients are based on experiments in a wave flume, so strictly speaking it is only valid for normal incidence waves. Since there are no data available on oblique waves it is assumed that the transmission coefficient does not depend on direction. The training walls will be modelled as dam with slopes in the Deflt3D-WAVE module, and since local hydrodynamics around the obstacles can affect the re-suspension of sediment, morphological patterns could be affected at the proximity of the obstacles. The walls that run along the length of the river has be modelled as obstacles, which means 2 obstacles were inputted (north wall, south wall) with the X, Y coordinates of 21 and 20 segments respectively, which delimit the walls extent. 2.2.5 Output Grid Output values are provided on the computational grids or on grids that are independent from the computational grids, which could be either the Delft3D-FLOW or Delft3D-WAVE grid. These last two grids are independent, and information is obtained by spatial interpolation, which implies that some inaccuracies are introduced. It also implies that bottom or current information on an (output) plot has been obtained by interpolating twice: once from the input grid to the CG grid and once from the CG grid to the output grid. However, the FLOW and WAVE grids are created similar enough (grid resolution and covered area) to reduce these interpolation errors (refer to Figure 2.3 below).


Figure 2.3 � WAVE-grid (green) overlapping the FLOW-grid (red)

Note:

• The extended area of the WAVE-grid on the left side prevents inaccurate flow patterns in relation with the wave-disturbed area on the updrift side.

• A river boundary is imposed for the FLOW-grid, but is not required for the WAVE-grid.


3 WAVES DATA INPUT The numerical model boundary does not match those of the physical model. Calibration of the WAVE module has been carried out to retrieve the identical wave characteristics crossing the �virtual� green curve of the offshore physical model boundary. Being located in intermediary water, waves will transform rapidly between the up-wave numerical boundary and the location of the up-wave physical model boundary (Refer to Figure 2.2 in previous Section). Wave height and wave direction will be slightly different from the physical test wave input at the location of the physical boundary within the numerical domain. The scale of the parameters, which induced numerical effects that still have to be understood, complicated the calibration stage of the wave module. 3.1 Grid parameters The grid used is a rectangular grid and includes the inlet (See Figure 3.1 in Appendix A). It has 142 cells along the x-direction (M) and 293 cells along the y-direction (N). Dimensions: M=142, N=293 3.2 Specification of Boundaries

• Parametric o Spectral Space

A Jonswap type spectrum is assumed as in the physical model with a Peak enhancement parameter of 3.3 (default value).

o Period

A peak period Tp is used as characteristic wave period. o Width energy

The directional width is expressed as the directional standard deviation of the [cosm(θ-θpeak)] distribution, which has been expressed in degrees.

• Boundary Type o Side

The boundary is considered along one full side of the computational grid.

• Condition type o Constant

The wave conditions are constant along a side.

• Boundary orientation

By default, the positive x-axis points East, which simplify our problem coordinate system. The side does not have to face exactly the given direction (the nearest direction of the normal of the side is taken). The offshore boundary orientation is NE (North-East).


• Wave conditions

SWAN asks for the Significant wave height, the Peak wave period and Mean wave direction (direction of wave vectors in o), which are supposedly the main input of the physical model (Hs=0.067m, Tp=1.15s, θ=20 degrees). Nevertheless the rapid transformation of the wave at the offshore numerical boundary forces us to implement slightly different values, which were retrieved from various calibration runs (refer to Section 6.3). Hsig = 0.074m Tp = 1.15 s θ = 29.5 degrees (99.5degrees on real input, when corrected with the numerical grid orientation)

• Directional spreading The distribution of the incident wave energy over the directions takes place according to the directional spreading function D(θ)=(cos θ)n. The directional standard deviation, also called width energy distribution, is 5 degrees to account for the relatively narrow spectrum. Width energy Distribution = 5 degrees

• Water level The water level is defined relative to the horizontal datum from which the bottom depths are measured. The level is set to zero so that the water surface coincides with the Mean Still Water level of the physical model. Water level = 0 m (MSWL) 3.3 Tidal Information In the data group Tidal information, a number of times [Ntides] are specified, at which computations must be carried out. In the WAVE module, time is an artificial parameter, as it is designed to simulate stationary wave fields. Internally, the WAVE module uses time to distinguish different phases in a tidal cycle. For each internal time, referred to as wave times, a simulation is made. For all these wave times, the wave quantities (wave height, direction, etc.). The flow data that is used for the computation of the wave fields is read from the communication field at wave time (e.g. time when high and low water, maximum ebb and flood occur). The FLOW module includes wave effects; it requires wave data at each time steps of the flow module. However, for time reasons, it is quite impossible to compute the wave fields at each calculation steps. Therefore, we reduce the wave fields to significant period, such as high, low and mean water level (and on maximum flood, ebb and slack if current refraction is also included). The FLOW module will interpolate between the appropriate wave data available on the communication field (See Figure 3.2 below)


In this practical application, the water level is kept constant, but we need to include the effect of ebb and flood river discharge on the wave refraction pattern (incoming waves) at the entrance of the inlet. For this purpose, seven time points have been selected to cover the entire wave-flow simulation period, with a 0m water level correction to maintain a constant water level within the domain. An example of the flow-wave interaction for T3&T4 simulations is displayed in Appendix A, Figures 3.3 to 3.9, which show how important it is to choose relevant wave simulations.

Figure 3.2 - Indication of Waves over tidal cycles (from Delft3D-WAVE user manual)

3.4 Physical parameters In the data group Physical parameters, we may specify a number of Physical parameters, which are Constants, Winds, Processes and Various. Constants

• Gravity = 9.81 m/s2 • Water density = 1000 Kg/m3 • North (direction with respect to the x-axis (Cartesian convention) = 90o • Minimum depth (threshold depth in m; any positive depth smaller than

[depmin] is made equal to depmin = 0.002m • Convention = nautical for wind and wave direction. The direction of the

vector from geographic North measured clockwise +180o (the direction where the waves are coming from or where the wind is blowing from)

• Setup: No This option should be used only if SWAN is used on stand-alone mode or if wave-induced setup is not accounted for in the flow computations. The wave-current interaction is required to account for the morphological changes of the model, which prevents the use of the setup option

• Forces: The wave forces are computed on the basis of wave dissipation rate, not on the gradient of the radiation stresses tensor, which is also another option

Wind Wind is not taken into account for the test cases. Processes

Water levels

Velocities

Wave simulation

Velocity [m

/s]W

ater

leve

l [m

]

- 0.5

+ 0.5

+ 1.0

1 2

3

4

0 0

- 0.5

+ 0.5

+ 1.0

0:00 30:00 1:00 1:30


SWAN contains a number of physical processes that add or withdraw wave energy to or from the wave field. The processes included are: wave growth by wind, whitecapping, bottom friction, depth induced wave breaking and non-linear wave-wave interactions (quadruplets and triad). SWAN can run in several modes, indicating the level of parameterisation. Type of formulations

• 1st generation As there is no need to implement the processes related to wind growth, whitecapping and quadruplets interactions, the 1st generation mode is sufficient to cover the model requirements (refer to Table 3.0 below).

Table 3.0 � Physical processes involved in the Generation modes of SWAN (from SWAN Cycle III version 40.11 � USER Manual)

Generation Mode of SWAN

1st 2nd 3rd

Linear wind growth: Cavaleri & malanotte-Rizzoli (1981) [modified] x x

Cavaleri & malanotte-Rizzoli (1981) x Exponential wind growth: Snyder et al. (1981) [modified] x x

Snyder et al. (1981) x1 Janssen (1991, 1991) x2 Whitecapping Holthuijsen and de Boer (1988) x3 x4

Komen et al. (1984) x1

Janssen (1991), Komen et al.(1994) x2

Quadruplets interaction: Hasselman et al. (1985) x x x Triad interactions: Elderberky (1996) x x x Depth-induced breaking: Battjes & Janssen (1978) x x x Bottom friction Hasselman et al. (1985) x x x Collins (1972) x x x Madsen et al. (1988) x x x Obstacle transmission: Seelig (1979) x x x

1 gives the wind input and whitecapping as used in WAM cycle 3 2 gives the wind input and whitecapping as used in WAM cycle 4

3 Pierson-Moskowitz spectrum as upper limit 4 scaled Pierson-Moskowitz spectrum as upper limit


Bottom friction This command is not used, because of the lack of information relative to the use of bottom friction with scaled down wave parameters. Nevertheless its influence has been assessed during the calibration phases. Depth-induced breaking This B&J (Battjes and Janssen (1978)) bore-based model is activated for computation of energy dissipation in random waves due to depth-induced wave breaking in shallow water.

• Rate of dissipation Alfa = 1 • Value of the breaker parameter defined as Hm/d, Gamma = 0.8

Non-linear triad interactions This command is deactivated, as the non-linear wave-wave interactions due to the triads are not taken into account. Various In the subdata group Various some of the physical processes of SWAN may be activated. Processes de-activated Wind growth, White capping and Quadruplets. Processes activated Wave Refraction and Frequency shift. 3.5 Numerical parameters In this data group, parameters that affect stability of the numerical computations can be modified. To obtain robust results with acceptable accuracy, default diffusion parameters were applied. Spectral space The amount of diffusion of the implicit scheme is controlled in the directional space through the Directional space (CDD) parameter and frequency space through the Frequency space (CSS), which determine the numerical scheme.

• Directional space (θ-space) A value of [CDD] = 0 corresponds to a central scheme and has the largest accuracy (diffusion ≈ 0) but the computation may more easily generate spurious fluctuations. A value of [CDD] = 1 corresponds to a upwind scheme and it is mode diffusive and therefore preferable if (strong) gradients in depth and current are present. Default value of 0.5 was applied, as we need to minimize the influence of numerical factors in the simulations. CDD = 0.5

• Frequency space (σ-space) A value of [CSS] = 0 corresponds to a central scheme and has the largest accuracy (diffusion ≈ 0) but the computation may more easily generate spurious fluctuations.


A value of [CSS] = 1 corresponds to a upwind scheme and it is mode diffusive and therefore preferable if (strong) gradients in depth and current are present. Default value of 0.5 was applied, as we need to minimize the influence of numerical factors in the simulations. CSS = 0.5 Accuracy Criteria (to terminate the iterative computation) We influence the criteria for terminating the iterative procedure in the SWAN computations, which is related to convergence criteria. SWAN stops iteration if: • The �Relative change� in the local significant wave height (Hs) and local mean

wave period (Tm) from one iteration to the next is less than 0.02 (2%) • The �Relative change with respect to mean value� in the local significant wave

height (Hs) and local mean wave period (Tm) from one iteration to the next is less than 0.02 (2%) (Average over all wet grid points)

The two conditions above are fulfilled in more than fraction �Number of wet grid points� % of all grid points. Relative change = 0.02 (default) Relative change w.r.t mean value = 0.02 (default) Number of wet grid points = 98 % The terminating procedure can also be controlled by giving the maximum number of iterations, after which the computation stops: Max. number of iterations [itermx] = 15 3.6 Output Curves In order to retrieve data to calibrate the wave model, (curved) output curves can be specified at which wave output will be generated by Delft3D-Wave. This curve is a broken line, defined by the user with its corner points. The values of the output quantities along the curve are interpolated from the computational grid. The following output quantities are provided by Delft3D-Wave at the output location: • XP, YP Coordinates of output locations (with respect to the problem coordinates); • DIST Distance along the ouput curve (m); • DEPT Depth (in m); • HSIG Significant wave height (in m); • PER Mean wave period (Tm01) in s; • DIR Mean wave direction (deg) • DSPR Directional spreading of the waves (in o) • DISS Dissipation rate (J/m2/s); • WLEN Mean wave length (in m); • U, V Current velocity (in m/s). We specified 3 output curves:

- Offshore boundary of the Physical Model (Green Boundary in Figure 2.2 in Section 2.2.2);


- 2 Cross-shore sections south and north from the entrance to monitor the longshore transport.

All the data of each output curve is presented in a Table and saved in only one file. 3.7 Output Parameters Output results are written on the computational grid, which is called flow2swan grid, as SWAN has created a new grid, which is compatible with the FLOW module. The output from the computational grid (Wave computations) is interpolated to the FLOW model grid for the computation of wave-current interactions. Although WAVE and FLOW modules are coupled together to produce the wave-current interaction, computational grids are different for each module, which means there exist:

• 2 Computational grids (WAVE and FLOW) • 2 Input grids (WAVE and FLOW)

Nevertheless, bathymetry remains the same for obvious reasons, as it would be inaccurate to link outputs from FLOW and WAVE Grid computed using a different bathymetry at the same location. It was important to check that the bathymetry remains located at the same exact location (X, Y coordinates) on each grid, as interpolation on different grids can sometimes lead to discrepancies between the Depth contours for the WAVE and FLOW modules.


4 FLOW DATA INPUT 4.1 Grid Parameters The grid used in a curvilinear grid to account for the bending inlet entrance (See Figure 3.1 in Appendix A). It has 85 cells along the x-direction (M) and 139 cells along the y-direction (N). Dimensions: M=85, N=139 In Delft3D-FLOW, a staggered grid is applied, i.e. not all quantities are defined at the same location in the numerical grid. The staggered grid applied is given in Figure 4.1 below, with the following legend: • full lines: the numerical grid • + Water level • Horizontal velocity component in ksi-direction (also U- and M-

direction) • | Horizontal velocity component in eta-direction (also V- and N-

direction) • grey area items in the same grid co-ordinates {M,N} • water depth defined at the crossing of the grid lines

Figure 4.1 � Staggered grid of Delft3D-FLOW (from Delft3D-Flow manual)

Closed boundaries are defined through U- or V- points; open boundaries through either U-, V- or water level (zeat-) points depending on the type of boundary condition such as velocity or water level. All grid related quantities required for calibration with the physical model data can be located at one or more locations in the grid. Grid is coarser offshore and refined at the entrance of the inlet and on the beach surrounding the training walls (as displayed in Figure 3.1 in Appendix A).

n + 1

n

n - 1

m - 1 m m + 1


4.2 Bathymetry XYZ sample file of the model has been supplied from the Physical model surveyed original profile. Bathymetry was extended to fit the boundaries of the numerical domain and bathymetry was compared with the original after interpolation on the FLOW grids. The coordinate system of Delft3D does not handle negative coordinates. The origin point (0,0) of the original survey was located such as the coordinate provided were sometimes negative. Thus, the grid and samples have been translated in a positive coordinate system to prevent the simulations to crash when reading the grid inputs. 4.3 Dry Points / Thin dams Dry points are cells centred around a water-level point that are permanently dry during a computation, irrespective of the local water depth. A series of consecutive dry points are defined by lines though the grid. Thins dams are thin objects defined at the velocity points which prohibit flow exchange between two computational cells at the two sides of the dam without reducing the total wet surface and the volume of the model. It is used to represent small obstacles (e.g. breakwaters, dams) in the model which have sub-grid dimensions, but large enough to influence the local wave pattern. Thin dams separate the flow on both sides, but they do not separate the bathymetry on both side. This means depth points, which are located at the thin dams, are used on both sides of the thin dams, which also causes troubles when visualizing morphological changes with depth contours displayed across the breakwaters. In our case, different depth contours occur along the training walls, which is incompatible with the use of thin dams. Therefore the training walls are modelled as dry points. These are specified along the lines of cells that cover a cell in width (N-direction) and many cells in length (M-direction) as displayed in Figure 3.1 in Appendix A. 4.4 Time Frame In the data group Time Frame we define the relation between the time axis of the real world and that of the simulation. Reference date In the simulation all time instances are expressed in the number of time steps relative to time [00 00 00] of the reference date, which has no real influence on the simulation as long as it is a valid date. Reference date = 15 10 2002 (15, Oct 2002) Simulation period FLOW simulations are time-consuming, particularly with a small time step and large grids. The Physical model ran simulation over more than 40 tidal cycles in average, which means we need to simulate the flow-wave current interaction over the same period to achieve the similitude.


Numerical simulation enables the reduction of this time by applying a cyclic reduction to the entire simulation. Only 1 complete tidal cycle (Flood and ebb) will be computed, and averaged to evaluate the sediment transport and morphological changes repeated over 40 tidal cycles, which will be carried out by the MOR module. As the tidal cycle is approximately 104 minutes and a certain time to allow disturbances to smooth out at the start of the simulation (cold start) is required, the total simulation time will be marginally longer than the tidal cycle (as displayed in the first 8 minutes of signal in Figure 4.2 in Appendix A). Nevertheless, the sole tidal cycle period (after the cold start) will be averaged for sediment transport computation. The first simulations displayed a Cold Start (Smoothing time) of approximately 8 minutes. Smoothing time = 8 minutes A simulation period of 140 minutes was chosen, to allow for the 8 minutes of smoothing time and 132 minutes of �clean� simulation where we can retrieve the 104 minute period of the tidal cycle. The total simulation time is 140 minutes. Simulation Start Time 15 10 2002 [00h 00mn 00 s] Simulation stop time 15 10 2002 [02h 20mn 00 s] Time step The Delft3D-FLOW system should give a solution, so robustness has highest priority. Following (Stelling, 1984), the discretizations have to satisfy the followings demands: • unconditionally stable • at least second order consistency • suitable for both time-dependent and steady state problems • computationally efficient An explicit time integration of the shallow water equations on a rectangular grid would lead to a time step condition based on the courant number for wave propagation:

1112 22 <∆

+∆

∆=yx

gHtCFLwave

with ∆x and ∆y the smallest grid spaces in the physical space. For many practical applications this requires a time step of few second to simulate tidal propagation. Exceeding the time step would generate instability and from the view of robustness this is not acceptable. Given the grid size parameters, the time step chosen is small enough to cover these conditions, although a small time step requires more computational steps to achieve a simulation. Time step = 0.01 minute (0.6 s) defined as <TSCALE> In our case, the CFLwave will be less than 10, which is largely acceptable for the simulation.


4.5 Processes In the data group are specified which processes or quantities that might influence the hydrodynamic simulation are taken into account. For our main requirements, salinity, temperature, wind, tidal forces and secondary flows are not taken into account. However, waves are included within our simulations. This means we take into account the influence of the wave field on the bed-stress and the wave energy dissipation rate in a depth averaged model (refer to Section 4.8). The results of the wave module are read from the communication file. 4.6 Initial Conditions In the data group Initial conditions, we specify what kind of values the computation will start with. As the smoothing time required is quite short, there is no read information from a previous simulation run and thus water level is kept uniform: Water level = 0m 4.7 Boundaries In the data group Boundaries we define the open boundaries, their location, type and all input data related to driving the simulation. It is required to input the flow and transport condition at each boundary. They represent the outer world beyond the model are, which is not modelled. The flow may be forced using water levels, currents, discharges and/or a combination of water levels and currents. This forcing can be prescribed using harmonic or astronomical components or as time-series. There are four types of boundary conditions that can be applied: • Water level boundaries • Velocity boundaries • Discharge or flux boundaries • Riemann boundaries (weakly reflective boundaries) The choice of the type of boundary condition used depends on the phenomena to be studied. For instance, when you are modelling water levels at the inland side of an estuary, you will prescribe the known water levels at the entrance of the estuary. However, the same internal solution may be achieved by prescribing flow velocities, fluxes or weakly reflective conditions. But, the latter three yield a much weaker type of control over the final solution to be reached, since velocities are only weakly coupled to water levels, especially for the more complex flow situations. The Riemann type of boundary is used to simulate a weakly reflective boundary. The main characteristic of a weakly reflective boundary condition is that the boundary up to a certain level is transparent for out-going waves, such as short wave disturbances. Out-going waves can cross the open boundary without being reflected back into the computational domain as happens for the other types of boundaries. A weakly reflective form of the other boundary types is obtained by specifying a reflection coefficient (Verboom et al., 1984, 1986).


Because there is more than one open boundary in the model area, we must apply different type of boundary condition at all boundaries, which may lead to continuity problems if the fluxes resulting from velocity components and their respective water levels are not compatible. When prescribing water-level boundaries, we must keep in mind that both in nature as well as in the model, water level is a globally varying variable while behaving rather stiffly, i.e. there is a substantial correlation between water levels in locations being not far apart, meaning that a small error in the prescription of water levels can only be compensated by (large) responses of the internal forces in the model, i.e. high velocity components. The area of influence of this phenomenon is not limited to a certain number of grid points near the boundary, but rather to the entire physical area. Since we do not want small errors in the boundary conditions to significantly influence the model results, we locate boundaries as far away from the areas of interest as possible. The Numerical domain includes four boundaries that define the model limits (as displayed in Figure 4.3 on the following page) and main physical forcing types (as displayed in the following Table 4.0). There are:

• Offshore • Right Side • Left Side • River

Table 4.0 � Type of Numerical Boundaries

Type of Boundary Forcing Type Reflection Coefficient Alfa

Offshore Water elevation Harmonics 100 Right Side Riemann Harmonics Left Side Riemann Harmonics River Discharge Time-series 0

Figure 4.3 - Location of the numerical Boudaries

Left Side

Right Side Offshore

River


Offshore Boundary The water level at the offshore boudary is forced to constant water level with a 0-m level correction (refer to input Table 4.1 below). The reflection coefficient is Alfa = 100, which enable the flows to escape through the boudary without reflecting into the domain.

