IN DEGREE PROJECT ENVIRONMENTAL ENGINEERING,SECOND CYCLE, 30 CREDITS
, STOCKHOLM SWEDEN 2018
A study of sedimentation problems in the lower reaches of the river Österdalälven
LOUISE SJÖLUND
KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ARCHITECTURE AND THE BUILT ENVIRONMENT
TRITA -ABE-MBT-18375
www.kth.se
A study of sedimentation problems in
the lower reaches of the river
Österdalälven
Louise Sjölund
Supervisor
Bijan Dargahi
Examiner
Anders Wörman
Degree Project in AF283X (Environmental engineering and sustainable infrastructure)
KTH Royal Institute of Technology
School of Architecture and Built Environment
Department of Sustainable Development, Environmental Science and Engineering
SE-100 44 Stockholm, Sweden
i
Abstract
The river Österdalälven deposits large amounts of sediment when it passes through the city of Mora. The
sediment deposition risks clogging the inlet to the lake Siljan, hampers navigation, and creates a risk of
the river forming new channels. This study has addressed the problem by creating a numerical 2D depth-
averaged combined hydrodynamic and sediment transport model of the reach. The study focused on the
mechanisms behind the sedimentation and erosion patterns. River training structures in the form of
groynes were added to the model to investigate whether mitigation of the problem by physical structures
was possible. Because of the lack of field data, some of the flow and sediment transport parameters had to
be estimated. Sensitivity analyses were performed to analyse the model’s response to the choice of
boundary conditions, input parameters, and auxiliary models. The study concluded that erosion occurs in
areas where the shear stress or flow velocity is high and sedimentation in areas with flow circulation and
lower flow velocity. The sediment yield at the problem area, i.e. at the mouth in Siljan was flow-
dependent and increased with larger flow discharges. The yearly sediment yield was low compared to
stations downstream. The model was sensitive to the choice of boundary conditions, Manning’s
roughness coefficient, and sediment transport mode and transport capacity formula. The main conclusion
was that it is crucial to collect the relevant field data to obtain more reliable result for further studies. It
was further concluded that physical structures in the form of groynes could decrease the amount of
sediment that deposits at the mouth of Österdalälven in Siljan. The study has shown that it is possible to
create a working numerical river model based on the physical understanding of the flow despite the lack
of field data.
ii
Sammanfattning
Österdalälven avsätter stora delar sediment när den passerar genom Mora. Sedimentavsättningarna
riskerar att täppa igen inflödet till sjön Siljan, hindrar navigation samt ger upphov till en risk att älven
bryter igenom och skapar nya kanaler. I denna studie har en tvådimensionell medeldjupsmodell för
hydrodynamik och sedimenttransport av Österdalälvens sträckning som passerar Mora skapats. För att
undersöka om sedimentavsättningen kunde minskas med hjälp av fysiska strukturer testades modellering
med erosionskyddet hövder. Då fältdata var begränsad har vissa parametrars värde uppskattats och
studien har därmed fokuserat på mekanismen bakom sedimenteringen och erosionen. Känslighetsanalyser
av modellen har gjorts för att undersöka hur känslig modellen var till val av randvillkor, parametrar och
hjälpmodeller. Det kunde konstateras att erosion sker i områden med hög flödeshastighet och hög
skjuvhållfasthet och sedimentering i områden med cirkulation och låg flödeshastighet.
Sedimenttransporten i problemområdet vid mynningen i Siljan var beroende av flöde och ökade med ett
ökat flöde. De årliga transporterade mängderna sediment var lägre än vid mätstationer nedströms Mora.
Modellen var känslig till val av randvillkor, Mannings tal, samt till val av transportsätt och
transportkapacitets-formel för sediment. Den viktigaste slutsatsen var att för att förfina modellen till att på
ett pålitligt sätt kunna kvantifiera de relevanta aspekterna av hydrodynamik och sedimenttransport krävs
att relevant fältdata samlas in. Därutöver visade studien att fysiska strukturer i form av hövder kunde
minska mängden sediment som avsätts i flodmynningen i Siljan. Slutligen drogs slutsatsen att det är
möjligt att skapa en fungerade numerisk modell baserat på de fysikaliska flödessambanden trots
avsaknaden av fältdata.