Table 4.1 � Flow Boundary condition input (Delft3D-Flow) Frequency Ampl.-A Phase.-A Ampl.-A Phase.-B 0.00000 0.00000 0.00000 0.00000 0.00000 30.0000 0.00000 0.00000 0.00000 0.00000 Left and Right Boundaries These boundaries must be transparent to out-going waves as the wave travel into the domain with an angle to produce the required longshore transport. These boundaries have been defined as Riemann Boundaries to prevent using the same type of boundary as the adjacent offshore boundary. Nevertheless, as no physical forcing must come from these side boundaries, we choose a harmonic input identical to the offshore boundary (refer to Table 4.1 above). River Boundary The river boundary is the main forcing of the flow model, which reproduce the idealized tidal flows exchanged through the inlet entrance. As for the Physical model, water elevation has been kept constant through the model area, whilst current velocities has been set-up through the entrance. The river boundary must be located as far as possible of the area of interest, which is the entrance itself. This distance prevents a total control of the velocities through the entrance itself, which is the main interest. Thus, we choose to model the River Boundary as a discharge boundary, imputing a time series of water discharge through the river. As we defined the width of the entrance, the control of the discharge enables a better control on the entrance current velocities.

• Switch Flood/ebb discharge Delft3D-FLOW is very sensitive to abrupt changes occurs at the boundaries. It induces disturbances that propagate through the model. These disturbances, which are known as �Cold Start� when simulation is initiated, are repeated in the simulation when you switch abruptly the direction of the discharge through the boundary. These disturbances in the middle of the tidal cycle would rule out the computation of averaged sediment transport over a tidal cycle. This would complicate the morphological process tree, as truncated period of flow-current interaction pattern would have been used for computation of the averaged transport. It was necessary to input a time-series with a smooth transition period between Flood and Ebb to prevent the apparition of disturbances. Using a small program with MATLABTM, modified from a previous version of Dr. Dano Roevlink (WL|Delft Hydraulics), we create a time-series that reproduce the exchange of flows through the entrance, with smooth transition period through an exponential formula.

• Discharge time-series


The discharge is prescribed at both ends of a boundary section and intermediate values are determined by linear interpolation. The river includes eight grid cells though its cross-section. Discharge has to be specified for each cell. The depth is constant (0.1m) at each of these cells. This means we input the equivalent discharge used from the physical model through the whole cross-section, which has to be divided by the number of cells, is constant (Figure 4.4 below).

Figure 4.4 � Discharge distribution through the River Boundary

In the T1 and T2 cases for instance, the total discharge account for 0.059496 m3/s in order to get velocities of about 0.3 m/s within the river entrance. For the T3 and T4, the total discharge account for 0.028 m3/s in order to get velocities of about 0.14 m/s within the river entrance (refer to Section 6 � Calibration). The time-series is used for the whole cross-section of the river boundary, which inflows identical individual discharge trough each cell. 4.8 Physical Parameters In this data group you can select or specify a number of parameters related to the physical condition of the model area. The physical parameters can be split into two classes, those that vary spatially and those that are uniform throughout the model area. These uniform valued parameters are used as calibration parameters, providing a correct overall solution rather than representing the locally correct physical values. The data group Physical Parameters contains four subgroups, i.e. Constants, Heat model, Roughness and Viscosity. Constants We specify the following constants: • Gravity = 9.81 m2/s • Water Density = 1000 kg/m3 (The background water density. This value is

only required for a homogeneous simulation, i.e. the processes temperature and salinity are not selected)

Q1 Q8 Qi

Training Walls

Training Walls

Bottom

1 2 3 4 5 6 7 8

0-m


• Temperature = 15 degrees C (The background water temperature used in the equation of state. This value is only required if the processes temperature is not selected)

• Salinity = 31 ppt (The background water salinity used in the equation of state. This value is only required if processes salinity is not selected) The exact value of this parameter will be checked when data from conductivity gauges will be processed.

Roughness In the sub-data group roughness you can specify the bed roughness and for specific situations the roughness of the side walls. The bottom roughness can be computed with several formulae and we can specify different coefficients for ksi- and eta-direction; either as a uniform value in each direction, or space-varying imported from an attribute file. Bed roughness The bed roughness can be computed according to: • Manning • White-Colebrook • Chezy • Z0 (for 3D simulations only). The bed roughness is used for the computation of the depth-averaged flow. For 2D depth-averaged flow the shear stress at the bed induced by a turbulent flow is assumed to be given by a quadratic friction law:

222

0 UC

g

Db

ρτ = (4.8.1)

where 2U is the magnitude of the depth-averaged horizontal velocity. The 2D-Chézy coefficient C2D is determined according to the White Colebrook's formulation given as follows:

)12(log18 102s

D kHC = (4.8.2)

where H is the total water depth ks is the Nikuradse roughness length

The White-Colebrook option is used with a bed roughness of 0.001m. Bottom stress The bottom stress due to wave forces can be computed with several Formulation formulae; in Delft3D six formulae are provided. We can either select: • Fredsoe (1984) • Huynh Thanh and Temperville (1991) • Davies et al. (1988) • Myrhaug and Slaattelid (1990) • Grant and Madsen (1979) • Bijker (1967)


The Fredsoe Formulation is used (see details in Appendix C: Fredsoe�s model) Partial slip condition For simulations of small-scale flow (e.g. laboratory scale) the influence of the side walls on the flow can be significant and should be activated. The friction of side walls is computed from a 'law of the wall' formulation if you select this option. The partial slip treatment is applicable for dry points only. The tangential shear stress is calculated based on a logarithmic law of the wall where the roughness length needs to be specified. The partial slip treatment for the training walls has been used to account for the friction of the sidewalls. We calibrate the flow at the entrance of the inlet in varying the Roughness length parameter. The primary input was determined from the mean diameter of the rocks used for the training wall construction, which ranges from 20 to 30 mm. Various calibration tests on entrance flow velocities and delta growth helped to define the correct Roughness Length. Partial slip condition Roughness = 0.015 [m] Viscosity The horizontal eddy viscosity and horizontal eddy diffusivity can either be entered as one uniform value for each quantity (uniform for both directions) or as non-uniform values read from a user-specified file. No values have been specified for the vertical eddy viscosity and vertical eddy diffusivity, which are used for 3D simulations. The value for both the horizontal eddy viscosity and the horizontal eddy diffusivity depends on the flow and the grid size used in the simulation. At this scale we used: Horizontal Viscosity (Vicouv) = 0.001 [m2/s] Horizontal Diffusivity (Dicouv) = 0.01 [m2/s] Numerical parameters In the data group Numerical Parameters you can specify parameters related to drying and flooding and some other advanced options for numerical approximations. We must select or define one or more of the following parameters: Extra Drying/Flooding We determine if an additional check is applied on the water depth in the water level points. We can select among: • Max An additional check is made on the maximum water depth. • Mean An additional check is made on the minimal water depth. • No No additional check in made. Due to the physical scale of the model, simulations are sensitive to small variations in water level. We chose to use the Mean criteria.


Threshold depth = 0.002 [m] The threshold depth above which a grid cell is considered to be wet. Marginal depth = 0.010[m] The marginal depth below which local gradients are approximated by one side (up-wind) differences. Smoothing Time = 8 [minutes] The time interval used at the start of a simulation for a smooth transition between initial and boundary conditions (refer to Section 4.4). In some cases, the prescribed initial condition and the boundary values at the start time of the simulation do not match. This can introduce large spurious waves that enter the model area. Subsequently, the wave will be reflected at the internal boundaries and along the open boundaries of the model until the wave energy is dissipated completely by bottom or internal (eddy viscosity) friction forces. These reflections can be observed as spurious oscillations in the solutions and they will enhance the spin-up (warming-up) time of the model. To reduce this time, a smooth transition period can be specified, during which the boundary condition will be adapted gradually starting from the prescribed initial condition value. The calibration simulations carried out gives an approximate 8 minutes transition period (Cold Start), which is used in the model as the smoothing time. 4.9 Discharges In Delft3D-FLOW intake stations and waste-water out-falls can be considered as localised discharges of water and dissolved substances. The river could have been modelled as a discharge. As there is no other constituent than water at the river boundary discharge, we model the river boundary as an open boundary. 4.10 Monitoring Computational results can be monitored as a function of time by using observation points, drogues or cross-sections. Monitoring points are characterised by a name and the grid co-ordinates of its location in the model area. Observation points Observation points are used to monitor the time-dependent behaviour of one or all computed quantities as a function of time at a specific location, i.e. water elevations, velocities, fluxes, salinity, temperature and concentration of the constituents. Observation points represent an Eulerian viewpoint at the results. Observation points are located at cell centres, i.e. at water level points. For the first stage of the calibration process, seven observation points (as displayed in the \igure 4.5 and 4.6 below) have been preliminary strategically positioned within the model area to monitor the flow velocity and water levels. Their names and locations are: River entrance: �C1�, �C2�, �C3� River Boundary: �River� Offshore boundary: �Offshore� Lateral boundaries: �South Side�, �North Side�


Figure 4.5 � Observation Points at the entrance

Figure 4.6 � Observation Points within the domain area

Calibration with data collected from the physical model simulations For the first stage of numerical modelling, all data from the Physical model had not yet all been retrieved and processed; the observation points listed above were used to check the physical viability of the model. Once real data have be collected, the exact positions of the instruments is positioned within the model and a detailed

C1 C2 C3

River

Offshore

North Side

South Side

Cross-Section


calibration have been carried out to increase the accuracy of future simulations (see Section 6). Nevertheless, we must keep in mind that the signals retrieved from the Physical model instruments are soiled with irregular noise due to natural variations in the hydrodynamics of the model. There is the risk that the numerical model would give averaged and idealized signals (due to larger sampling rate and computational approximations) at the virtual location of the instruments and therefore would prevent a perfect match with the data from the Physical model. This concerns particularly the current velocities, which can vary slightly due variations in pumping rate in the Physical model (as displayed in Figure 4.7 below).

Figure 4.7 � Example of current velocities extracted from ADV data (cm/s)

Cross-Section Cross-sections are used to store the sum of computed fluxes (hydrodynamic), flux rates (hydrodynamic), fluxes of matter (if existing) and transport rates of matter (if existing) sequentially in time at a prescribed interval. Three cross-sections are presently used to monitor the entrance discharge and the longshore transport rate downdrift and updrift of the entrance (refer to blue cross-sections displayed in Figures 4.5 and 4.6 in the previous page). 4.11 Output parameters In the data group Output Options you can specify which computational results will be stored for further analysis or for other computations and which output shall be printed. Delft3D modules use one or more Map, History, Communication and Restart file to store the simulation results and other information needed to understand and interpret what is on the files. Maps are snap shots of the computed quantities of the entire area. As we (can) save all results in all grid points a typical Map file can be many hundreds of Mega Bytes large. So typically Map results are only stored at a small number of instances during the simulation. In a History file you store all results as function of time, but only in the specified monitoring points. The amount of data is usually much smaller than for a Map file, and we typically stores history data at a small time interval to have a smooth time function when plotting the results.


In the Communication file you store data required for other modules of Delft3D, such as the hydrodynamic results for a water quality simulation or the wave forces for a wave-current interaction. As the results must be stored in all grid points a Communication file can typically be as large as or even larger than a Map file. So, we only store the results in the Communication file as far as needed for the other simulations. Storage We apply the following options:

• Store Map Results Start Time 15 10 2002 00 00 00 [dd mm yyyy hh mn ss] Stop Time 15 10 2002 02 20 00 [dd mm yyyy hh mn ss] Interval 1.00 [mn] History Interval 0.01 [mn] The history interval must be small enough to retrieve a smooth signal from the monitoring points.

• Communication File Start Time 15 10 2002 00 00 00 [dd mm yyyy hh mn ss] Stop Time 15 10 2002 02 20 00 [dd mm yyyy hh mn ss] Interval 1.00 [mn] Restart Interval 0.00 [mn] The communication file is the core file that is used for each module to write and retrieve information. It is important to keep a relative small interval as data is interpolated between these time points by each module for their own computation. Detail In the sub-data group Output Options - We select the details of all possible data to be stored in the files or selected for printing. Upon selecting the sub-data group Figure 4.8 is displayed.


Figure 4.8 � Output Specification window

5 MOR DATA INPUT 5.1 Introduction A steering module allows you to link model inputs for the model components. The morphological process can be specified as a hierarchical tree structure of processes and sub-processes where time intervals for the elementary processes are defined. Processes may be executed a fixed number of times, for a given time span or as long as a certain condition is not satisfied. A transport module calculates sediment transport and bed changes activated by the flow-wave interaction process. The link between the involved process modules (Waves, Flow, Transport and Bottom) occurs via a dynamic coupling. This allows a feedback between the processes, which can affect water flow and sediment movement. The following section describes how the simulation of morphological processes can be achieved through the use of process trees. 5.2 Process Tree � Morphodynamic simulations under a tidal regime Delft3D-MOR uses a process tree to control the complete process simulation: it starts the processes, activates and de-activates process controllers and modules, takes care of the data communication between the modules and stops the process simulation.


We construct a process tree in which the updated bed levels are used by the hydrodynamic module to update the wave and flow fields (i.e. a morphodynamic simulation). The Waves and Flow modules are executed together in one loop to take the effects of wave-current interaction into account. Based on the hydrodynamic data the Transport and Bottom modules are executed a number of times by applying the continuity correction. When a user-specified maximum bed level change has been computed, the hydrodynamic module is executed again with the most recent bed level to update the wave and flow fields. In the following Figure 5.1 the physical modelling process is shown schematically.

Figure 5.1 - Schematic overview of a morphodynamic simulation (Extracted from the Delft3D-MOR Manual)

The tree consists of a set of branches that control the hydrodynamic and the morphological modules separately. We applied stop criteria and time management options to control the simulation. The hydrodynamic and morphological time scales are separated. The tree is shown in Figure 5.2 below. This process tree is executed in the following order: • A flow simulation is made in Node 1. This node is executed once to prepare water

level and current data for the Waves model. • The Wave and Flow model are executed in Node 2. This node automatically will

use the hydrodynamic data from Node 1. Node 2 can be executed a fixed number of times or can be controlled by an accuracy check.

• The Transport and Bottom modules are executed consecutively in Nodes 3 and 4. These nodes are always executed together via Controller 5. An intermediate update of the hydrodynamics is made automatically (via the continuity correction) if Node 5 is executed more then once. The <Stop Criterion> for Node 5 is usually a pre-set number of executions or an accuracy check.

• Controller 6 controls the actual morphological process tree. This node can be executed a fixed number of times, but usually a maximum simulation time is prescribed here.


Figure 5.2 - Process tree for a morphodynamic simulation under a tidal regime (Extracted from the Delft3D-MOR Manual)

In the following sub-sections the actual input file for the Steering module will be explained and documented to achieve the simulation related to the entire set of cases carried out in the Physical model, e.g. T1, T2, T3 and T4. 5.3 Time management for coastal applications One of the basic assumptions of most morphological modelling carried out with Delft3DMOR is that residual transports determined over a short period (e.g. one tide) can be used to simulate bed level changes over long time periods (e.g. days or months). As a result, two time frames can be distinguished in a morphodynamic simulation. The time axis over which the hydrodynamic models are run, is referred to as the hydrodynamic time frame. The time progress associated with the bed level changes, is referred to as the morphological time frame. In typical applications the hydrodynamic time frame is in the order of one or two tides in a tidal regime. In a river the hydrodynamic time frame may be even smaller when representative discharges are used to obtain stationary solutions. The morphological time frame can be in the order of days to months or even years. When applying Delft3D-MOR it is essential to be aware of this conceptual approach as it lies at the basis of any morphodynamic modelling exercise. Coastal Approach In this approach the hydrodynamic time frame is fully decoupled from the morphological time frame. The hydrodynamic and transport modules are running in a fixed time interval (e.g. over a representative tidal cycle), whereas the Bottom module is running in an increasing time interval (i.e. morphological time frame). This approach is used to ensure correct communication with the Waves module. The time management of the Coastal Approach is shown schematically in Figure 5.3


Figure 5.3 - Time progress for Coastal Approach (from Delft-MOR manual)

In the time progress diagram it is assumed that all physical process modules are executed consecutively in a loop. The hydrodynamic and transport modules are executed on a fixed time interval. For example, the subsequent executions 1, 5, 9 and 13 of the Waves module all coincide with period 1. Although the time interval is shifted back to the initial period, each execution uses the most recent bathymetry. So, they can (and should) be interpreted as if they had been running in shifted time intervals, which are indicated by [5], [9] and [13] in the Figure 5.3 above. The Bottom module is running in an increasing time interval. 5.4 Description of the modules within Delft3D-MOR Flow Module The time interval imposed by the Steering module on the Flow module overrules the time interval mentioned in the Flow input file. However, the indicated numerical time step specified in the Flow input file is used. Furthermore, the interval over which data is stored to the Flow data group on the communication file is arranged in the Flow input file. The reason for the double specification is that the Flow module can also be used in standalone mode. It is important to ensure that the times associated with the Flow module are not in conflict with the times imposed by the Steering module and with the times used by the other physical modules (e.g. Flow time step must be multiple of the elementary time step <Tscale> used throughout Delft3D-MOR). The Flow module can be regarded as the core on which all other modules operate. It is therefore essential that the output times of the Flow module to the communication file are selected such that the relevant flow data is available for further processing by the other modules. Obtaining the correct behaviour of the Flow module (e.g. a quasi-stationary discharge or a periodic flow cycle) requires the appropriate specification of the flow input (in particular boundary conditions). In general, the Flow module will have initial disturbances, which damp out with simulation time. As a consequence, the simulation interval of the Flow module is usually longer than the time period over which data is written to the Flow data group on the communication file. Because the Flow module is applied in combination with the Waves module, we use a fixed, non-increasing, time interval for both modules. Wave module As described in Section 3.3 a simulation is made for each internal time, referred to as wave time. For all these wave times, the wave quantities (wave height, direction, etc.) are computed within one call to the Waves module. The results are written to the Waves data group on the communication file, together with the wave times. Within


one call to the Waves module the same bed level is used. The Waves module uses the most recent bed level available on the communication file. Transport module The Transport module computes the sediment transport rates for an imposed time interval. From these transport rates, averaged transports are derived and stored in the Transport data group on the communication file. The Transport module uses both the Waves and Flow data groups from the communication file, depending on the selected sediment transport formula. Similar to the procedure in the Flow module, the selection of a wave field is done by a linear interpolation in time. The selection of a flow field occurs by the choice of the flow field with the nearest (reduced) time. The Transport data group is overwritten after each call to the Transport module. The Transport module can be called a number of times (in combination with the Bottom module without an intermediate flow computation) as it uses the discharge and water level data on the Flow data group. It will determine the velocities based on these discharges, water levels and the bed levels. This so-called continuity correction is applied to reduce the number of calls to the Flow module. In coastal, tide dominated areas, where the residual transports are an order of magnitude smaller, the continuity correction can usually be applied about 10 to 30 times before the FLOW module has to be run again. To determine the velocities, the Transport Module always uses the most recent computed bed levels. Bottom module The Bottom module is a sediment budget model which computes the bed level increment based on the computed sediment transports of the Transport module. The bed level increments are added to the most recent bathymetry available on the communication file. The module performs one numerical time step which is equal to the time interval imposed by the Steering module. However, this time interval may be overruled by an automatic optimal time step that can be determined by the Transport module. The module reads the averaged sediment transport rates from the communication file. The Transport data group on the communication file contains the averaged sediment transport of the last execution of the Transport module. The final Morphological tree process linking the 4 modules is displayed below in Figure 5.4.


Figure 5.4 - Morphological Tree processes

5.5 Description of Input file for Transport module Although the physical model was defined as a bedload model due to the scale of the basin, simulations have been executed in both Total and suspended modes to bring to light differences between the two modes. Very few numerical models have been undertaken at this particular scale and it was necessary to assess the influence of Transport modes as well as critical scaled factors. The input parameters for Total transport (bed load) are described in the following section, as a primary requirement of the physical model. Outcomes of the suspended mode simulations will not be given at this stage, as they are irrelevant to the bed load transportation that occurs in the Physical model. However, it would be addressed in the discussion Section 8. 5.5.1 Module Options

• The transport mode selected is the Total mode, which computes the sediment transport from algebraic transport formulas. The total sediment transport contribution is the summation of the bed load and equilibrium suspended load Sb + Se

MODSA=1 (TOTAL MODE) • The types of flow and wave fields within an elementary time interval of a

Transport module execution is assumed stationary


5.5.2 Time parameters In this section of the transport input file the time parameters have to be set. All time related parameters are in <TSCALE> (see Section 4.4). The computation time step for the transport calculations has to be given in the Transport module, the simulation start and the Steering module specifies stop time. • The Time step of transport computation is defined as 20 times <TSCALE >. Transport Time Step = 12 s • We indicate the length of the initial part of the time interval imposed by the

Steering module, which will not be used to compute the time-averaged sediment transport. A separate time integral of the sediment transport will be computed over this initial part of the time interval.

Initial time interval = 40 Transport Time steps (8 minute) • No Cyclic time reduction is applied to the reading of flow and wave fields from

the flow and wave data group of the communication file. 5.5.3 Spiral Motion and gravity (bed) slope effects These parameters are included for specification of the direction of the sediment transport vector. The formulations are based on the bed shear stress, including effects such as the spiral motion and gravity effects on sloping beds: • The secondary flow effect on the direction of the bed load or total load

transport is not included, as it produces inaccurate results when coupled with waves.

• The influence of a bed slope on the direction of the transport is specified by three parameters:

o Correction coefficient for the Shields number to be used in sediment transport direction (bed load) = 1.0

o Bed slope correction coefficient = 1.0 o Bed slope correction coefficient (power) = 0.5

5.5.4 Bed Characteristics The model allows for the specification of a non-erodible layer. The non-erodible layer is included via the specification of a rigid bed level for the complete model domain. The rigid bed level can be horizontal (spatially uniform level) or spatially varying in height. Nevertheless, there is no need to implement a non-erodible layer in the simulations as the 0.1m sand layer thickness of the physical model was sufficient to cope with possible scouring. • Non-erodible layers 5.5.5 Initial Distribution of sediment concentration • As the total transport is used, there is no need to implement an uniform

concentration.


5.5.6 Boundary conditions In this section the boundary conditions are specified. As the Transport module operates on the flow grid, the number of boundary segments (including numbering) should follow the specifications of the flow module. • All boundaries = Bed level condition imposed (which will be kept constant

in the bottom module, see Section 5.6) 5.5.7 General sediment parameters This section of the Transport input file contains the general sediment parameters. • Density of sediment = 2,650 [Kg/m3] • Kinematic viscosity of water = 1E-6 [m2/s] • Grain size D50C = 0.00019 (Entire domain) [m] 5.5.8 Sediment transport relation – Bijker with wave effects This part of the input file contains the selection of a sediment transport formula and the appropriate parameters for the selected transport formula. BIJKER (with wave effect)

• <BS> Coefficient b for shallow water = 5.0 [-] • <BD> Coefficient b for deep water = 2.0 [-] • <CRITS> Shallow water criterion (Hs/h) = 0.4 [-] • <CRITD> Deep water criterion (Hs/h) = 0.05 [-] • <D90> 90% sediment grain size = 0.00028 [m] • <RK> Bottom roughness height = 0.00115 [m] • <W> Sediment fall velocity m/s = 0.035 [m/s] • <POR> Porosity = 0.4 [-] • <T> Wave period = 1.15 [s]

Calibration of the longshore transport proved to be very sensible to the Bottom Sediment grain size and the Roughness height. Preliminary simulations have been carried out with higher values of <D90> and <RK>, which influenced dramatically the longshore transport rate. The bedload transport due to wave action differs from the transport due to current only. Sediment transport calculations revealed that Bijker�s formula overestimates the bedload transport in the river and must be consequently calibrated for a true representation of the Physical processes. A full review of this calibration phase is described in Section 6 dedicated to the Model Calibration.

5.5.9 Slope effect on magnitude of sediment transport We provide a coefficient to include the effect of bed slope on the magnitude of bedload transport:

• Coefficient for bed slope effect (bed load) = 1.0 [-]

5.5.10 Stability options A range of options is available to ensure a numerical stable solution. The stability criterion is actually required in the Bottom module to determine the updated bed level. However, the stability criterion is implemented as a correction on the calculated sediment transport rates and is therefore included in the Transport module.


We specify the stability correction option for bed level computation in Bottom module:

• Stability option <NSTAB> = 3 (Spatially varying stability correction using the grid increment, applied to the instantaneous sediment transport rate)

The stability correction uses the approximate bed level celerity according to the following equation (5.5.10) which is then based on the time averaged quantities:

hSb

cpor

ebed ε−

=1

(5.5.10)

with be constant depending on the applied transport formula (see next item BBTRS) h water depth

porε bed porosity, not included in the sediment transport rate S sediment transport magnitude Then, two items must be specified:

• the estimated velocity power of the transport relation, <BBTRS>, used for the approximate celerity = 5.0

• the porosity <PORSTA>, used for computation of time step and stability coefficient have to be given = 0.4

The estimated velocity power depends on the selected transport. As we applied a spatially constant correction coefficient, the numerical stability coefficient <ALFSTA> according to the definition of the stability criterion <NSTAB> has to be specified. In case a spatially varying correction is applied, <ALFSTA> ideally equals 1, but to suppress small instabilities it is often slightly larger than 1.

• Numerical stability coefficient <ALFSTA> = 1 The automatic time stepping switch <NTYDA> and a maximum Courant number <CRNMAX> have to be specified. <NTYDA> specifies whether the Transport module will compute an optimal morphological time step, which overrules the time interval of the Bottom module, prescribed by the Steering module. We apply:

• Automatic time stepping switch <NTYDA> = 1: Variable time step based on the Courant criterion

The approximate expression for the bed celerity is used to determine the optimum time step (via the Courant condition). For a numerical stable solution the Courant number should be lower than 1. Usually a value of 0.9 is applied. The Courant number should not be set too low since this will cause numerical diffusion.

• Maximum Courant number used for automatic time stepping = 0.9

In practical applications it is advised to use the stability correction options, which apply to the time-averaged transport rates. Nevertheless, the modelling of tidal inlets


implies contradictory common practices, as the use of instantaneous transports will be used in river modelling as opposed to the use of time-averaged transports for coastal areas. Averaging the transports for a combined ebb-flood cycle resulted in a predominance of the transport driven by ebb flows, which reduced the infilling of sand within the inlet mouth as observed in the physical model. The spatially varying stability correction methods, which were used, are likely to give more reliable results than the constant stability correction method; even coupled with instantaneous transport. The time interval <INTVAL> to be used for averaging of the water depth required when determining the stability correction (and bed celerity) has to be specified in this particular case:

• <INTVAL>=2: averaging water depth excluding the initial time interval

5.5.11 Output options This section of the Transport input file specifies which data is stored on specific transport history and map files. The transport fields used for the bed updating by the Bottom module are not influenced by the settings in this section. We do not need to describe the output options and files, which are similar to the one described for the WAVE and FLOW modules. 5.6 Description of Input file for Bottom Module In the bottom module, the bed level variations are determined based on (the gradients in) the sediment transport fields as calculated by the Transport module. The module will execute one time step, being the time interval imposed by the steering module Morsys or the time step calculated by the Transport module. Similar to the Transport module, it operates on flow grid. Consequently it has the same open boundaries as the flow module. 5.6.1 General Input Data The bottom module is executed in combination with the Flow and Transport modules. Relevant data form the communication file is already loaded into memory and does not need to be read from file again. ALL switches for flow, transport, bottom and auxiliary outputs are set to 0 (Record 1)

• <INORES(1)>, <INORES(2)>, <INORES(3)>, <KSWITS> = 0 The porosity is defined again and must correspond to the Transport formula used in the transport module:

• <POROSY> = 0.4 Initial transport is excluded within the computation:

• <IINTRA> = 0 5.6.2 Output Options Output times (start, stop and saving intervals) have to be specified for the history and map file, in combination with a switch how bed levels have to be stored on the communication file.


In this case, we need to store every new bathymetry to visualize the morphological changes and compute the ebb delta growth in volume. All switches of output quantities, such as integrated sediment transports have been activated.

• <ILUST>, <ILUEN>, <ILUDP>, <IAPPEND> = 1 Observation Points are similar to the monitoring points used in the flow module. 5.6.3 Boundary conditions As specified in the Section 5.5.6 of the Transport file, the Bottom module operates on flow grid, which means the number of boundary segments (including the numbering) should follow the specifications of the Flow module. The boundary type for each external boundary is set to a constant bed level:

• Boundary type <IBNDTP> = 4 5.6.4 Dredging option The sand bypassing scenarios (T2 and T4) are modelled through the implementation of a dredging option in the bottom module. This dredging option concerns automatic dredging, which is active during the whole morphodynamic simulation. A dredging scenario involves the specification of a reference dredging bed level and a dredging allowance. The reference dredging bed level, <DPBREF>, has to be specified for the whole grid in a separate file. The file format is identical to the depth file of the Flow module and can be constructed with the Delft-QUICKIN program. The dredging allowance, <DDPMIN>, is constant over the complete computational domain. Dredging is implemented as: DPnew=DPBREF+DDPMIN if DP<DPBREF (5.6.4) So, if at a grid cell the actual bed level, DP, is above (i.e. smaller than) the user-specified dredging bed level, <DPBREF>, the dredging takes place only at this grid cell. The new water depth is set by the reference dredge level and the dredging allowance according to Equation (5.6.4). Dredging is executed after each computation of a new bed level. The dredging, if required, is executed immediately following on this test. If a fixed layer is present, the dredging takes place till the fixed layer. To avoid dredging outside designated areas, the reference dredging level is specified sufficiently above (i.e. smaller than) the initial bed level (to account for sedimentation during the simulation). The results of the dredging are stored on the file �bagr-<RUNID>� only at times of dredging. The cumulative values of the dredged depth are written to the file. The following input is added to the usual bottom file md-bott.<Runid> : **************************************************** * ACTIVATION of the DREDGING OPTION **************************************************** DREDGE1 * Record 9: Dredging allowance 0.00 * Record 10: Dredging reference file bypassjet.dep


Dredging The reference-dredging file, which is the original bathymetry file, was modified to force the dredging at the location of the jetty trench only. The trench depth was estimated from computed sand deposition volume for each bathymetry update (bottom time step). The bottom time was approximately 30 minutes, and a designed cross-section trench of 1.5 cm below the reference depth was sufficiently deep to prevent its complete infilling during each update of bathymetry. It was therefore judged sufficient to trap longshore transport and acts as a successful bypassing system. However this option is subject to improvements, because of the effects of the trench on the downdrift morphological patterns along the southern wall. These effects have not been minimized to reproduce accurately the volume of sand that was extracted at constant time interval in the physical model (manual sand bypassing). Sand deposition The deposition of downdrift sand was not modelled, as this option is unavailable with the versions of Delft3D modules available. It was however not judged essential, as the observations from the physical model do not give evidence of sand backpassing from the deposition area (Tomlinson et al., 2003).


6 MODEL CALIBRATION Various calibration runs have been simulated to reproduce the exact conditions of the Physical model. Numerical parameters have been modified to input the identical wave climate and flow velocities that defined the physical model conditions. Numerical Grids have been modified many times to match the physical model data and prevent discrepancies due to numerical errors. A first assessment of the numerical model outcomes has provided a general overview of the model accuracy. It gave the insurance the computed velocities from the flow-wave interaction was correct and physically acceptable (see Figures 6.1 and 6.2 in Appendix A). We must keep in mind, that with such a short time step (0.6s) and such a grid size, simulations can run for more than 5 full days to reproduce 48 hrs of physical model simulation, which slow the calibration process. Once the model is set-up for one test case, the other simulations can be undertaken in a short time frame, as only the input parameters will be modified to suit the requirements of the following test cases. The preliminary phases of calibration process has been carried out with arbitrary monitoring points, which helped to evaluate the physical viability of the model. Nevertheless, during the modelling period, data have been retrieved from the Physical model and the position of the monitoring points has been changed to match the positions of the instruments used within the Physical model. This induced minor changes in Flow and Transport input files. 6.1 Instrument repositioning The outlines of the physical model were primarily designed with the help of CAD software, in order to position correctly the physical boundaries before construction. The origin of the coordinate system was implemented such as negative coordinates can come across the positioning of instruments and boundaries. Delft3D does not accept input grids with negative X and Y coordinates. Therefore, it was necessary to �translate� the spatial positions of the physical boundaries into a new coordinate system with strictly positive coordinates. Then the positions of the monitoring instruments, the training walls and bypassing jetty have to be translated also in this new coordinate system. Bathymetry of the physical model has also been translated into this new system of coordinate to ensure an exact replica of the original model. Delft3D can display as many observations points as there grids cells available, which means approximately 11,800 locations for this grid. Obviously, our interest lies in the comparison of numerical and physical model signals at few locations. These locations changed slightly during the four tests T1-4, and virtual instruments have been implemented for each test within the numerical model domain to match the position of the real instruments used in the physical model simulations. The instruments used for the physical model monitor the water level, wave height and velocities, which are easily retrieved from the numerical model output files. Water levels are expressed at the centre for the cell, where the observation point is positioned, while velocities are expressed across the sides of the cells. The bypassing jetty or borrow pit area is also relocated into the numerical domain. The new coordinates and related grid cell positions are referenced in Appendix B. An example of the position of the monitoring points for the Test case T1 is given below in


Figure 6.3. The probe P26 was located outside the domain below, because of the position of the inlet channel has been modified to suit the requirements of the grid.

Figure 6.3 � Position of the monitoring points within the numerical domain in reference

to the T1 case (26/10/2002 physical model simulations).

6.2 Calibration of the FLOW module For each Test Case, there are at least 6 probes, which monitor the physical model hydrodynamic outputs at once. Data are stored in files with an extension *.adv, which are processed with WINADV software (Whal, 2000). The U and V velocities are compared between the physical model and the numerical model outputs, which must be located at the exact same location. The related location of the Numerical gauges is displayed in Appendix B. For this stage, water levels and flow velocities only are relevant to the calibration of the numerical model and will be compared between the two models. Probes in the physical model and numerical model will be called respectively P<id>_p and P<id>_n. 6.2.1 Water levels Hydrodynamic maps Numerical models allow for extensive data output, which can be used to create hydrodynamic maps of the domain. This includes the mapping of the water levels over the entire domain to check for numerical inaccuracies or instabilities. Some probes would not be able to account for water level anomalies within the modelled domain and it is thus necessary to have a numerical overview of the model, which would replace the visual overview of the physical model in the reality.


Detailed of these maps at different times are displayed in the following figures in Appendix A: Figure 6.4: T1, T2 � Flood Tide Figure 6.3: T1, T2 � Ebb Tide Figure 6.4: T3, T4 � Flood Tide Figure 6.5: T3, T4 � Flood Tide Results show that for the following test cases: the set-up of set-down within the river inlet is limited and does not greatly influence the water level. Numerical domain T1, T2 current dominated:

• Set-down of 2-cm at the river boundary and 0.5-cm at the inlet entrance for the Flood Tide (Figure 6.4)

• Set-up of 1-cm at the river boundary and 0-cm at the inlet entrance for the Ebb Tide (Figure 6.5)

T3, T4 wave dominated:

• Set-down of 0.2-cm at the river boundary and 0-cm at the inlet entrance for the Flood Tide (Figure 6.6)

• Set-up of 0.2-cm at the river boundary and 0-cm at the inlet entrance for the Ebb Tide (Figure 6.7)

Physical domain Although the probe P26_p is located outside the domain, its was processed to retrieve the variations of the water level within the inner part of the channel to compare with the maps of the numerical simulations. We can approximate the position of the probe P26_p in the bending of the inner part of the inlet channel with the Probe ADV_n, which is located closer to the entrance. The water levels at the location of the ADV_n will be underestimated compared to the P26_p signal. T1, T2 current dominated:

• Averaged Set-down of 1-cm for the Flood tide at the location of P26_p (see Figure D1.4 in Appendix D) in agreement with the values of the hydrodynamic maps (Figure 6.4) and the ADV_n (Figure 6.8 in Appendix A).

• Averaged Set-up of 1.75-cm for the Ebb tide at the location of P26_p (see Figure D1.3 in Appendix D), which is underestimated in the hydrodynamic maps (Figure 6.5) and the ADV_n (Figure 6.8).

T3, T4 wave dominated:

• Averaged Set-down of 0.5cm for the Flood tide at the location of P26_p (see Figure D3.4 in Appendix D), in agreement with the values of the hydrodynamic maps (Figure 6.6 in Appendix A) and the ADV_n (Figure 6.9 in Appendix A).

• Averaged Set-up of 0.75cm for the Ebb tide at the location of P26_p (see Figure D3.3 in Appendix D), which is underestimated in the hydrodynamic maps (Figure 6.7 in Appendix A) and ADV_n (Figure 6.9 in Appendix A).

The variations in water level (set-up and set-down) between the numerical and physical models are summarized in the Table 6.0 below:


Table 6.0 � Water level variations within the inlet

Water Level Variations

Inlet Entrance (Numerical)

P26 (Physical)

ADV (Numerical)

Inlet Boundary (Numerical)

T1, T2 � EBB (Set-up) 0.0 cm + 1.75 cm + 0.075 cm + 1.0 cm

T1, T2- FLOOD (Set-down) - 0.5 cm - 1.0 cm - 0.9 cm - 2.0 cm

T3, T4 � EBB (Set-up) 0.0 cm + 0.75 cm + 0.02 cm +0.2 cm

T3, T4 � FLOOD (Set-down) - 0.08 cm - 0.3 cm - 0.2 cm - 0.3 cm

The analysis of the water levels from the Probe P26_p (Physical model) and ADV_n (numerical model) located inside the inlet shows that the geometry of the channel inlet influences the set-up and set-down occurring in closed inlet channels. The rest of the probes will be analysed thanks to history file outputs. History diagrams Output file in Delft3D can easily account for more than 1 or 2Gb of storage, which is dependant on the time step and the number of grid cells. The history time step has a value of 1s, which is sufficient for a smooth visualization of the water level variations due to the currents but might be too small to represent the variations due to the passage of the waves, with a period of 1.15s. The analysis of the hydrodynamic maps displays a quite stable environment with no or small disturbances. This will now allows the comparison of the water level variations at one or more locations, where data from the physical model is available. The previous example (Probe P26_p) shows that the probes are so sensitive they account for all 3D flow movement occurring into the physical model. The 2DH numerical model is far more �stable� in term of water level variations, and is not capable for computing such irregular and turbulent variations that occur into the hydrodynamics-wave basin. Furthermore, as said previously, variations in pumping rate (discharge) will neither be represented within the simplified numerical model. It can lead to some discrepancies occurring between the two models. The water level variations recorded at the offshore numerical probes (P13, P18, P19 and P27), which occur mostly during the ebb tide phase (release of flows into the domain) account for less than:

• 1.0 mm in the Current-dominated cases T1 and T2 (Figure 6.8 in Appendix A)

• 0.2 mm in the Wave-dominated T3 and T4 cases (Figure 6.9 in Appendix A)

These variations cannot be compared with the physical model output signals, because the waves are not taken into account into the numerical signal, due to a relative larger time step used to store the data in the history files. However, the numerical maps of water levels are in accordance with the small water level variations occurring in the physical domain.


6.2.2 Flow Velocities The input parameters in the numerical model are idealised which therefore lead to idealized output signals. Delft3D-FLOW is sensitive to abrupt changes in boundary forcing such as water levels or flow velocities. Disturbances in the boundary-forcing signal would lead to unwanted numerical errors propagating into the model. Therefore, it is not advised to input directly the physical model signals of which variations are too brutal for the numerical stability of the computations. As the model produces �general tendencies� or averaged data sets, the measured data will be filtered and averaged thanks to the WINADV software. On this particular case, the calibration will be assessed against the required entrance velocity defined for the test cases.

• Inlet entrance flows The objective is to reproduce within the inlet entrance a design current magnitude of 0.3m/s for the current-dominated T1 and T2 cases, and 0.14m/s for the wave-dominated T3 and T4 cases. The distribution of the velocities within the mouth of the inlet is displayed in Figures 6.10 and 6.11 for T1 and T2, and Figures 6.12 and 6.13 for the T3 and T4 cases (Appendix A). The bending of the entrance, as well as the friction effect along the training wall forces the parallel flow lines to get closer or move away from each other. The classic Venturi effect (Bernouilli) creates local flow acceleration or deceleration, to compensate for pressure variations within the fluid. T1, T2 cases The pressure of the flow is located along the northern wall where the flow is naturally directed at ebb tide and along the southern wall at flow tide. The distribution of the flow magnitude at the end of the training wall is centred on the thalweg centreline, with a maximum localised velocity of 0.36 m/s at Ebb tide (Figure 6.11) and 0.40 m/s at flood tide (Figure 6.10). The average velocity across the inlet section is 0.3 m/s. The U and V velocity components of the probes ADV_n and P17_n located inside the inlet are displayed in Figure 6.14 in Appendix A. The current magnitude differs by a 15% decrease for the flood tide when compared with its counterpart tide. The distribution of flow between Ebb tide and Flood tide is slightly dissymmetrical, because the water is flowing into the entrance with a radial profile distribution at flood tide while the current is flowing out of the entrance at ebb tide in a symmetrical profile centred on the thalweg. The flow lines follow the geometry of the channel inlet, which explains the value of the V-component accounts for approximately 30% of the U-component. As the P17 probe is located closer to the entrance than the ADV and P26 probes, where the flow can spread freely into a larger domain, the maximum velocities are slightly less for this probe. Data from the physical model gives after filtering, an averaged current magnitude of 0.3m/s for the flood tide and 0.28 m/s for the ebb tide at the location of the ADV probe (Figures E1.1 and E1.3 in Appendix E). This is considered as the reference calibration value to obtain. The components of the ADV_p probe (physical) differ from the ADV_n probe (numerical), which is explained by some difference in shape for the channel curve. The grid in the numerical model has been modified to verify


orthogonality and smoothness criterion, which are indispensable to obtain accurate numerical flow computations. Therefore, the width of the channel upstream is slightly narrower than the upstream channel width the Physical model. This increases the constriction of the flow lines, which accelerate in the curve of the numerical inlet, and emphasize the V-component of the current. The numerical model outputs (maps and probes) gives an approximation that is considered as sufficient (if not too good) to achieve the flow calibration phase for T1 and T2. T3, T4 cases Though the magnitude of the currents is approximately half of the T1 and T2 cases, the distribution of the flow at ebb and flood tide is similar. The maximum current magnitude reaches 0.18 m/s within the inlet at Flood tide, while reaching 0.16 m/s for the ebb tide. Between the extremities of the training walls, a maximum 0.12 m/s velocity is obtained at Flood tide and 0.14m/s at Ebb tide (Figures 6.12 and 6.13). The average velocity is 0.14 m/s across the inlet section. The same observations are made for the U and V components of the ADV_n and P17_n probes for the Current and Wave dominated cases (respectively in Figures 6.14 and 6.15), with V-component accounting for 30% of the U-component. Maximum velocities for ADV_n and P17_n are similar (less than 5% difference) due to the weak magnitude of the current. Data from the physical model gives after filtering, an averaged current magnitude of 0.154 m/s for the flood tide and 0.142 m/s for the ebb tide at the location of the ADV_p probe (Figure E1.5 in Appendix E). The current magnitude is slightly underestimated (-10%) for the ADV_n probe in the numerical model (see Figure 6.15), due to technical constraints related to the physical model pump functioning. Nevertheless, the level of accuracy is still quite high for this sort of modelling. 6.2.3 Conclusion on Flow calibration The comparison between the physical model and the numerical model outputs gives a good agreement between the two models. With the knowledge of the simplifications and approximations used in a numerical model, the analysis of the data concludes that the hydrodynamics in Delft3D is in accordance with the Physical model. 6.3 Calibration of the WAVE module The calibration of the wave module is of primary importance as the longshore transport depends on the accuracy of the wave transformation by refraction and wave breaking. Acceptable wave transformation across the shore must be reproduced. Although the waves characteristics through the physical model boundaries (virtual green lines) must be similar to the wave paddle requirements, it is more important we achieve the measured longshore transport occurring in the physical model. Therefore, this wave calibration phase benefits directly the following morphological calibration phase, which is described in Section 6.4. For this calibration, water levels outputs from the physical model are filtered against the average water level over the chosen period. This simplistic approach enables a quick visualization of the water level variations due to the passage of the waves. As expected, disturbances into the physical model basin have produced an unsteady


water level plane, which complicate the filtering of the signal to retrieve accurate wave conditions at this point. An example of this signal is displayed in the Figure F3.2 (Appendix F), which shows the level of accuracy required to match the numerical model outputs. Moreover, Delft3D-SWAN is a spectral model, which prevents the direct comparison between signals from the physical (time series) and numerical (magnitude) models monitoring points. This is an additional reason to direct the calibration phase through the reproduction of the longshore transport more than the replica of the wave conditions.

• Wave height and wave direction maps The longshore transport is directly dependent on the wave height and the wave angle at breaking point. It is important to recreate in the numerical domain an order of longshore velocity magnitude similar to those of the Physical model. Maps of wave height and wave direction transformation are useful to assess any discrepancies in wave propagation, which could reveal errors in bathymetries or wave decay. Wave Height (HSIGN) The size of the waves modelled was a concern, as the various parameters defined in SWAN have not been designed for this scale. Therefore, it was expected that the wave propagation would be affected in some extent. Although not yet situated into the capillarity effect domain, the small size of the wave would tend to be more easily affected by the approximations made in the numerical computations. The calibration of the wave module was the most time-consuming phase when compared with the calibration of the FLOW and MOR modules. The primary objective was to reproduce the measured longshore transport from the physical model. Waves have to be at least similar in height and angle at the breaking point to produce the required radiation stresses that will move the sediment alongshore. The first calibration phase aimed to retrieve similar wave characteristics through the virtual green offshore boundary (see Figure 2.2, Section 2.2.2), which represents in the reality the offshore limits of the physical domain at the location of the wave paddle. This was done through a series of tests on a stand-alone WAVE-SWAN simulation. The output of the wave height and direction are retrieved thanks to the use of virtual curves, replacing the offshore boundary of the Physical Model. For obscure reasons, the HSIGN input through the offshore boundary was different from HSIGN measured at the offshore boundary of the numerical domain, where wave enter the area. After various simulations with a large range of HSIGN input, a wave height of 0.074 m was found to be the right input to obtain a design wave height 0.067-m at the physical model up-wave boundary, which was used for the Physical Model. This value of 0.074 appeared to be the threshold value, which triggered the correct wave input for the numerical domain (see Figure 6.20 in Appendix A). The meaning for this behaviour is still to be uncovered, as the variation of various parameters such as bottom friction or width energy distribution did not solve the discrepancies between the model input and model output at the offshore numerical boundary. The decay of the waves into the model seems to be physically correct, when checking the maps of Wave Height and cross-shore sections, visualizing the wave height transformation and alongshore currents (see Figure 6.21 in Appendix A).


The correct calibration of the wave height was achieved through the use of the input parameters given in Section 3.1. WAVE Direction Although the outcomes were satisfactory on a stand-alone use of the WAVE module, the coupling with FLOW and MOR underestimated the longshore transport by a factor four to five. The external walls of the physical model act as a wave-guide, which forces the wave crests to keep a constant direction, at least along these side limits. The wave input boundary is located further offshore and in deeper water than the physical model. The numerical domain, being an extended reproduction of the Physical model area without hard side concrete boundaries, does not act as a wave guide and let the wave refracting naturally and earlier into the domain. This early and �free� refraction reduces the angle of the waves propagating towards the shoreline and thus reduces the longshore transport rate in a considerable extent. Before using the correction factors of the transport formulas to increase artificially the longshore transport, numerical simulations were undertaken with increased offshore wave angle input. Maps and cross-sections revealed the wave angle at breaking point was indeed smaller than the required 20 degrees. After few simulation runs, the angle of 29.5 degrees for the offshore boundary was judged adequate to reproduce a 20 degrees wave angle at breaking point (see Figures 6.22). 6.4 Calibration of the MORPHOLOGICAL module The morphological calibration phase consists primarily in choosing the transport formula, which is suitable to the environment to model, and then calibrates its formulation to obtain accurate computation of sediment transport. A tidal inlet is a complex system, which combines estuarine and coastal processes. The formula is derived from bed load river computations and has been adjusted to fit the transport due to the wave action. However, it is difficult to obtain accurate transport computation for both environments with the use of one formula. The transport formula must be used with the knowledge of their limitation and capabilities, as they are very sensitive to variations in input parameters such as sediment size and roughness height. Camenen and Larroude (2002) pointed out the extreme dependence of the grain size, current and orbital velocities. It is sometimes extremely difficult to approximate the parameters used in the formula; as a slight misjudgement can lead to serious discrepancies between the measured and predicted transports. 6.4.1 Bijker Formula (1971) with wave effects: basic formulation This formulation was derived from a method used in a river environment (Frijink formula (1952)) and was adapted to a coastal environment. The bottom shear stress has been modified using a wave-current model. The sediment flux is always in the direction of the current since the formula was developed to estimate the lonsghore transport rate. The bed load term of the sediment transport formula (taking into account the influence of waves) according to Bijker is given by:

)exp()1(50 rb AgCqbDS ε−=

where C Chezy coefficient (as specified in input of Flow module)


h water depth q flow velocity magnitude ε porosity and

)),100min(,50max( rar AA −=

)()/(

,1min,0max BDBSCC

ChhBDb

ds

dw −

−

−−=

where BS Coefficient b for shallow water (default value 5) BD Coefficient b for deep water (default value 2) Cs Shallow water criterion (hs/h) (default value 0.05) Cd Deep water criterion (default value 0.4) rc Roughness height for currents [m] and

+

∆−=

22

250

5.01

27.0

VU

q

CDA

b

ra

ψµ

( )

5.1

9010 /12log18

=

DhCµ

2*

.01

+

=

qU

Cgq

wzbψ

κ

)sinh(2 hkhU

W

Wb

ω=

Tπω 2=

194.00

123.5977.5exp(a

fw +−=

),2max(0c

b

rUaω

=

if wave effects are included (T>0)

otherwise where C chezy coefficient (as specified in input flow module) hw wave height (HRMS)

=

02gfC w

ψ


kw wave number T wave period computed by the waves model or specified by the user (Tuser) Ub wave velocity w sediment fall velocity [m/s] ∆ relative density (ρs- ρw)/ ρw κ von Karan conastant (0.41) For this modelling task, the suspended transport term has been neglected as the requirement of the model was bed load transport only. The following formula specific parameters have to be specified in the input files of the Transport module (refer to Section 5.5.8): BD, BS, Cs, Cd, D90, rc, Tuser and w. 6.4.2 Influence of roughness and friction coefficients The total roughness value ks is difficult to estimate as it allegedly influences significantly the total sediment transport. There are many ways of computing bed form characteristics and roughness, but it often leads to uncertainties. Observation of the bed forms from the Physical model provided some details of the ripple height and length. These values can be used to estimate the possible value of ks, which is indispensable to calculate the bed shear stress due to current and waves. A wrong estimation of the bed roughness results in significant errors in sediment transport computations. The roughness is used to calculate the friction coefficient due to the current fc, or (and) due to the waves fw. The review of different transport formulas by Camenen and Larroude (2002) provide advice on the use of the friction and roughness factors:

• The friction coefficients are increasing function of grain size diameter, but are dominated by the hydrodynamics if the total roughness is computed.

• Because ripples appear more often for fine sediment, a small current has a bigger effect on the friction coefficients.

• The friction coefficient waves fw is very sensitive to small orbital velocity with coarser sediments.

• The total friction factor is very sensitive to grain size and current (or wave) velocity, and explain the sensitivity of the transport formulae to these parameters.

Friction coefficients due to wave-current interaction do not have the same physical basis and displays very different values (10<fw/fc<100), which emphasize the difficulties to calculate a correct value of bed shear stress and thus sediment transport. 6.4.3 Calibration of the longshore transport Model layout A new model layout has been set-up for the use of the longshore transport calibration. The same grid is used, but the bathymetry is modified to plug the inlet entrance, from which the flow can disturb the measurements of the lonsghore transport. The physical process parameters (wave conditions and hydrodynamics) have been kept identical to the original model. The river boundary and associated discharge time series are now useless. Time frame Time frame simulation has been shortened to allow for a fast visualization of the outputs. There is no need for the model to include a smoothing time and long


iteration process because of the hydrodynamic stability of the newly designed simulation. Indeed, the sole processes driving the current variations are the radiation stresses produced by the wave transformation nearshore. The nearshore wave-current interaction is bound to this phenomenon. The time frame was designed as follows: Reference date: 2002-10-15 Starting time: 000000 (0 minutes) Stop time: 001400 (14 minutes) Smoothing time: 0 minutes Transport simulation period: 2 minutes (period [12..14 mn] of flow simulation) Bottom simulation period: 20 minutes As soon as the first Flow-Wave-Flow simulation is completed (which takes about 15 minutes), the first transport and bottom outputs are written in the communication file, providing sufficient data to stop the simulation. Calibration of sediment transport formula The bed load transport can now be integrated along designed cross-sections. Three cross sections were used along the beach profile over which is computed the alongshore sediment transport rate. The parameters that influence the longshore transport rate in the numerical model are listed below:

• wave height • wave angle • physical processes:

o spectral width o dissipation rate o bottom friction

• grain size (Transport module) • roughness height ks (Wave and Flow modules) • Flow-wave interaction formula (Fredsoe, Bijker) used in the Flow

module The objective of this calibration was to obtain an average 33 kg/hr lonsghore transport on a straight beach, without the influence of the inlet flow discharge, as formulated in the physical model. The relevant outcomes from the simulation are displayed in the Table 6.1 in Appendix G. Wave height and wave direction These two parameters affect dramatically the rate of bed load transport. The calibration through the wave height and wave angle will provide the quickest answer to modify the sediment transport magnitude. However, the limitations of the physical model imply that these variations must not be detrimental to the entire hydrodynamics driving the system. The numerical model aims to reproduce the morphological changes but the wave and flow conditions must be as close as possible from the design requirements. This involves the respect of wave height, wave angle at breaking point and flow velocity magnitudes within the inlet. Wave height The increase in wave height from 0.074 to 0.08 m (9%) displays a approximate 30% increase in sediment transport rate, which means wave height is a extreme sensitive


input in the numerical model but it must be carefully used as it could interfere with the shape and ruling depth of the ebb delta. Although the wave height input of 0.08m was satisfactory for producing the right transport rate, it was decided this value would have too much influence on the ebb delta ruling depth and shape. The wave height was kept at 0.074 m (input), which account for a 0.067 m at the physical virtual boundary as discussed in the Section 6.3.

Influence of Wave height in measured longshore Transport(d50=0.19mm)

01020304050

0.072 0.074 0.076 0.078 0.08 0.082

Hs (m)

Bed

load

(kg/

hr)

ks=1mm, Rc=2.8mmks=1mm, Rc=1.15

Figure 6.23 � Influence of Wave height in measured transport

Wave direction The wave angle input of 29.5 degrees revealed to be the right choice as it perfectly matches the physical model requirements. The longshore transport is primarily driven by the angle made by the wave crests with the shoreline. The longshore transport angle has an effect on wave refraction pattern, but has less influence than the wave height on the shape of the ebb delta. As discussed previously in the Section 6.3, the chosen wave angle of 29.5° (offshore numerical boundary) is accurately representing the physical model inputs.

Influence of Wave angle in measured lonsghore Transport

(d50=0.19mm, Hs=0.074m)

02468

101214

20 22 24 26 28 30

Wave Angle (degrees)

Bed

load

(kg/

hr)

ks=1mm, Rc=1.15mm

Figure 6.24 � Influence of Wave angle in measured longshore transport


Physical Processes The influence of the physical parameters affecting the wave propagation has been assessed. A primary assumption was to think the wave driving process for sediment transportation was underestimated, as the required rate of 33 kg/hr could not be obtained naturally. Nevertheless, various tests including bottom friction switch, spectral width and dissipation rate did not actually modify the longshore transport rate. Only the beaker index, which was increased from 0.73 to 0.8 to force the wave to break sooner, had a slight effect on the transport by increasing its rate by 10%. Roughness height for currents rc (Transport Module) The bed roughness used for the Bijker formula accounts for the estimation of the wave friction coefficient (see Appendix C - Formulations). The current fiction and wave friction coefficients affect the value of the combined shear stress (wave + current) and thus the sediment transport rate. As displayed in Figure 6.25 below, an increasing value of rc will dramatically increase the sediment transport rate in a linear fashion.

Influence of Roughness Height for current Rc in measured longshore Transport

(d50=0.19mm, Theta=29.5 Degrees)

05

101520253035

1 1.5 2 2.5 3

Rc (mm)

Bed

load

(kg/

hr)

Hs=0.074m

Figure 6.25 � Influence of Roughness height for current rc in measured longshore

transport

Bed Roughness ks (Flow Module) The bed roughness used in the flow module determines the Chezy coefficient of the White-Colebrook formula (see Formula 4.8.11 in Section 4.8). It has an opposite effect than the roughness Height for current used in the Bijker formula in reducing the transport rate with increased values of ks for wave simulations (see Figure 6.26 below). This contradicted the theory used in the models. The various uses and definitions of bed roughness make very difficult the analysis of the interaction between the input of the Wave and Flow parameters. It could be possible conflicts occur between the Fredsoe formulation used in the flow module and the Biker�s formulation in the calculation of the combined bottom shear stress. The use of two separate friction coefficient (wave and current), which does not have the same physical basis, and calculated by two different formulae at different time step, could explain this contradiction when they are combined (see Section 6.4.2) in a wave-flow interaction. Therefore, it was advised to follow examples of basin modelling displayed in the literature (Roelvink, 2001) and keep the value of ks=0.001m as acceptable.


Influence of Bed roughness Ks in measured longshore Transport


0

10

20

30

40

0.5 1 1.5 2 2.5 3

ks (mm)

Bed

load

(kg/

hr)

Hs=0.074m,Rc=2.8mm

Figure 6.26 � Influence of Bed roughness ks in measured longshore transport

Grain size The grain size plays also an important role in the way the sediment is carried (rolled or temporarily suspended (small jump) in a bed load transport. The sediment transport is an increasing function of the sediment grain size. The requirements of similitude for the physical model lead to the assumption of bed load model and the choice of a particular type of sediment. Therefore it was decided not to change the original grain size of the sediment (0.19mm) for the area where the wave are predominant, e.g. outside the inlet.

Influence of Grain size in measured longshore Transport


05

1015202530

0.00 0.10 0.20 0.30 0.40 0.50

Grain size (mm)

Bed

load

(kg/

hr)

Rc=1,15mmRc=2.8mm

Figure 6.27 � Influence of Grain size in measured longshore transport

Bottom shear stress due to the waves: Bijker or Fredsoe? Bijker was chosen as the reference transport formula used in the transport module. It would have been logical to choose the Bijker�s wave boundary layer model in the Flow module (see Section 4.8) for the formulation of bed shear stress due to the waves. However, the calibration process evaluated that the use of Fredsoe was more


adequate to compensate the underestimation of the longshore transport due to the waves in the Bijker formula. Each formula is using different assumptions, which are described in Appendix C. These opposite assumptions lead to differences in bed shear stress values. At this stage, the use of Fredsoe for bed shear stress provided a better way to obtain the required longshore, as Bijker tends to underestimate the solid transport in wave-current interactions, where the error may reach several orders of magnitude. This can be explained by the fact that the Bijker formula takes into account waves only as an active term of suspension. Thus, even when the orbital velocity is high, if the steady current is low, which is the case in coastal area outside the inlet entrance, the net sediment transport will also be low (Carmenen and Larroude, 2002). There is still much to do to understand the implications of the use of two different bed shear stress formulas in a combined wave-current simulation with Delft3D. Nevertheless, the primary objective of calibrating the lonsghore transport was fulfilled and there was no need to slow down the process with further theoretical considerations at this stage. 6.4.4 Calibration of the inlet bed load transport The ebb delta growth at the entrance of the inlet is driven by two sediment transport inputs, which are:

• Alongshore transport due to the waves • Cross-shore transport due to the inlet flows along the chennel

centreline The calibration of the first input has been discussed in previous Section 6.4.3. The calibration of the bed load transport due to the river is discussed in this section. Model layout The model layout is the model used for the wave-flow interaction as displayed in Section 2. This is the model of the straight beach used in the longshore transport calibration process with the inlet mouth reopened. Time frame The time frame is identical to the one used for the longshore transport calibration phase. Flow conditions The current dominated flow velocity (0.3m/s) has been chosen to calibrate the model, as the transport input of the inlet is non negligible against the transport due to the waves for this current magnitude. The magnitude of flow velocity for the wave-dominated cases (0.14m/s) was too little for measurements and computations to be accurate. This assumption was comforted by the preliminary measurements of delta growth, which were similar to the physical model outcomes. Wave conditions The first results account for great variations in bed load transport when combining the flows and varying wave conditions in the simulation. It seems that the Bijker formula used for the computations overpredicts the bed load transport within the inlet (see Table 6.2 in Appendix G). The transport rate decreases along the length of the inlet thalweg, as the waves penetrate deeper into the inlet mouth. Waves have been reduced to an acceptable minimum, to decrease the influence of the waves into the measured transport inside the inlet and compare with existing bed load formulas (with no waves). It is understood that this calibration phase gives a broad feeling of the transport occurring inside the inlet more than accurate values.


Reference transport formulations for bed load estimation There is no data available from the physical model that gives estimation or measurements of the bed load transport within the inlet. It was necessary to compute a theoretical estimation of the sediment transport with the acknowledged formula the most accurate for bed load transport vales. Three formula have been chosen:

• Einstein (1950) • Kalinske (1952) • Meyer-Peter (1948)

The methods of bed load computation are described in Appendix C. It involves the estimation of bottom shear stress and effective bottom shear stress through the use of various methods, which are summarised below: Meyer-Peter formula Meyer-Peter (1948) formula is based on large amount of experimental data and it based on the critical Shields parameter and effective Shields parameter. Einstein-Brown formula The principle of Einstein's analysis is as follows: the number of deposited grains in a unit area depends on the number of grains in motion and the probability that the hydrodynamic forces permit the grains to deposit (Liu, 2001). Einstein formula (1950) is based on experimental data fitting and use the effective Shields parameter. Kalinske-Frijlink formula Kalinske-Frijlink (1952) formula is based on curve fitting of all the data available at that time and is close to the bed load transport component of the Bijker formula. The formulas have been tested varying the bed roughness ks and the grain size to account for theoretical assumptions with no waves included, measured data from the Physical model and the calibration tests undertaken with the numerical model (the method of theoretical bed load computation is given in Appendix H). The order of magnitude is quite similar between Einstein and Kalinske formula. However, the Meyer-Peter formula generally gives higher sediment transport than the previous formulae. Meyer-Peter formula uses the critical shields parameter, while the other use effective bed shear stress. Due to the depth of the entrance inlet (0.1 m), significant wave energy enter the channel. The combined effect of orbital velocity and current stirs up the sediment, which is carried away by the flood and ebb currents. It is difficult to estimate a theoretical average bed load transport within the inlet, as the wave height has a great influence on the transport rate (see the following Figure 6.28). Nevertheless, a preliminary estimation of the maximum transport due to the current with no waves has been made using the three transports formulae listed above. Numerical model bed load measurements The relevant outcomes from the simulation are displayed in the Table 6.2 in Appendix G.


Sensitivity to waves entering the entrance The numerical model is very sensitive to the wave parameter, as the bed shear stress due to the wave action often accounts for more than 4-5 times the order of magnitude of bed shear stress due to the current. The mean bed shear stress computed by Fredsoe or Bijker is deeply dependant on the value of the wave bed shear stress and the wave boundary layer (Liu, 2001). Transport is an increasing function of the wave height, as displayed in Figure 6.28 below.

Influence of Wave height in measured inlet Transport

(U=0.3m/s, Rc=2.8mm)

0102030405060

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Hs (mm)

Bed

load

(kg/

hr) ks=1mm,

d50=0.19mmks=1mm,d50=0.50mmks=2.8mm,d50=0.19mm

Figure 6.28 � Influence of Wave height in measured inlet transport

Sensitivity to bed roughness ks The bed roughness (Nikuradse ks) used in the flow module has an obscure influence over the transport occurring within the inlet (wave and current combined). No clear trend is detected, which displays any influence of this parameter when currents and waves are combined (see Figure 6.29 below), though in this case the current is opposed to the wave propagation.

Influence of Bed roughness ks in measured inlet Transport

(Hs=0.074m, U=0.3m/s)

0102030405060

0 0.5 1 1.5 2 2.5 3

ks (mm)

Bed

load

(kg/

hr) Rc=1.15mm,

d50=0.19mmRc=2.8mm,d50=0.50mmRc=2.8mm,d50=0.19mm

Figure 6.29 � Influence of Bed roughness ks in measured inlet transport


Sensitivity to bed roughness rc As for the longshore transport calibration, rc increases dramatically the transport with higher values within the inlet (see Figure 6.30). The use of rc=2.8mm is necessary to obtain the correct longshore transport rate and therefore can not be changed in the transport file input. This reduces the calibration process to the use of grain size factor, which can be spatially varying for the numerical domain.

Influence of Roughness Height for current Rc in measured inlet Transport

(Hs=0.074m, U=0.3m/s, ks=1mm)

0102030405060

1 1.5 2 2.5 3

Rc (mm)

Bed

load

(kg/

hr)

d50=0.19mmd50=0.40mm

Figure 6.30 � Influence of Roughness height for current rc in measured inlet transport

Sensitivity to grain size As discussed in the previous (Section 6.4.3), the same conclusion can be drawn for the use of the grain size as a calibration parameter. The finest the sediment the more the transport is increased. Through the use of sediment mapping, Delft3D enables a non-uniform spatial distribution of sediment size, which can be defined at any location of the grid. The comparison between theoretical and measured bed load transport rate (small waves), as well as the observation of ebb delta growth curves provide sufficient evidence the sediment size must be increased within the inlet to reduce the overestimated bed load transport (see Figure 6.31 below). We first tried to implement a sediment size d50=0.5mm within the inlet area, e.g approximately 2.5 times the �outside� d50 size used in the maritime zone. However, the morphological features were too far affected at the boundary between the d50=0.5mm and d50=0.28mm at the entrance of the inlet. The difference of grain size led to the scouring of the layer of finer sediment between the entrance and the ebb delta accretion zone. Tanaka et al., (1991) already described a similar effect, in the study of morphological changes at the boundary between a surface of hard concrete layer and a sand layer, over which occurs a constant flow. After having simulated the four complete test cases with the two layers domain with no satisfactory results, it was decided to keep the sand layer uniform as preliminary designed in the physical model.


Influence of Grain size in measured inlet Transport(Hs=0.074m, U=0.3m/s, Rc=2,8mm)

0

10

20

30

40

50

0 0.1 0.2 0.3 0.4 0.5 0.6

Grain size (mm)

Bed

load

(kg/

hr)

ks=1mmks=2.8mm

Figure 6.31 � Influence of Grain size in measured inlet transport

Sensitivity to flow velocity The velocity of the current (averaged over the depth in the case of 2DH model) remains one of the fundamental parameters for sediment transport. Camenen and Larroude (2003) state that Bijker clearly overestimates sediment transport when current velocities are lower than 1.5 m/s, which can be explained by its sensitivity to roughness. The current velocity has been decreased to 0.27 m/s (-10%) to assess the influence of this parameter. With the case with waves, this have a strong effect on the bed load transport, which was reduced by approximately 50% (see Figure 6.32 below).

Influence of Flow Velocity in measured inlet Transport(Hs=0.074m, ks=1mm, Rc=2,8mm)

0

5

10

15

20

0.26 0.27 0.28 0.29 0.3 0.31

Hs (mm)

Bed

load

(kg/

hr)

d50=0.50mm

Figure 6.32 � Influence of the current velocity in measured inlet transport

Al Salem (1993) found that net sediment transport is proportional to the velocity moment to the power three (U3). Any slight change in flow velocity can have a major impact on the computation of sediment transport, through modified values of bed shear stress. This is an important factor of calibration, as it affects the sediment discharged by the river. It thus influences the sediment budget of the ebb delta growth and could explain the discrepancies in delta volumes observed between the physical and numerical model when currents prevail (T1 and T2 cases). The


numerical model provides a near too perfect steady flow discharge, which barely occurs in the physical model due to obvious technical reasons. The ideal scenario would be to input time-series of measured discharge from the physical model into the numerical model, though difficult to implement. At this stage, flow velocities within the inlet entrance have been inputted as preliminary designed. Sensitivity to Bed Shear Stress Fredsoe formulation overestimates Bijker�s transport rate (as displayed in Figure 6.33), in a similar manner than for the longshore transport calibration phase. As only one formula can be chosen, Fredsoe formulation was used because it already proved successful for the longshore transport calibration.

Influence bed shear stress formula in measured inlet Transport

(Hs=0.074m, U=0.m/s, Rc=2.8mm, ks=1mm)

0

5

10

15

20

Bed

load

(kg/

hr)

BijkerFredsoe

Figure 6.33 � Influence of the bed shear stress formulae in measured inlet transport

Comparison between measured and computed bed load transports The main results of this process are summarised below: Theoretical Physical model assumptions (similitude) - Inlet entrance cross-section

• Rippled bed (ks=0.003m): 1.46-6.37kg/hr (no waves) • Flat bed (ks=0.00019m): 1.52-5.78kg/hr (no waves)

Theoretical model - Inlet entrance cross-section

• Rippled bed (ks=100d50=0.019m): 1.62-6.37kg/hr (no waves) • Flat bed (ks=2.5d50=0.00475): 1.58-6.13kg/hr (no waves) • ks=0.00115m, d50=0.00019m: 1.5-5.67kg/hr (no waves) • ks=0.0028m, d50=0.00019m: 1.58-6.37kg/hr (no waves) • ks=0.0028m, d50=0.00019m: 1.58-6.37kg/hr (no waves)

Numerical model � Western Inlet cross-section

• ks=0.0010m, rc=0.0028m, d50=0.00019m: 3.7kg/hr (Wave height=0.01m) • ks=0.0010m, rc=0.0028m, d50=0.00050m: 0.25kg/hr (Wave height=0.01m) • ks=0.0028m, rc=0.0028m, d50=0.00019m: 5.3kg/hr (Wave height=0.01m)


Conclusion Due to the variability in bed load transport theory, the lack of experimental data, the variability of transport along the inlet centreline and the fact waves are included, it is extremely difficult to calibrate the transport theoretically. Moreover, no simulation has been undertaken with flows only to calibrate accurately the river sediment discharge. The first measurements of the ebb delta growth with the calibrated longshore transport provided better information about the volume of sediment transported by the river. Cross-sectional measurements have been made around the ebb delta shape to assess the percentage of littoral drift that contributes to the delta growth. Results give a 50% contribution from the lonsghore drift at full growth (start of simulation), which means 50% of the lonsghore transport is deposited along the updrift wall. Considering there is a negligible backpassing of sediment from downdrift of the entrance, this value gives an estimation of the inlet contribution in the sediment budget of the ebb delta growth. Sediment transport has been reduced empirically through the calibration of the various parameters (presented in the sections above) to match the growth curves of the ebb delta. Although the interdependence of the calibration parameters has complicated this process, the calibration phase has been pushed as far as possible to obtain transport rates that would fall into the same range of magnitude.


7 RESULTS The following section gives the overview of the outcomes relevant to the morphological changes occurring at the entrance and at the vicinity of the inlet. Depth contours and erosion/accretion areas will be described, as well as comparing the sediment volumes of the ebb delta growth between the physical and numerical models. Perpendicular (River section) and longitudinal (section across the delta) cross-sections are used to understand the re-distribution of sediment across the profiles. 7.1 Summary table of the simulations The four test cases have been summarised in Table 7.1 below to show the differences between the simulations.

Table 7.1 � Review of the simulated test cases

Test Case T1 T2 T3 T4

Flow Velocity (m/s) 0.3 0.14 0.3 0.14

Type Current dominated

Current dominated

Wave dominated

Wave dominated

Sand Bypassing NO YES NO YES

River Discharge (m3s) 0.059 0.028 0.059 0.028

Flow Tstep (s) 0.6 0.6 0.6 0.6

Transport Tstep (s) 12 12 12 12

Bottom Tstep Automatic (30-120 mn)

Automatic (30-120 mn)



7.2 Description of morphological changes The maps of depth contours and difference in depth contours have been used to assess the morphological evolution of the entrance for each simulation. As the influence of the sand bypassing must be addressed in priority, we will compare together T1 and T2 for the current-dominated simulations, and T3 and T4 for the wave-dominated simulations. The depth contours and morphological changes are displayed for all test cases in Appendix T. 7.2.1 Comparison between current-dominated simulations T1 and T2 Evolution of the entrance After 500 minutes • T1: Figures T1.0, T1.6 • T2: Figures T2.0, T2.6 Erosion in the river mouth starts immediately with the occurrence of material settling along the ebb jet. We observe a rapid build-up of the ebb delta, which becomes


shallower by +0.025m for both T1 and T2 (in Figures T1.6 and T2.6 respectively). The volume eroded from the bed channel inlet balances the volume of accretion of the ebb delta. Sand deposition occurs along the south side of the inlet channel close to the extremity of the south training wall. It is likely the combination of flood tide and wave penetration helps to balance the dominant ebb flow (over one tidal cycle) to create a calmer zone where the sand can be deposited. The bypass system has no effect on this pattern as it occurs with the same magnitude for both T1 and T2. In T2, the sand bypassing trench depth remains constant (+0.015m) supported by the presence of eroded area (in yellow) updrift of the north wall in figures T2.6 to T2.10. It is always preferable to keep the trench as minimal as possible to minimize the adverse effects (such as sand slides into the trench). However, the trench had to provide a minimum depth to trap most of the littoral drift. The resolution of the grid is sufficiently fine to minimize the impact on the adjacent cells, but there remains some doubts that the manual dredging undertaken during the simulation of the physical model has been reproduced with accuracy. The comparison of the final morphological changes gives us reasonable confidence to assume the numerical dredging design was close enough to reproduce T2 and T4 bypassed simulations. The centreline of the ebb delta (shallowest area) is already offset from the thalweg centreline to the north. The combination of flows being pushed along the north wall and the southerly longshore transport shift the delta (so-called �head� of the ebb delta) towards the north (downstream direction). The shape of the delta is still premature following the contours of the ebb jet. Sediment is deposited when the hydrodynamics forces becomes less than the gravity forces, which explains the form of the �young� delta. In T1 and T2, the morphological changes affect the 0.24m depth contours in a very short simulation time (as displayed in Figures T1.0 and T2.0). After 1000 minutes • T1: Figures T1.1, T1.6 • T2: Figures T2.1, T2.6 The scouring of the inlet increases by -0.035m for T2 and -0.037m for T1. The accretion of the ebb delta reaches +0.054m in height for T1 and T2. Ebb delta spread around the centreline of its head extending its reach downdrift and updrift of the respective north and south walls. The ebb delta shape is not limited to the entrance width of the inlet, which was not expected to extend towards the south. This is due to sand bypassing offshore of the bypass jetty or dredging trench, which feed the updrift slopes of the delta. Furthermore, the rapid build up of the delta forces its slopes to search for a more stable state by spreading around the delta head. In T1 and T2, the accretion due to the presence of the training walls and on the ebb tidal delta trapped the available sand, disrupting the natural bypass of the inlet. Thus, the beach downdrift starts to erode with the lack of sediment supply. Sand accumulates on the ebb delta for T1 and is retrieved from the beach system in T2 as the sand discharge to the downdrift area of the entrance is not modelled for the bypassing cases (see Section 5.6.4) As observed in the physical model (dye tracers) and at the prototype scale (Smith, 1990), the existence of a circulation cell downdrift of the north wall is responsible for a local accretion zone in the corner of the beach and the north wall (Figures T1.6 and T2.6). Sediment from the downdrift beaches moves along the north groyne and likely


feed the delta growth. However, the volume backpassed is limited and does not contribute in a great extent to the total volume growth of the ebb delta. After 1500 minutes • T1: Figures T1.1, T1.7 • T2: Figures T2.1, T2.7 While the delta tries to reach equilibrium with a constant littoral drift, the head of the delta is skewed to the north while becoming shallower. The updrift extent of the delta spread around the offshore tip of the bypassing jetty. The deltas in T1 and T2 provide similar locations at the updrift and downdrift boundaries, but reach deeper waters offshore for T2. More sand deposition occurs between the south wall tip and the ebb delta, which behaves as if the bypassing jetty did not exist. This deposition area might be caused by the incoming flood tide, which flows are constricted between the flat of the ebb delta and the extremities of the training walls. The maximum of the inlet scouring is located along the inner north wall reaching 0.043 m for T2 and 0.045 m in T1. The pattern of erosion continues on the beaches downdrift of the entrance as the sediment supply is still blocked upstream. After 2000 minutes • T1: Figures T1.2, T1.7 • T2: Figures T2.2, T2.7 A trend appears more clearly now with the delta spreading toward the north while the head position is aligned with the north wall. The ebb delta head is now +0.1m above the original offshore profile for T2 and +0.12 m for T1. The inlet seems to have found its equilibrium cross-section with a decreasing rate in the erosion pattern within its main channel. However, the scouring shadow of the channel spreads offshore toward the ebb delta as the littoral drift starts to bypass around the delta instead of infilling the entrance. Becoming a more stable platform, the delta now starts to build up toward the surface in T1 because there is still sediment available, which is not the case in T2. Between 2500 and 4500 minutes • T1: Figures T1.2 to T1.4, T1.8 to T1.9 • T2: Figures T2.2 to T2.4, T2.8 to T2.9 The extension of the delta continues with the help of the littoral supply for both T1 and T2, as sand has now bypassed offshore of the dredging trench in T2, although in limited volume. The inlet channel is pushed seaward eroding gradually the inner inlet side of the delta, while the head of the delta spreads around the entrance. There is a pronounced accretion updrift of the south groyne in T1, while T2 has limited build up due the lack of sediment supply. The ebb delta continues to grow up in T1 toward the surface with the ebb flat reaching 0.125 m in depth, while it remains limited in T2 providing a 0.165 m depth.


The erosion of the channel slows in T1 with less sediment infilling due to the protection of the accreted bar and a reduction in river transport capacity around 3000-3500 minutes. The deepening of the channel slows considerably after 4500 minutes providing a more stable access channel with depth ranging from 0.16m for T1 to 0.18 m for T2. The beach downdrift still follows the pattern of erosion due to the lack of sediment bypassing. This was expected, as the sediment is not mechanically bypassed in the numerical model for the reasons advanced in the Section 5.6.4. After 5200 minutes • T1: Figures T1.5, T1.10 • T2: Figures T2.5, T1.10 The main difference between T1 and T2 remains the direction of the channel. T1 provide the same channel minimum depth but has shifted downstream and is flanked upstream by a shallower bar (0.07-0.1 m) than T2 (0.12-16 m) The entrance if protected offshore from the waves by a shallow barrier. T1 and T2 have the same delta offshore extent but T1 is shallower. The inlet channel equilibrium seems to be reached at a maximum depth of 0.19 m for T1 and 0.20 m for T2. Obviously, the trench greatly influenced the shape of the delta and the channel direction, but did not influence the volume in a great extent. It seems the lack of sediment supply in T2 increases the scouring of the inlet channel, which supply the build up of the ebb delta. The sediment available in the river in part balanced the lack of updrift supply from the southern beaches (Tomlinson, 1991). The extent of the delta on the northern boundary is similar for T1 and T2, but still extends further offshore for T2. 7.2.2 Comparison between wave-dominated simulations T3 and T4 After 500 minutes • T3: Figures T3.0, T3.6 • T4: Figures T4.0, T4.6 We observe the build-up of the ebb delta, which becomes shallower by 0.012 m for T3 and 0.015 m for T4, which is twice as slow as for the current-dominated T1 and T2. As opposed to T1 and T2, the inlet starts to erode closer to the entrance and the deeper scouring occurs along the inlet side of the south wall (0.013 m for T3 and 0.015 m for T4). This trend is mainly due to the weaker ebb flow, which allows increased wave penetration when combined with the flood flow. The slower ebb velocities allow more sediment to fill up the inlet channel for the unbypassed simulation T3 than for the bypassed T4. Generally speaking, T3 and T4 displays the same features to the exception of the dredged trench updrift of the south wall in T4, which limits the sand accretion updrift of the south wall. As for T1 and T2, the volume eroded from the bed channel inlet balances the volume of accretion of the ebb delta. At this stage, the influence of the sand bypassing is limited. After 1000 minutes • T3: Figures T3.1, T3.6 • T4: Figures T4.1, T4.6 The maximum channel scouring reaches -0.025 m in T3 and T4. The delta flat has accreted toward the surface by +0.026 m for T3 and +0.027 m for T4.


In T1 and T2 the force of the flow create a typical �horse shoe� delta shape, while in T3 the combined action of littoral drift and slow ebb flow velocities spread the delta in a alongshore direction, with the delta head extending its flat in the same direction. The shape of T4 is similar to the delta shape of T1, although located less offshore. The sand is pushed less offshore by the weaker ebb flow and the delta build up in shallower depths, allowing for a rapid recovery of the interrupted littoral drift. The sediment comes across the delta and is rapidly redistributed by the wave action in a downstream direction, as it is not used anymore to stabilise the slopes of the delta. The channel already starts to shift to the north under the increased influence of the littoral transport against a weaker inlet transport. After 1500 minutes • T3: Figures T3.1, T3.7 • T4: Figures T4.1, T4.7 The scouring of the channel in T4 has increased (-0.034 m) because there is less sediment bypassing the tip of the south wall to fill in the channel as occurring for T3 (-0.031 m). The bending of the channel is slightly more pronounced for T3, while the scouring is more important for T4 along the inner side of the south wall, with depth values of 0.16 m for T4 and 0.147 m for T3. The differences in delta accretion start to be expressed with T4 being shallower than T3 over the flat of the delta. The deepest section of the channel in T3 and T4 is located along the south wall, while it is the opposite for T1 and T2. While the flat of the delta is wider for T4, the spreading of the ebb delta in T3 is greater in extent, with northern boundaries located now at 3 m from the north wall for T3 against 2.3 m for T4. It shows how the sediment can be spread by the waves around shallower delta, while the lack of sediment accounts for a slower stabilisation of the delta. The head of the delta being shallower for T3 (+0.037 m), it increases the interaction with the waves, which forces quicker accretion of its shallowest area. However, maps of depth contours show more accretion in deeper areas for T4 (+0.046 m), with the inlet forced to provide the exceedance of sediment by scouring its channel. The circulation cell downdrift of the north wall is still present for the wave-dominated scenario supported by the pattern of accretion along the northern wall on the beach corner. After 2000 minutes • T3: Figures T3.1, T3.7 • T4: Figures T4.1, T4.7 The trend continues for T3 with the delta spreading towards the north (limits extended by 0.7 m downdrift) and the occurrence of increased erosion on the downdrift beaches. The width of the delta flat increases for T4, while spreading slightly in a downdrift direction at a slower rate (+0.5 m). The accretion of the delta reaches +0.043 m in height for T3, far less than +0.054 m for T4 because the delta in T3 is located closer to the shore in shallower depths. As a balance the inlet channel has provided the sediment for T4 with scouring reaching a maximum of -0.04 m, while in T3 it is limited to -0.03 m. The lack of updrift sediment supply in T4 is balanced by sediment coming from the inlet, because the ebb delta must provide the same level of protection against the waves and the hydrodynamic flows with less sediment available from the littoral drift.


Between 2500 and 4500 minutes • T3: Figures T3.2 to T3.4, T3.8 to T3.10 • T4: Figures T4.2 to T4.4, T4.8 to T4.10 As the updrift accretion of the channel in T3 provide an efficient protection against the waves, the access channel start to be slightly deeper than T4, while skewing downstream to account for the constant sediment infilling. There is still however more scouring inside the channel along the south wall for T4 due to the increased wave and lateral flow penetration. As expected, the delta in T3 continues to spread out in a longshore direction as the ebb extent is limited offshore and forced to bend downstream under the action of the waves. T4 has a localized ebb delta centred on the entrance but reaches deeper depth to stabilise, as no sand is pushed across the entrance. The channel depth is equivalent for T3 and T4, though the protective bar is shallower for T3 (+0.07-0.08 m) than for T4 (+0.12-0.14 m) due to variations in sediment supply. The equilibrium seems to be reached at a depth of 0.14m. There is still slightly less channel erosion for T3 than for T4 and there is a stronger accretion along the downdrift side of the northern wall. The delta accretion has reached +0.1 m after 4000 minutes in T4 and remains stable around this value. The access channel (outside the training walls) stabilises around a depth of 0.14-0.16 m for T3 and T4, while the inlet scouring remains greater for T4 than for T3. The offshore extent of the ebb delta in T3 is limited to the 0.22 m depth contour line, while it pushes well beyond the 0.24 m depth contour for T4. 7.3 Ebb delta Growth curves The outcome of the ebb delta growth curves from the numerical model displays strong similitudes with the physical model patterns. On a general overview, it seems the bypass of sediment around the entrance does not reduce the volume of delta growth and can even produce the opposite in the case of wave-dominated simulations. We will compare the current-dominated and wave-dominated simulations but we first must explain the differences in accretive volumes and time scales between the physical and numerical models. 7.3.1 Why are the simulations periods of the physical model extended in the numerical model? While there are many time constraints for financial and technical reasons in the use of a physical model, numerical models are only limited by computer capabilities, which can slower or fasten a simulation. Simulations have been undertaken with the help of two or three computers running in parallel to speed the process, which can take up to 10 full days (for an 86 hr equivalent real time) to achieve the desired simulation. Numerical model provides real time data, which are used to monitor the accuracy and progresses of the simulations. This was helpful to decide whether or not it was necessary to extend the modelling time to obtain the equilibrium of the delta growth. It was originally decided to restrain the modelling time to match the simulation time of the physical model. Nevertheless, it would have been inadequate


to stop the simulations at this stage, with no insurance the equilibrium of the delta was obtained in the numerical model. As Delft3D-MOR enables the restart of a simulation at any requested time, as long as data are already computed and stored in the communication file (data file), we doubled the modelling time for the four test cases. It surely bring about the flexibility of numerical models compared to physical model, though physical model provide essential data for the calibration of the numerical model. 7.3.2 Why is the volume of delta greater in the numerical model than in the physical model? As already commented in the calibration Section (6), the calibration of the longshore transport was favoured over the calibration of the bed load transport within the inlet. Therefore, the estimated transport within the inlet is approximately 3 times the expected transport that occurs in the physical model. This is related to the sensitivity of the transport formula to the bed roughness ks, which seems to be a linear increasing function of the bed load for this range of parameters. This explains the difference when comparing the final volume (approximately 3 or 4 times the expected volume) between the physical and numerical models. The ebb delta growth is mainly driven by the river flow, while the longshore transport feed the delta in the transition period of initial growth (Tomlinson, 1991). Then the system finds its balance when there is not enough sediment available within the inlet. The sediment transported finally flows around and through the stabilised delta without major loss or gain of sediment. It only happens when sufficient sediment reaches the tip of the updrift training wall to start moving across the inlet entrance. Once the equilibrium is reached in the numerical model, which happens later than in the physical model due to discrepancies in the magnitude of bed load transport within the inlet, we observe the typical formation of a flat with no more delta growth. However, it must be added that the chosen area boundaries for the ebb delta volume monitoring have been underestimated, as they do not cover the entire area of delta growth. Nevertheless, our interest lies mainly in what happens at the entrance or in the vicinity of the entrance. T1/T2 current-dominated case

The delta growth stays similar for the first 1500 minute period and split in two separate rates (see Figure 7.1 below). Though at different levels, both cases stabilise in a plateau shape after 3000 minutes. The final volume is greater by 23% for T1 than for T2, with respective values of 0.99 m3 and 0.77 m3 after 5200 minutes. These volumes however, account for approximately 3 to 4 times the measured delta growth in the physical model. These values range from 0.68m3 after 2280 minutes for numerical T1 (vs. 0.23 m3 for Physical T1) to 0.60 m3 after 2080 minutes for numerical T2 (vs. 0.23 m3 for Physical T2). The stability seems to be achieved in the physical model after 2000 minutes, while it takes a little more than 3000 minutes in the numerical simulation.


CRC Numerical Model - Comparison T1 & T2 Ebb delta Growth

0.000.200.400.600.801.001.20

0

1000

2000

3000

4000

5000

Modelling Time (mn)

Ebb

Del

ta V

olum

e (m

3 )

T1 - PhysicalT2 - PhysicalT1 - NumericalT2 - Numerical

Figure 7.1 � Ebb delta growth for T1 and T2 (Physical and Numerical model) T3/T4 Wave-dominated case The volume growth of the delta is less for the wave-dominated test cases. The sand pushed outside of the bed inlet provides most of the sediment supply. With the assumption that the inlet bed load transport has been overestimated, a greater difference between the current and wave dominated ebb delta volume growths was expected. Contrarily to T1 and T2, the volume of the delta in the numerical model is similar in the physical model, although data from the physical model do not provide an extensive reliability due to the lack of additional modelling time. It seems the wave-dominated cases struggle to produce a stability or plateau in the given time. When compared to the T1 and T2, the 3000 minute simulation time, where the curve bend to a plateau regime seem to come out at the time 5000 minutes in T3 and T4.

CRC Numerical Model - Comparison T3 & T4 Ebb Delta Growth

0.00

0.20

0.40

0.60

0.80

1.00

0

1000

2000

3000

4000

5000

Modelling Time (mn)

Ebb

Del

ta V

olum

e (m

3 )

T3 - PhysicalT4 - PhysicalT3 - NumericalT4 - Numerical

Figure 7.2 � Ebb delta growth for T3 and T4 (Physical and Numerical model)

After 3200 minutes, data from the physical and numerical models are similar (0.42 m3 against 0.47 m3 respectively) for the T3 unbypassed case. T3 and T4 display an inverted trend to the current-dominated simulation, with a greater ebb delta growth for the bypassing scenario T4.


It shows once again that the ebb delta growth is hardly driven by the sediment supply updrift of the inlet mouth. Due to time constraint, the simulation time was stopped at 5200 minutes, but the stability or �plateau� of the curve can be expected after this period to reach approximately 0.85 m3 for T4 and 0.75 m3 for T3. It must be noted that the numerical stability of the morphological time step was obtained faster for the wave-dominated simulations, which shortened the simulation times by approximately 2 days (over 10 days for T1 and T2). 7.3.4 Deposition rate of the delta

Figure 7.3 � Deposition rate of the ebb delta for all test cases

At the start of the simulations the deposition rates for the current-dominated cases largely exceed the rates for the wave-dominated cases. It is due to the transition from tidal flow to dominated deposition to a state of dynamic equilibrium between the tidal flow and the wave-induced transport across the delta. This transition is a function of the changes in sediment transport capacity, as the ebb tidal flow becomes less like a momentum jet (Tomlinson, 1991). The growth of the delta due to the ebb tidal flow dominated deposition continues until the depth on the crest allows for a dominant wave-induced sediment transport. The wave-dominated cases provide higher deposition rates at the end of the simulation (5200 minutes) as the equilibrium of the delta is not slower to obtain. In the early stage of the delta development, there is an instantaneous scouring of the riverbed to provide the sediment available to feed the delta. The reestablishment of the littoral transport in T1 after 1500 minutes results in major differences in deposition rates between T1 and T2 from this period. The deposition rate follows its decreasing trend in T2 the accretion of the delta in T1, because the river cross-section becomes deeper and is does supply the sediment at the same rate due to its decreasing transport capacity. Once the transition between the tidal-dominated and wave-dominated processes is nearly achieved (3000 minutes), the deposition rates in T1 dramatically reduces to reach T2 as the sediment path is now bypassed around the entrance by the wave

Delta Deposition rate

0.0000

0.0050

0.0100

0.0150

0.0200

0.0250

0.0300

0 1000 2000 3000 4000 5000 6000

Simulation time (mn)

Dep

ositi

on ra

te (m

3/hr

)

T1T2T3T4


dominated transport. The lack of sediment available in T2 explains the difference in volumes (0.2 m3) between T1 and T2 at the end of the simulation. The entrance in T1 benefited from the availability of sediment when still dominated by the tidal forcing. When the transition period ends to enter a wave-dominated environment, deposition rates of the delta are then decreasing to zero, while the path of sediment transported goes across the ebb delta without losses or gains. As T3 and T4 are already in a wave-dominated environment, it takes longer to build up a sufficient protection against the waves. It takes even longer for the entrance in T4, which lacks of updrift supply due to the sand bypassing system and kept the location of the delta offshore in deeper water where the sediment cannot be transported onshore by the waves. The deposition rates in T4 stays almost constant (compared to the other test cases) to the delta build up in deeper water offshore with less sediment available. 7.3.5 Impact of sediment bypassing around the entrance From the growth curves obtained for all cases, there is no obvious pattern that proves that the sediment bypassing is effective or not. Although there is always a logical explanation to the influence of variations in sediment supply, we will agree on the following outcomes provided both physical and numerical simulations: • A sand bypassing system has no or limited influence on the growth rate of the

ebb delta. • Whichever state (wave or current dominated) is the inlet entrance in, the delta will

still continue to grow ignoring the direct effects of the updrift sediment supply. This leads us to the conclusion the inlet controls the ebb delta growth as long as there is enough sediment supply available in its mouth. The shape of the delta is nevertheless defined by the ebb jet shape and the amount of sediment flowing across the entrance. For current dominated cases, the delta will be located further offshore but the main channel will be forced to migrate downstream under the pressure of the littoral drift. The effect of the ebb flow is limited by an increase in wave refraction against the jet, which forces the reduction of the hydrodynamic forces to the benefit of gravity forces (sand deposition). 7.4 Cross-sections The delta cross-shore section has been monitored to assess the evolution of the profile of the delta while building up. It provides informative data on the offshore extent and ruling depth of the delta, which give an insight of the ebb delta path to stability. The section chosen is slightly offset from the thalweg of the inlet entrance to account for the drifting of the delta toward the north and accurately represent the ruling depth for all test cases. The section is 12 m long (red line in the Figure 7.4 below). It starts inside the inlet at a depth of 0.1 m and ends up in a 0.3 m depth further offshore).


Figure 7.4 � Representation of the delta longitudinal cross-section (AA�)

The location of this cross-section has been optimised from the observations of morphological changes for all test cases. The end of the training walls occurs at the 5.2 m chainage along the section AA�. 7.4.1 Ruling depth and evolution of the ebb delta profile When comparing the profiles on the same graph, we clearly express the differences in ruling depth and the offshore extent of the delta flat. The ruling depth and offshore extent have been summarised in the following table:

Table 7.2 � Ruling depth and ebb flat position for all test cases

Test case Ruling depth* (m) Position of the ebb flat (chainage � m)

T3 � Wave dom. Unbypassed 0.090 7.5

T1 � Current dom. Unbypassed 0.125 9.5 T4 � Wave dom. Bypassed 0.140 9.5 T2 - Current dom. Bypassed 0.165 10 *the depth of the ebb flat is named �ruling depth� at this stage, although the delta might not be in equilibrium yet. We assign this term to the shallowest part of the cross-section of the delta. The following graph displays the evolution of the ruling depth at different chainage, representing the shallowest depth in each test case (refer to Table 7.2).

A

A’


Ruling Depth Tracking (numerical model)

-0.25

-0.2

-0.15

-0.1

-0.05

0

0 1000 2000 3000 4000 5000 6000

Time (m)

RL

(m)

T3T4T2T1

Figure 7.5 � Ruling depth tracking The origin of the profiles for T2, T3 and T4 start at deeper depth because the growth of the ebb delta is located further offshore than for T1. The stability of the flat is reached at different times. As expressed earlier, the unbypassed cases provide deeper ruling depths than the bypassed cases. This suggests that the delta would be safer for navigation even though the volume of the delta is unaffected. 7.4.2 Scouring of the inlet T1 and T2 obviously provide greater scouring of the inlet mouth than T3 and T4 due to the force of the flow in the current-dominated case. The evolution of the channel depth is similar for T1 and T2 with a scouring ranging from -0.05 m to -0.1 m (see Figures 7.6 and 7.7). It seems to stabilise around a 0.2 m depth in the section located between the tip of the training walls (chainage 5.2 m) and the inshore slopes of the delta (chainage 7.5 m). The oscillations observed in the inlet section might be due to numerical interpolation errors due the relative coarse size of the grid (20 cm wide and 30 cm in the direction of flow propagation). T3 and T4 provide slight differences in the behaviour of the cross-sections between the inlet and the delta head, where some accretion occurs across the section between the delta head and the training wall tips. The inlet erosion ranges from -0.03 m to a maximum of -0.05 m (see Figures 7.8 and 7.9). 7.4.3 Ebb delta cross-shore profiles Figure 7.6 below demonstrates the differences between all test cases, again supporting the previous observations. T3 ebb delta is shallower and located closer to the entrance, while the delta spread further offshore for the other cases. It must be noted that the depth and shape of the ebb flat between T1 and T4 is similar. It means the ebb delta in the current-dominated unbypassed case would be similar to the ebb delta in the wave-dominated bypassed case. The exception remains in the volume of sediment that has been removed from the inlet in T1 to feed the build up of the delta, while it is fed by the updrift littoral transport in T4.


Evolution of Ebb delta profile - All test cases

-0.35-0.3

-0.25-0.2

-0.15-0.1

-0.050

0 2 4 6 8 10 12 14

Position (m)

Dep

th (m

) T1 - d3_1330T2 - d3_1440T3 - d3_1440T4 - d3_1440

Figure 7.6 - Evolution of ebb delta cross-section for all test cases

Wave-dominated Unbypassed T3 T3 provides the shallowest ebb flat with a ruling depth of 0.09m (see Figure 7.7 below), which is approximately equivalent to the breaking depth of the design waves of 0.067 m. It implies the river mouth is protected from the incident waves. This depth is even shallower updrift of this cross-section with a minimum depth of 0.07 m in some areas. T3 ebb flat is also the closest to the inlet entrance with a minimum penetration offshore at the 7.5 m chainage as the littoral drift is predominant against the tidal ebb flow.

Evolution of delta profile - T3 Wave-dominated bypassed

-0.35-0.3

-0.25-0.2

-0.15-0.1

-0.050

0 2 4 6 8 10 12 14

Position (m)

Dep

th (m

)

d0_0000d0_0714d0_1205d0_1802d1_0039d1_1054d1_1809d1_2321d2_0607d2_2012d3_0258d3_1440

Figure 7.7 � Evolution of ebb delta cross-section for T3

Current-dominated Unbypassed T1 T1 provides the second shallowest ebb flat of the simulations with a ruling depth of 0.125 m (see Figure 7.8 below), which could however become even shallower as we are not certain it will grow up again, though the total volume of the delta remains the same. The ebb flat is located further offshore at the 9.5 m chainage.

Time (dd_hhmm)

Time (dd_hhmm)


Evolution of delta profile - T1 Current-dominated bypassed

-0.35-0.3

-0.25-0.2

-0.15-0.1

-0.050

0 2 4 6 8 10 12 14

Position (m)

Dep

th (m

)d0_0000d0_0315d0_0600d0_0820d0_2055d1_0906d1_1734d2_0031d2_1146d3_0248d3_1330


Wave-dominated Bypassed T4 T4 provides slightly deeper ebb flat (see Figure 7.9 below) with a ruling depth of 0.14 m and located at the same position (9.5 m chainage).

Evolution of delta profile - T4 Wave-dominated bypassed

-0.35-0.3

-0.25-0.2

-0.15-0.1

-0.050

0 2 4 6 8 10 12 14

Position (m)

Dep

th (m

)

d0_0000d0_0506d0_1224d0_2305d1_0652d1_1634d1_1806d2_0231d2_0851d3_0042d3_0834d3_1440


Current-dominated Bypassed T2 T2 provides the deeper ebb flat with a �ruling depth� of 0.16 m located at the 10 m chainage, slighter more offshore than T1 and T4. This flat is deeper because it tries to find equilibrium, while its slopes are being pushed in deeper waters (see Figure 7.10 below). There is not enough sediment available to build up a shallower delta so far offshore.

Time (dd_hhmm)

Time (dd_hhmm)


Evolution of delta profile - T2 Current-dominated bypassed

-0.35-0.3

-0.25-0.2

-0.15-0.1

-0.050

0 2 4 6 8 10 12 14Position (m)

Dep

th (m

)

d0_0000d0_0434d0_0615d0_1105d0_1905d1_0652d1_1648d1_2346d2_0843d3_1440


7.5 Channel cross-section The cross-sectional area of the river has also been monitored to retrieve more details of the eroded channel. This section is located approximately 0.6 m from the extremities of the walls (perpendicular to the 4.6 m chainage along AA� longitudinal cross-section (see Figure 7.11 below).

Figure 7.11 � Representation of the channel cross-section BB�

An example of the evolution of the channel cross-section for T2 is displayed in the Figure 7.11 below.

B�

B

Time (dd_hhmm)


T2 - Cross Section Evolution - Inlet entrance

-0.210-0.190-0.170-0.150-0.130-0.110-0.090-0.070-0.050

0 0.5 1 1.5 2

North-South

Dep

th (m

)CS r0_0000CS r0_0434CS r0_1109CS r1_0309CS r1_1404CS r1_2349CS r2_0843CS r2_2246CS r3_0701CS r3_1440

Figure 7.12 � Evolution of the Channel cross-section for T2 simulation.

At the start of the simulation, sediment eroded from the inner bed channel is pushed toward the entrance to accumulate on the downslope (after 4 hours and 34 minutes). Then the bed of the whole entrance gradually erodes to feed the build up of the ebb delta located offshore. There is an obvious dissymmetry in the way the channel erodes as the main flow is forced along the northern training wall. This meandering deepens the section of the channel along the north wall and provides some deposition area along the south wall (chainages 1.8 m to 2 m). This has been already observed on the contour maps displaying for the morphological changes in the T2 simulations in Appendix T. These results are in accordance with the cross-section AA� where a 0.07 m channel bed erosion can be observed at chainage 4.6 m. T1 provide similar result, while in T3 and T4 the deposition/erosion pattern is inverted, with the channel eroding along the downdrift side of the south wall, due to the greater influence of the flood tide and wave penetration.

Run time (run_hhmm)


8 DISCUSSION 8.1 Accuracy of the 2DH approximation There is a major concern about modelling 3D effects (wave, flow and transport patterns) using depth-averaged computations. The 2DH method neglects the vertical dimension, which implies that some of the processes involved in the morphological changes cannot be accounted for. The validity of the 2DH approach must be questioned when it comes to the prediction of three-dimensional morphological processes. Waves Wave and current refraction are accounted in SWAN wave computations. Although the water surface elevation is small compared to the still water level, the influence of these variations on the wave pattern is included. This provides much more accuracy for wave�current interactions over morphological interesting shallow areas, such as the entrance of the inlet (ebb delta). A 2DH approach seems acceptable in this case. Currents The inaccuracies in computed velocities generally result from an incorrect estimation of bed roughness, which proved to influence in a great extent the bed shear stress and its associated sediment transport rate. Relationships between roughness and friction factors (wave and current), which are commonly based on experimental data, are extremely sensitive. There was no measurement available to calibrate the computed longshore velocities. Longshore transports were underestimated in the surf zone, while the opposite situation prevailed in the inlet area. Because no velocity values were available to verify the bottom roughness, the longshore velocities and associated longshore transport rates had to be calibrated in adjusting this value during a time-consuming calibration phase. The best approach was to adjust the roughness such that the required longshore transport was obtained in the area outside the inlet, and adjusts the inlet currents according to the measurements of the physical model. No secondary effect has been included as the water density is constant across the domain (inlet and offshore). Moreover, we can ignore the Coriolis force with such small model area. It means a 2DH approach in this case in sufficient. Transport Bijker�s formulae is based on the assumption of local equilibrium, meaning the transport is only related to local and time averaged parameters. This concept fails for suspended sediment (Roelvink et al., 1992; Delft Hydraulics, 1992) but can be accepted for bed load computations. Gravitational effects, which influence the direction of transport, have not been included in the simulations, as they do not give accurate results when combined with waves. In the steady flow situations, the contribution of the downslope transport to the total transport is quite insignificant. Neglecting the downslope gravitational term can lead to an inherently unstable system, and excludes a reliable approximation of the equilibrium state (De Vriend, 1986). For the �River outflow�, the inclusion of the gravitational term would result in flattening the sloping beach. To ensure the stability of the system, it would be necessary to account for the slope generating processes


as well, which requires a 3D or at least a quasi 3D approach of the problem (Roelvink et al., 1992; Delft Hydraulics, 1992). 8.2 Overall assessment of morphological changes between the Physical and Numerical simulations. The morphological changes from the physical and numerical models were compared. As there have been some technical problems in the physical simulations, it was impossible to survey the depth contours at a same time. Therefore, the morphological maps of depth changes have been retrieved in the numerical model to match the simulation time of the physical model morphological outcomes. The following conclusions are supported by the set of comparative Figures 8.1, 8.2, 8.3 and 8.4, which represent T1, T2, T3 and T4 respectively. Offshore area (except ebb delta area) Zones of accretion and erosion are in accordance with the physical model predictions, due to calibrated longshore transport and a correct model hydrodynamics (wave and flow). Rip cells are well represented within the model, which have been also observed during the physical model simulations (downdrift of the northern wall, and in the lower updrift corner of the southern wall). Inlet area Localised problems influence the modelled balance of the inlet channel, where 3D morphological processes must be accounted for. Curvatures effects have not been included, which affect the patterns of sedimentation within the inlet mouth. The numerical model does not display as much sediment infilling into the channel as the physical model. It can be explained by the choice of the transport stability options, which computes averaged transport over one tidal cycle (refer to Section 5.5.10). Time averaged transport underestimates the influence of flood tide in the residual transport, as the ebb flows are stronger in magnitude. Moreover, the direction of transport is deeply favoured toward the offshore sea, as it is more difficult for the sediment to be transported across the slopes of the entrance during flood tides than rolling down with a simple gravity effect during ebb tide, knowing the depth at the extremities is already 0.136 m. However, the deepening and turning of the channel, as well as the accretion downstream, seems qualitatively correct for the Current-dominated cases (T1 and T2) and quantitatively correct for the Wave-dominated case (T3 and T4). Ebb delta area The area of real interest is the ebb delta itself and the changes in shape and volume are the most difficult to predict in this area. • Current-dominated - Bypassed T1 The pattern of erosion/accretion is similar with the exception of inlet infilling, which is limited to the entrance of the inlet in the numerical model (see Figure 8.1). The accretion against the updrift side of the north wall is well represented, as well as the migration of the delta downdrift of the entrance. The �bridge� of accretion between the updrift beaches and the delta is similar in both cases. The erosion pattern on the downdrift beaches is similar, though it seems more serious for the physical model. The sediment infilling of the inlet in the physical model could have caused an


increased rate of erosion for the downdrift beaches, while the reestablishment of the sand bypassing is faster in the numerical model. However, the physical model displays a longshore erosion downdrift of the entrance, between the shoreline and the migrated delta, which is not represented in the numerical model. As said previously, the inlet sediment infilling could have delayed the reestablishment of sand bypassing and slow the infilling of this channel. The updrift extension of the delta in the numerical model (in blue) is well represented by the green patches in the physical model (see Figure 8.1 below).

Figure 8.1: Morphological changes between physical (left) after 2280 minutes and numerical (right) after 2500 minutes - T1 simulations

• Current dominated - Unbypassed T2 As opposed to Figure 8.1, the delta migrates downdrift with a slower rate as displayed in the physical and in the numerical model of T2 (see Figure 8.2 below). The �central� position of the ebb flat is similar in both simulations, though the patches of light erosion (in pink) connecting the south of the channel to the updrift side of the delta) in the physical model, are not represented in the numerical model. The trench of the sand bypassing jetty is well represented in the numerical model, though slightly overestimated.


Figure 8.2: Morphological changes between physical (left) and numerical (right) after

2000 minutes - T2 simulations

• Wave dominated - Unbypassed T3 Although the mouth accretion is totally absent from the numerical simulation, due to the choice in transport computations (averaged transports), the migration of the delta to the north is impressively similar (see Figure 8.3). Erosion of the downdrift beaches is represented as well, though with a greater extent in the physical model. The explanations provided for T1 are even more real in this case as the inlet loss of sediment is greater and deprives the downdrift beaches of sediment supply even more.

Figure 8.3: Morphological changes between physical (left) after 3120 minutes and

numerical (right) after 3000 minutes - T3 simulations

• Wave dominated � Bypassed T4 The head of the delta is located further offshore than T3, which is supported by the physical and numerical models outcomes (see Figure 8.4). The centreline of the flat is however skewed slightly further to the north in the physical model than in the numerical model. The scouring channel, which bends to the south, is similar in the numerical model, as well as some accretion along the south wall inside the channel.


The erosion of the downdrift beaches is again underestimated in the numerical model, which might come from temporary storage in the physical model (green patches) inside and updrift from the inlet mouth.

Figure 8.4: Morphological changes between physical (left) and numerical (right) after

2500minutes - T4 simulations

8.3 Choosing the right calibration? 8.3.1 Acting on the sediment grain size to reduce the inlet sediment transport? The objective was to reproduce the hydrodynamic conditions and thus the expected volume of delta growth. The growth rate being too high, it was decide to reduce the transport in the river by modifying the sediment grain size parameter. The D50 sand distribution was 0.19 mm outside the inlet mouth and 0.5 mm inside the entrance. This helped to produce a satisfactory ebb delta growth, as displayed in the Figures 8.5 and 8.6 below.

CRC Numerical Model - Comparison T1 & T2 Ebb delta Growth

00.10.20.3

0.40.50.6

0

500

1000

1500

2000

2500

3000

Modelling Time (minutes)

Ebb

Del

ta V

olum

e (m

3 )

T1 - Numerical

T2 - Numerical

T1 - Physical

T2 - Physical

Figure 8.5 �Ebb delta Growth curves for Physical and Numerical simulations (T1 & T2)

with coarser sediment size within the inlet.


CRC Numerical Model - Comparison T3 & T4 - Ebb Delta Growth

00.050.1

0.150.2

0.250.3

0.350.4

0

500

1000

1500

2000

2500

3000

3500

Modelling Time (minutes)

Ebb

Del

ta V

olum

e (m

3 )

T3 - Numerical

T4 - Numerical

T3 - Physical

T4 - Physical

Figure 8.6 �Ebb delta Growth curves in Physical and Numerical simulations (T3 & T4)

with coarser sediment size within the inlet.

However, the morphological stability was affected at the boundary between the D50 (0.19 mm) and the D50 (0.5 mm) sand layers, which was located at the direct entrance of the inlet. Figure 8.7 displays the scouring induced by the abrupt change in sediment layers at chainage 3 m. The bed inlet provides coarser sediment (d50=0.5 mm) while the outside domain provides finer sediment (d50=0.19 mm). The differences in transport rates between the two layers act as if the coarse layer is a fixed bed and the finer layer is a movable bed. It results bed scouring occurring at the boundary between the two layers, which does not represent accurately the physical model, where the sand layer is uniform (d50=0.19 mm).

Evolution of delta profile - T1 Current-dominated unbypassed

(non uniform sediment layers d50(0.19mm)/d50(0.5mm)

-0.3-0.25-0.2

-0.15-0.1

-0.050

0 2 4 6 8 10 12Position (m)

Dep

th (m

)

Figure 8.7 Evolution of a mixed bed layer with two sediment grain sizes (d50=0.5 mm from 0 to 3 m chainage / d50=0.19 mm from 3 m to 10 m chainage) 8.3.2 Acting on the transport mode The suspended transport has been tried by �accident�, while setting up the transport processes in the transport definition file. The following Figure (8.8) displays a snap shot of the morphological changes after 1500 minutes of simulation in suspended transport mode. Unlike the bed load transport, the suspended transport takes into account the cross-shore processes, as we can clearly see in the Figure 8.8.


Figure 8.8 Morphological changes for T1 simulations with suspended transport (after

1500 minutes)

The beaches downdriftt and updrift of the entrance provide evidence of cross-shore sand redistribution, while the patterns of erosion/accretion are totally different from the simulations in total transport mode (bed load). 8.3.4 Acting on the stability correction option? The choice of the stability correction was discussed in Section 5.5.10, where it was decided to use instantaneous transport used in river modelling as opposed to the common practice of using time-averaged transport rates in coastal areas. Averaging the transports for a combined ebb-flood cycle resulted in a predominance of the transport driven by ebb flows, which reduced the infilling of sand within the inlet mouth as observed in the physical model. The morphological changes are mainly driven by the inlet tidal flow at the early stages of the ebb delta development, which supports the use of instantaneous transports. In practical applications, the spatially varying stability correction method is likely to give more reliable results than the constant stability correction method; even coupled with instantaneous transport. Calibration runs have been carried out with other stability options with no satisfactory results or no significant changes in the morphological computations. At the scale of the processes involved, the stability correction options do not seem to influence in a great extent the computational processes. We must nevertheless be cautious about this assumption, as not all options have been tested for this study.


9 CONCLUSIONS 9.1 1st objective: reproduce the physical model outcomes The qualitative outcome of the morphological computations look sufficiently reliable and satisfactory to use the numerical model as a complementary tool to the physical model usually implemented to assist studies of coastal sediment movement. However, the use of numerical models must be decided before the design process of the physical model, as the data retrieved from the physical model must be relevant to the numerical model. The optimisation of data measurements within the physical model must be optimised in accordance with its relevant use within the numerical model. A thoughtful set-up of the physical model can save a lot of time and money while supplying valuable data for the complementary studies with a numerical model. There is still some progress to achieve before replacing physical models with numerical model implemented at the same scale. Numerical computations are coming closer to the model capabilities at the physical model scale and it becomes more hazardous to carry out simulations without an insight of the driving processes and internal parameters that affect the computations, as discussed in the Section 6 � Model Calibration. The hydrodynamic equations and the interactions between input parameters drive the computational processes, which could rapidly become inaccurate. This was observed during the calibration process where the variation of the input parameters led to unexpected computational outcomes. The calibration process is an optimisation phase, which can often be defined as a trial and error stage. Preliminary model set-up is important to refine the computation, but it also important to implement a similar approach for the calibration process. This will considerably postpone the completion of the task, because of the infinite variations possibilities, which are offered to the modeller when using the calibration parameters. Tidal inlets combine river and coastal environment, which cause modelling conflicts in view of the processes involved. There is often a choice to make between the riverine or coastal modelling approaches. This led to calibration issues between the longshore transport due to the waves and the bed transport due to the river. The approach of favouring the calibration of the river transport capacity led to extreme morphological discrepancies unacceptable for qualitative comparison and was not used. Moreover, it was extremely difficult to estimate an accurate transport rate from the various empirical formulas. The transport due to the river was not measured in the physical model simulations. Calibration of the longshore transport was thus favoured over the calibration of the inlet transport capacity, which led to differences in ebb delta volume growth, because the delta is fed by the sediment coming deposited from the river and the littoral drift. Quantitative observations between physical and numerical models provide some discrepancies in delta growth volume, due to the overestimation of the transport capacity within the inlet of the numerical model. Although some differences occurred


in some areas of the model, the shape of the ebb delta and the erosion/accretion patterns were sufficiently satisfactory to give a strong confidence for a future reproduction of physical models thanks to the use of a numerical model at the same scale. 9.2 2nd objective: Validate the outcomes related to the sand bypassing systems The second objective was to ascertain the preliminary results obtained with the physical model (Tomlinson et al., 2003). As observed in the physical model, the numerical model validates the theory that the sand bypassing system has a limited influence on the growth of the ebb delta. The four model tests undertaken as part of the numerical and physical studies showed that ruling depth was not greatly influenced by artificial bypassing, however the bypassed cases tended to yield slightly higher ruling depths (see Figure 7.5). Both tests showed that artificially bypassed inlets T2 & T4 formed narrow ridge type ebb deltas whereas for natural systems the unbypassed cases T1 & T3 formed wide ebb deltas formed with sand bridges between the updrift beach and the delta, which is verified for both physical and numerical models (see Section 8.2). TEST 1 & 2 Results from the physical model showed that for the ccCurrent- dominated case; there was little difference in the growth rate of the ebb delta between the bypassed and un-bypassed cases. This result is due to the erosion from the inlet bed in the bypassed case matching the sediment supplied to the delta from the updrift beach in the un-bypassed case. However, results from the numerical model showed that for the current-dominated case; there was approximately 20% more delta growth in the un-bypassed case, which is due to the availability of sediment in T1 when still dominated by the tidal forcing. It must be added that the numerical model underestimated the volume of inlet infilling, which could be responsible for the discrepancies with the physical model. Further outcomes of tests 1 and 2 in the Physical model were that bypassing of material effectively maintained updrift and downdrift beach alignments, while in the numerical model it could only be verified for the updrift beaches as it was chosen not to deposit the bypassed sand on the downdrift to simplify the model set-up. TEST 3 & 4 Results from the physical model showed that for the wwave- dominated case, the growth rate of the ebb delta was retarded by artificial bypassing, however, it was difficult to determine from the results whether the ebb delta equilibrium volume was reduced. Results from the numerical model do no show this trend and even showed the opposite trend after 2500 minutes of simulation time, which is the stoping time of the physical model simulation in T3 and T4. The extension of the simulation time (5200 minutes) was not sufficient to achieve the equilibrium of the ebb delta for the wave-dominated cases. The quantitative discrepancies observed between physical and numerical models are certainly linked to the differences in inlet transport capacity, which has changed the rate of sand deposition on the ebb delta during the tidal-dominated transition phase.


The differences in infilling rate of the entrance have also contributed to slow down the deposition rate in the physical model forcing variations in transport capacity within the inlet mouth in the physical model.


REFERENCES Al Salem, A. (1993). Sediment transport in oscillatory boundary layers under sheet flow conditions. Phd Thesis, Delft Hydraulics, The Netherlands Bailard, J.A. (1981). An energetics total load sediment transport model for plane sloping beaches. Journal of Geophysical Research, Vol. 86 (C11). Battjes, J.A and Janssen, J.P.F.M. (1978). Energy loss and set-up to breaking of random waves, Proc. 16th Int. Coastal Engineering, ASCE, 569-587 Battjes, J.A and Stive M.J.F. (1985). Calibration of a Dissipation model for random breaking waves. J. Geophysical Research 90(C5): 9159-91667. Bijker, E.W. (1966). The increase of bed shear in a current due to wave motion. Bijker, E.W. (1968). Littoral drift as a function of waves and currents. Proc. 11th Int. Coastal Eng. Conf., London, pp. 415-435. Bijker, E.W. (1971). Longshore Transport Computations. Journal of the Waterways, Harbours and Coastal Engineering Division, Vol. 97, No. WW4. Camenen, B. and Larroude, P. (2002), Comparison of sediment transport formulae for the coastal environment, Coastal Engineering 48 (2003), pp 111-132 Davies, A.M. and Gerritsen, H. (1994). An intercomparison of three-dimensional tidal hydrodynamic models of the Irish Sea, Tellus, 46A, 200 - 221. Engelund, F. and Hansen, E. (1967). A monograph on sediment transport in Alluvial Streams. Teksnik Forlag, Cpenhagen, Denmark. Einstein, H.A. (1950). The bed load function for sediment transportation in open channels flows, United States Department of Agriculture, Tech. Bull. No. 1026. Fredsoe, J.F. (1984). Turbulent boundary layer in wave-current interaction, Journal of Hydraulic Engineering, ASCE, Vol 110, pp1103-1120 Grant, W.D. and Madsen, O.S. (1979). Combined wave and current interaction with a rough bottom, Journal of Geophysical Research, Vol. 84 (C1), 1797-1808. Huynh-Thanh, S. and Temperville, A. (1991). A numerical model of the rough turbulent boundary layer in combined wave and current interaction, Sand transport in rivers, estuaries and the sea (Eds. R.L. Soulsby and R.Bettes), Balkema Rotterdam, 45-49 Liu. (2001) Sediment Transport. Lecture notes, Laboratorek for Hydraulik og Havnebygning, Aalborg University, Le Roux, J.P. (2002), Wave friction factors related to the Shields parameter for steady currents, Sedimentary geology 155 (2003), pp 37-43. Meyer-Peter, E. and Mueller, R. (1948). Formulas for Bed-Load Transport. Sec. Int. IAHR congress, Stockholm, Sweden.


Myrhaug, D. and Slaattelid, O.H. (1990). A rational approach to wave-current friction coefficients for rough, smooth and transitional turbulent flow, Coastal Engineering, Vol. 14, 265-293. Roelvink, J.A. (1992) Roelvink, J.A., Lesser, G., Van Ha, C. and Luijendijk, A. (2001). Morphological Pilot Experiment in a 3D wave-current basin. Seelig, W.N. (1979), Effects on Breakwaters on waves: laboratory tests of wave transmission by overtopping, Proc. Conf. Coastal Structures, 79, 2, 941-961 Stelling, G.S., Kernkamp, H.W.J. and Laguzzi, M.M. (1999). Delft Flooding System: a powerful tool for inundation assessment based upon a positive flow simulation. Proceedings Hydro-Informatics, Copenhagen. Tanaka, H., Yoshitake and Shuto, N. (1991). Bedload Transport of non-uniform sand due to waves and current, Proc. Euromech 262, compiled in Sand Transports in rivers, estuaries and the Sea, Brookfield, Rotterdam, 1991. (eds: Soulsby, R., Bettess, R.) Tomlinson, R. (1991). Processes of sediment transport and ebb tidal delta development at a jettied inlet, Proc. Coastal Sediments �91, Vol. 2, pp1404-1418. Tomlinson, R., Robinson, D., and Voisey, C. (2003). Investigation of Ebb Delta Development and Response using a Movable Bed Physical Model, Van Rijn, L.C. (1984). Sediment transport, Part I: Bed Load Transport, Journal of Hydraulics Engineering, ASCE, Vol 110, No10. Van Rijn, L.C. (1984). Sediment transport, Part II: Suspended Transport, Journal of Hydraulics Engineering, ASCE, Vol 110, No11. Van Rijn, L.C. (1984). Sediment transport, Part III: Bed forms and Alluvial Roughness, Journal of Hydraulics Engineering, ASCE, Vol 110, No12. Verboom, G.K. and Slob, A. (1984). Weakly-reflective boundary conditions for two-dimensional water flow problems. 5th Int. Conf. on Finite Elements in Water Resources, June 1984 Vermont, also Adv. Water Resources, Vol. 7, December 1984 Delft Hydraulics publication No. 322. Verboom, G.K. and Segal, A. (1986). Weakly reflective boundary conditions for shallow water equations. 25th Meeting Dutch Working group on Numerical Flow Simulations, Delft. Whal, T.L. (2000). Analyzing ADV data using WinADV. Proc. 2000 Joint Conf. On Water Resources Eng. And Water Resources Planning & Management, July-August 2000. WL | Delft Hydraulics. (1992). 2DH morphological computations in the vicinity of the river mouth. WL | Delft Hydraulics. (2001). Delft3D-MOR user manual. WL | Delft Hydraulics. (2000). Delft3D-WAVE user manual.


WL | Delft Hydraulics. (1999). Delft3D-FLOW user manual.


APPENDIX A*

*the following figures are direct Delft output files


APPENDIX B


INTRUMENTS POSITION WITHIN THE NUMERICAL MODEL DOMAIN T1 Instruments 26/10/2002 M N 202 43,263 46,348 -0.099 ADV 49 69 203 46,727 47,545 -0.104 P17 37 69 209 50,981 49,156 0.085 P13 26 69 211 51,91 49,44 -0.216 P10 24 69 2000 37,755 42,027 0.668 P26 OUT OUT 2001 60,439 39,422 0.775 P19 17 104 2002 56,979 54,26 0.782 P27 14 58 2003 56,394 58,332 0.819 P18 12 46 T2 Instruments Survey 16/10/02 (Probe positions) M N 2000 37,755 42,057 0.668 P26 OUT OUT 2001 60,439 39,452 0.775 P19 17 104 2002 56,979 54,29 0.782 P27 14 58 2003 56,394 58,362 0.819 P18 12 46 2004 52,801 49,661 0.78 P10 23 70 2005 50,024 48,661 0.84 P13 28 70 2006 46,851 47,512 0.873 P17 37 69 B-jetty 49.11 45.30 0.137 Offshore 33 81 B-jetty 45.90 44.12 0 Nearshore 43 81 T3 Instruments Survey 11/11/02 (Probe Positions) M N 2000 52,133 49,451 0.391 P10 24 69 222 50,169 48,714 0.404 P13 28 69 2002 46,628 47,553 0.5 P17 37 69 2000 37,755 42,057 0.668 P26 OUT OUT 2001 60,439 39,452 0.775 P19 17 104 2002 56,979 54,29 0.782 P27 14 58 2003 56,394 58,362 0.819 P18 12 46 T4 Instruments M N 317 53,381 50,014 0.385 P10 22 69 322 50,298 48,87 0.423 P13 27 69 328 46,882 47,61 0.49 P17 37 69 2000 37,755 42,057 0.668 P26 OUT OUT 2001 60,439 39,452 0.775 P19 17 104 2002 56,979 54,29 0.782 P27 14 58 2003 56,394 58,362 0.819 P18 12 46 B-jetty 49.11 45.30 0.137 Offshore 33 81 B-jetty 45.90 44.12 0 Nearshore 43 81 # ID X Y Z Name M-position N-position


BYPASSING JETTY POSITION WITHIN THE NUMERICAL MODEL DOMAIN T2 Bypassing Jetty X Y M N 44.67 43.413 48 82 47.384 44.529 39 82 T4 Bypassing Jetty X Y M N 44.78 43.53 48 82 48.44 44.82 35 82


APPENDIX C


Boundary layer of wave and current: Fredsoe�s model With wave alone, the wave boundary layer thickness is δ, and the flow is divided into two zones, outside the wave boundary layer (z > δ) where the flow is frictionless, and inside the wave boundary layer (z < δ). With the superposition of a weak current, turbulence is produced outside the wave boundary layer by the current. Inside the wave boundary layer both the wave and the current contribute to turbulence. But the current is so weak that the wave boundary layer thickness is app. the same. First we will consider the case where waves and currents are propagating in the same direction. Mean bottom shear stress With wave alone, the maximum bed shear stress and the wave friction velocity are

where Um is the maximum horizontal velocity on bed given by the linear wave theory. Because the wave boundary layer is very thin, Um can be taken as the velocity on the top of the boundary. The instantaneous bottom velocity and bottom shear stress are

Now the current is superimposed, the current velocity on the top of the boundary is Uδ, the combined instantaneous flow velocity on the top of the boundary is

The combined bed shear stress is

The mean bed shear stress is

If we know the wave (H, T, h) and the current (average velocity U), then δ, fw and Um can be calculated from wave alone, but Uδ is unknown at the moment because the velocity profile has been distorted by waves. Velocity profile outside the wave boundary layer Without the wave, the current velocity profile is

where u*,c is the current friction velocity, ks bed roughness, Van Karmen constant κ=0.4.


With the wave, Grant and Madsen (1979) suggest the velocity profile

(8-1)

The mean bed shear stress is (8-2)

kw can be interpreted as the bed roughness under the combined wave and current flow Inserting u|z=δ = Uδ into eq (8-1), we get

(8-3)

The average velocity of the current is

(8-4)

Combining eqs (8-2), (8-3) and (8-4) gives

Velocity profile inside the wave boundary layer Inside the wave boundary layer, turbulence comes from the wave and the current. The combined eddy viscosity is

Therefore the mean bottom shear stress is

which can be rewritten into


The integration of the above equation gives

where the integration constant z0 is the elevation corresponding to zero velocity (u|z=z0= 0). Nikurase gives z0 = 0.033 ks. Figure 8.1 gives an example of the velocity profile with and without waves.

Figure 8.1 Velocity profile with and without wave for the same water discharge. Wave and current forms an angle β Figure 8.2 shows the horizontal velocity vector on the top of the wave boundary layer (z=δ).


Figure 8.2. Instantaneous velocity on the top of the wave boundary layer. The combined velocity u is

The bottom shear stress is

which acts in the same direction as u, cf. Figure 9. The bottom shear stress in the current direction is

The mean bed shear stress in the current direction is


Boundary layer of wave and current: Bijker�s model Opposite to Fredse, Bijker (1971) assumes that the wave is so weak that it will not affect the thickness of the current viscous sublayer. First we consider the current alone. Bijker assumes that there is a viscous sublayer, starting from z = 0 to z = z0 e where the linear velocity distribution is tangent with the logarithmic velocity distribution, cf. Figure 9

Figure 9. Viscous sublayer in hydraulically rough flow.

By the logarithmic velocity profile we get

and the bottom shear stress is

Now the wave is superimposed, cf. Fig.9, the combined instantaneous .ow velocity on the top of the viscous sublayer is

The combined bed shear stress is

The mean bed shear stress is

where T is the wave period. Bijker�s mean bed shear stress is in the direction of the combined velocity u.


APPENDIX D


T1, T2 - WATER LEVEL � PROBE P26_p (Physical model)

T1 - Water level - Ebb Tide - P26

0.540.545

0.550.555

0.560.565

0.570.575

0.58

Wat

er L

evel

(m

)

Figure D1.1. Water Level � EBB TIDE

T1 - Water level - Flood Tide - P26

0.525

0.53

0.535

0.54

0.545

0.55

0.555

0.56

Wat

er L

evel

(m

)

Figure D1.2. Water level FLOOD TIDE


T1 - WATER LEVEL VARIATIONS� PROBE P26_p (Physical model)

T1 - Water level Variations - Ebb Tide - P26

-0.005

0

0.005

0.01

0.015

0.02

0.025

Wat

er L

evel

(m

)

Figure D1.3. Water level Variations � EBB TIDE

T1 - Water level Variations - Flood Tide - P26

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

1 28 55 82 109

136

163

190

217

244

271

298

325

352

379

406

433

460

487

514

541

568

595

Wat

er L

evel

(m

)

Figure D1.4. Water level Variations � FLOOD TIDE


T3, T4 - WATER LEVEL � PROBE P26_p (Physical model)

T3 - Water level - Ebb Tide - P26

0.54

0.545

0.55

0.555

0.56

0.565

0.57

0.575

0.58

Wat

er L

evel

(m

)

Figure D3.1. Water level � EBB TIDE

T3 - Water level - Flood Tide - P26

0.525

0.53

0.535

0.54

0.545

0.55

0.555

0.56

Wat

er L

evel

(m

)

Figure D3.2. Water level FLOOD TIDE


T3, T4 - WATER LEVEL VARIATIONS� PROBE P26_p (Physical model)

T3 - Water level Variations - Ebb Tide - P26

-0.005

0

0.005

0.01

0.015

0.02

0.025

Wat

er L

evel

(m

)

Figure D3.3. Water level Variations � EBB TIDE

T3 - Water level Variations - Flood Tide - P26

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

Wat

er L

evel

(m

)

Figure D3.4. Water level Variations � FLOOD TIDE


APPENDIX E


ADV PROBE � Example of Flow Velocities (T1 case)

Figure E1.1 Velocity Magnitude (cm/s) FLOOD TIDE

Figure E1.2 U (V-x) and V (V-y)-component (cm/s) FLOOD TIDE

Figure E1.3 Velocity Magnitude (cm/s) EBB TIDE

Figure E1.4 U (V-x) and V (V-y)-component (cm/s) EBB TIDE These ADV measurements were taken at the centre of the channel on the IX profile (Ebb is negative and Flood is positive)

ADV PROBE � Example of Flow Velocities (T4 case)

T41312A - Velocities (cm/s)

V-x

V-y

Time (seconds)

-10-20-30-40

01020304050

1000 2000 3000 4000 5000

Figure E1.5 U (V-x) and V (V-y)-component (cm/s) EBB TIDE and FLOOD TIDE (T41312a.Vf) These ADV measurements were taken at the centre of the channel on the IX profile (Ebb is negative and Flood is positive)


APPENDIX F


FILTERED WAVE SIGNALS P27 AND P 19 PROBES � T10710_005OUTPUT FILES

T1 - Wave signal filtered - FLOOD TIDE - P27

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0

Simulation time (s)

wav

e he

ight

(m)

Figure F3.1: Wave Height retrieved from water level signal North offshore inlet entrance � P27

T1 - Wave signal filtered - FLOOD TIDE - P19

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

Simulation time (s)

wav

e he

ight

(m)

Figure F3.2 Wave Height retrieved from water level signal South offshore of inlet entrance � P19


APPENDIX G


Table 6.1 � Influence of bed roughness and grain size on lonsghore transport

MODULE INPUTS WAVE WAVE FLOW TRANSPORT TRANSPORT Wave height (Hsign - m) Gamma=0.8

Wave angle (Degrees)

Bed roughness ks (White Colebrook -m)

Bed roughness rc (Bijker - m)

Grain size d50 (m)

BED LOAD (Kg/hr)

GRAIN 0.074 29.5 0.001 0.00115 0.00010 21 0.074 29.5 0.001 0.00115 0.00019 11.5 0.074 29.5 0.001 0.00280 0.00019 27 0.074 29.5 0.001 0.00280 0.00040 13 BIJKER Rc 0.074 29.5 0.001 0.00115 0.00019 11.5 0.074 29.5 0.001 0.00250 0.00019 24 0.074 29.5 0.001 0.00280 0.00019 27 NIKURADSE Ks 0.074 29.5 0.001 0.00280 0.00019 32 0.074 29.5 0.0028 0.00280 0.00019 15 Hs

0.074 29.5 0.001 0.00115 0.00019 11.5 0.008 29.5 0.001 0.00115 0.00019 16 0.074 29.5 0.001 0.00280 0.00019 32 0.008 29.5 0.001 0.00280 0.00019 43 θ 0.074 21.5 0.001 0.00115 0.0019 6.5 0.074 29.5 0.001 0.00115 0.0019 11.5


Table 6.2 � Influence of bed roughness and grain size on inlet transport WAVE FLOW TRANSPORT TRANSPORT

Wave height (Hsign - m)

Flow Velocity (m/s)

Bed roughness ks (White Colebrook -m)

Bed roughness rc (Bijker - m)

Grain size d50 (m)

BED LOAD (Kg/m3/section inlet)

NIKURADSE Ks

0.074 0.3 0.0010 0.00115 0.00019 27 0.074 0.3 0.0005 0.00115 0.00019 26 0.074 0.3 0.0028 0.00280 0.00050 14.5 0.074 0.3 0.0010 0.00280 0.00050 18 0.074 0.3 0.0028 0.00280 0.00019 47.5 0.074 0.3 0.0010 0.00280 0.00019 49 BIJKER Rc 0.074 0.3 0.0010 0.00115 0.00040 7.9 0.074 0.3 0.0010 0.00280 0.00040 25 0.074 0.3 0.0010 0.00115 0.00019 27 0.074 0.3 0.0010 0.00280 0.00019 49 Hs 0.010 0.3 0.0010 0.00280 0.00019 3.7 0.074 0.3 0.0010 0.00280 0.00019 49 0.010 0.3 0.0010 0.00280 0.00050 0.25 0.074 0.3 0.0010 0.00280 0.00050 18 0.010 0.3 0.0028 0.00280 0.00019 5.3 0.074 0.3 0.0028 0.00280 0.00019 47.5 U 0.074 0.3 0.0010 0.00280 0.00050 18 0.074 0.27 0.0010 0.00280 0.00050 9.5 GRAIN 0.074 0.3 0.0010 0.00280 0.00050 18 0.074 0.3 0.0010 0.00280 0.00040 25 0.074 0.3 0.0028 0.00280 0.00050 14.5 0.074 0.3 0.0028 0.00280 0.00019 47.5 FORMULA

0.074 0.3 0.0010 0.00280 0.00050 Bijker 13.5

0.074 0.3 0.0010 0.00280 0.00050 Fredsoe 18


APPENDIX H


Bed roughness ks One important question is how to determine the bed roughness ks? Nikuradse made his experiments by gluing grains of uniform size to pipe surfaces. In completely flat bed consisted of uniform spheres the bed roughness ks would be the diameter of the grains. This cannot be found in nature, where the bed material is composed of grains with different size and bottom itself is not flat but it includes ripples or dunes (see Section S.4.3). According to Liu (2001), the following ks values have been suggested based on different type of experiments:

• concrete bottom ks=0.001 - 0.01 m • flat sand bed ks= (1 - 10)d50 : ks=2.5d50 suggested here. • bed with sand ripples ks=(0.5 - 1.0)Hr : ks=Hr suggested here

Hr is the ripple height. The bed roughness is very important in calculating the bed load transport and in separating the bed load and suspended load layers. Characterisation of smooth and rough flow It is necessary to characterise the flow as hydraulically smooth or rough since it influences e.g. the thickness of the viscous sublayer etc. A very big series of experiments were carried out by Nikuradse for pipe flows. He introduced the concept of equivalent grain roughness ks, which is usually called bed roughness for open channel flow. Based on the experiments it was found that the following criteria can be used to characterise if flow is hydraulically smooth, rough or in the transitional zone:

Hydraulically smooth flow Hydraulically rough flow (S-1) Hydraulically transitional flow

, where u* is the friction velocity calculated using Eq. (S-1) below and � is the kinematic viscosity.

(S-2)

Connection between bottom shear stress and Chézy coefficient It is possible to derive a connection between C, u* and average velocity U.

(S-3)

Liu (2001) relate the Chezy coefficient, water depth h and roughness height/rough flow and critical velocity u* as follows:

(S-3) Hydraulically rough flows

ρτ bu =*

705

70

5

*

*

*

≤≤

≥

≤

ν

ν

ν

s

s

s

ku

ku

ku

guUC

*

=

)12log(18skhC =


Drag force Flowing water moving past an object will exert a force called drag force

(S-4)

where CD is the coefficient and A is the projected area of the object to the flow direction. Bottom friction coefficient f Liu (2001) shows derivation of a dimensionless friction coefficient f, which corresponds the Darcy-Weissbach friction coefficient originally derived for pipe flow. The derivation is based on examining the forces acting on a grain resting on the bed. The drag force is slightly modified from (S-32) by multiplying the depth averaged velocity U by an empirical coefficient � to take into account the fact that the true velocity near the grain on the bottom is somehow related to U. Then it is possible to examine the shear stress τ b acting on the grain by saying that the horizontal force is the drag force acting on A' which is the projected area of the grain to the horizontal plane:

(S-5)

(S-6)

where f is empirical friction coefficient corresponding the Darcy-Weissbach coefficient in pipe flow

(S-7)

Eq. (S-7) is not useful and therefore the following derivation is needed by utilising Eqs. (S-2), (S-3) and (S-6):

(S-8)

where it has been assumed that flow is uniform. Eq. (S-8) can finally be converted to hydraulically rough flow conditions by utilising (S-3).

Hydraulically rough flow (S-9)

Friction coefficient equation (S-9) together with Eq. (S-6) provide in some cases a useful way to calculate the bottom shear stress τ b. Sediment transport types The total transport of sediments, qs,tot can be divided to (e.g. Liu 2001)

2

21 AUCF DD ρ=

)(21 2UACF DD αρ=

222

21)

'(

21

'fUU

AAC

AF

DD

b ραρτ ===

)'

( 2

AACf Dα=

22

22C

ggU

f b ==ρ

τ

)12log(

06.022

skhC

gf ≈=


cb,ττ > 2*,, ccb uρτ =

20

2*,

)1( gdsu c

c −=θ

ν4)1( 5050

*

gdsdS

−=

• Bed load transport, qs,b • suspended load, qs,s • wash load, qs,w

Bed load transport is the part of the total load which is more or less continuously in contact with the bed. The bed load is in close relation to the effective shear stress which acts directly to the grain surface. Suspended load is the part of total load which is moving without continuous contact with the bed. The appearance of ripples will increase bed shear stress and thus the suspended load is related to the total bed shear stress. Wash load is composed of very fine particles transported by water but they are not originated from the bed. The calculation of wash load is not discussed here. The sum bed load transport, qs,b and suspended load, qs,s is called bed-material load . They are moving in different layers in the water. If the bottom is completely flat, which usually is not the case, the thickness of the layer is typically some grain diameters. E.g. Einstein (1950) suggested that the thickness of the bed load layer is 2d50. When the bed is rippled, the thickness of the bed load transport layer is often suggested to be the on the order of the ripple height Hr or the bed roughness ks (Bijker 1971). The transport formulas have been developed assuming that the lateral transport in the river is very difficult to forecast and therefore the unit is m3 (m s)-1, i.e. cubic meters per second per meter width. Shields diagram and the critical Shields parameters θ c. The parameter θ is defined as the Shields parameter and expressed as follows:

(S-10)

Now it is possible to define three different conditions when sediments start to move: critical friction velocity u*

Or critical bottom shear stress Or critical Shield parameter (S-11)

How to determine the critical Shields parameters θ c? Originally it was taken from the Shields diagram giving θ c as a function of the grain Reynolds number Re=dgu*/ν, where dg is a characteristic grain diameter. The Shields diagram (not shown here) is inconvenient because friction velocity u* is both in the x-axis in Re and y-axis which is calculated from Eq. (S-10). Madsen et al. (1976) converted the Shields diagram in to the diagram shown in Fig. S-13 giving the relationship between the critical Shields parameter θ c and a so called sediment-fluid parameter S*

(S-12)

50

2*

)1( gdsu

−=θ

cuu *,* >

cθθ >


Figure S-13. The modified Shields diagram giving critical Shields parameter θ c as a function of the sediment-fluid parameter S*. The diagram is also given as a fifth order polynomial.


=50

50

)10..1(

100

d

dks

"'bbb τττ +=

22

5010

2'

)5.2

12(log

06.021

21 U

dh

fUb

== ρρτ

Effective shear stress According to laboratory experiments the sequence of bedforms with increasing flow intensity is (Liu 2001):

• Flat bed • Ripples • Dunes • High stage flat bed • Antidunes

Ripples are formed at relatively weak flow intensity and are linked with fine material, with d50 less than 0.7 mm. The size of ripples is primarily controlled by grain size as follows Hr=100*d50 ; Lr=1000*d50 ; (S-14) where Hr is the ripple height (m) and Lr is the length of ripples. At low flow intensity the ripples have fairly regular form with upstream slope 6° and downstream slope 32°. The dunes have the small shape than ripples but they are much larger and they linked with d50 bigger than 0.6 mm. Antidunes are formed when flow is supercritical (Froude number greater than 1.0) Bed roughness ks was briefly discussed in Section S.3.4 for different kind of surfaces.

Rippled Bed (S-15)

Flat Bed Bed roughness is thus related to the absence/presence of ripples. In the presence of ripples, the total shear stress � b consists of two parts:

• Effective shear stress � b' originating from the skin friction (grain surface friction)

• Shear stress due to the form pressure of the ripples τ b''

(S-16)

Effective shear stress τ b' is important since it is acting on the single grains and therefore it is crucial for estimating the bed load transport as will be shown in the next section. In the case of flat bed τ b'' is zero and bed roughness is taken as ks=2.5d50 and the effective shear stress is calculated as (see Eqs. (S-6) and (S-9)):

(S-17)

where h is water depth and U is average velocity. In the case of rippled bed, τ b' is as given above but the total stress is larger due to ripples


22

10

2

)12(log

06.021

21 U

Hh

fU

r

b

== ρρτ

5050

,

)1( gdsdq BS

B −=Φ 5050, )1( gdsdq BBS −Φ=

5.1' )(8 cB θθ −=Φ

50

''

)1(/gds

b

−=

ρτθ

350

2

350

2

3'

)1(36

)1(36

32

)(40

gdsgdsK

KB

−−

−+=

=Φ

νν

θ

(S-18)

where it has been assumed that bed roughness ks equals the height of the ripples Hr. Calculation of bed load transport Meyer-Peter; Einstein-Brown;Kalinske-Frijlink equations In bed load transport it is essential to take into account both the bottom shear stress τ b and the effective shear stress τ b' acting on single sediment (skin friction). In many methods bed load transport is expressed in the form (e.g. Liu 2001).

or (S-19)

Therefore, the difference between the methods is in many cases the way to calculate the dimensionless function Φ B. Meyer-Peter formula Meyer-Peter (1948) formula is also based on large amount of experimental data and it based on the critical Shields parameter calculated using the equation displayed in Figure (S-13).

(S-20)

where � ' is effective Shields parameter calculated as

(S-21)

Einstein-Brown formula According to Liu (2001): "The principle of Einstein's analysis is as follows: the number of deposited grains in a unit area depends on the number of grains in motion and the probability that the hydrodynamic forces permit the grains to deposit. The number of eroded grains in the same unit area depends on the number of grains in that area and the probability that the hydrodynamic forces are strong enough to move them. For equilibrium conditions the number of grains deposited must be equal to the number of grains eroded, which, together with experimental data fitting gives"

(S-22) where θ ' is effective Shields parameter calculated as previously.


−−= '

5050,

)1(27.0exp2

b

bBS

gdsdq

τρ

ρτ

Kalinske-Frijlink formula Kalinske-Frijlink (1952) formula is based on curve fitting of all the data available at that time. It does not use the dimensionless function Φ B.

(S-23)

The algorithm for calculating bed load transport can be summarised as follows. 1) Estimate the bed roughness ks and the ripple height Hr. In the case that ripple

height is not measured, it can be assumed that Hr=100d50. If the bottom is assumed to be flat, bed roughness value ks is around 2.5d50. In the case of ripples it can be assumed that ks=(0.75..1.0)Hr. Various calculations have been made with different assumptions, varying the sediment size and bed roughness.

2) Calculate bottom friction factor f needed in the calculation of bottom shear stress

τ b in Eq. (S-35). Eq. (S-38) can be used to calculate f. The checking of the form of flow (rough or smooth) has to be done when friction velocity u* is known.

3) The critical Shields parameter θ c needed in many bed load transport equations is

calculated from Eq. (S-52) or taken from Fig. S-8 as a function of the sediment-fluid parameter S*.

4) Bottom shear stress � b and effective shear stress τ b'

have to be calculated in the next step from Eqs. (S-35) and (S-56).

5) Effective Shields parameter θ ' can also be calculated at this stage from Eq. (S-60). The summary of the variables calculated using the input data given in Fig. S-E2 is given in Fig. S-E3.


APPENDIX I* *the following figures are direct Delft output files.

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