Key words
Österdalälven, sedimentation, sediment transport, erosion, hydraulic modelling, river modelling, river
training.
iii
Acknowledgements
I would like to express my gratitude to my supervisor Bijan Dargahi for his dedicated and enthusiastic
guidance in this project.
iv
List of figures
Figure 1. Photos of the sandbanks by anonymous photographer (personal communication with B.
Dargahi, 2018) deposited on the island Sandholmen in Siljan. For the location of the island in the lake,
see Figure 4. .......................................................................................................................................2
Figure 2. Map retrieved from B. Dargahi (personal communication, 2018) of the reach showing depth
(light to dark blue), areas where dredging (dashed red area), and beach protection have been performed
(red dots). The volume of removed sediment is marked with red writing. ...............................................3
Figure 3. Map of the areas with deposition and erosion in Mora. Adapted from Mora municipality (2006
& 2017). (Esri, DeLorme, HERE & MapmyIndia) ................................................................................4
Figure 4. Study area location in Europe and Sweden with marked rivers, lakes and islands (Esri,
DeLorme, HERE & MapmyIndia). .................................................................................................... 10
Figure 5. Bathymetry map for the reach. The depth is ranging from 0-2 (light) to 10-12 (dark) ( (SMHI,
2000). .............................................................................................................................................. 12
Figure 6. Map showing the two SMHI measuring stations for hydrological data in Österdalälven
(Spjutmo) and Oreälven (Skattungen) (Esri, DeLorme, HERE & MapmyIndia). ................................... 13
Figure 7. A conceptual model showing the discharge and water surface elevation boundary conditions.
The boxes represent inlets and outlets, and the arrows represent the flux direction. The dashed line marks
the model domain. BC: Boundary Condition (Esri, DeLorme, HERE & MapmyIndia). ......................... 18
Figure 8. The final mesh split in two parts where the left part is the north part and the right the south part.
The black dotted line marks the I-line from which result was extracted. The red dashed box marks the
area where the groynes were located. ................................................................................................. 24
Figure 9. Water surface elevation [m]for one of the groyne configurations 45/6 (left) and standard
configuration (right) for Q=100m3/s. .................................................................................................. 26
Figure 10. Simulation results showing the uniformly scaled velocity vector field [m/s] for the standard
configuration for Q=100 m3/s marked by regions a-f. .......................................................................... 27
Figure 11. Velocity field in area e, with overlaid eddy viscosity layer [m2/s] for the standard configuration
for Q=100 m3/s. Circulation and reversal flow regions are apparent. ..................................................... 28
Figure 12. Velocity vector field [m/s] with reverse flow in east side of the channel in area d for the
standard configuration for Q=100m3/s. ............................................................................................... 29
Figure 13. Distribution of bed shear stress [N/m2] for the standard configuration for Q=100 m3/s........... 30
Figure 14. Velocity variation for varying flow discharges in Österdalälven along the constant I-line
marked in Figure 8 for the standard configuration. .............................................................................. 31
Figure 15. Shear stress variation for varying flow discharges in Österdalälven along the constant I-line
marked in Figure 8 for the standard configuration. .............................................................................. 31
Figure 16. Velocity field [m/s] in area e, for the standard configuration for Q=200 m3/s. ....................... 32
Figure 17 Sediment transport rate for the suspended load and bed load for the standard configuration for
Q=100m3/s along the I-line marked in Figure 8. .................................................................................. 33
Figure 18. Normalized sediment transport rate, shear stress, and velocity magnitude for the standard
configuration for Q=100m3/s along the I-line marked in Figure 8. ........................................................ 33
Figure 19. Bed level changes [m] for the standard configuration Q=100 m3/s after 1 year. ..................... 34
Figure 20. Sediment yield at outlets after1 year for the standard configuration for varying discharges. ... 35
Figure 21. Sediment yield at west outlet for Q=100m3/s after 1 year with variations in transport capacity
formula. The red bar marks the standard configuration. ....................................................................... 36
v
Figure 22. Sediment yield at west outlet Q=100m3/s after 1 year for variations in the configuration........ 36
Figure 23. Uniform vector velocity field [m/s] for configurations with groynes for Q=100 m3/s. The
groyne configurations are from top to bottom 4, 6, and 9 groynes......................................................... 38
Figure 24. Bed shear stress [N/m2] in Österdalälven for Q=100 m3/s. The groyne configurations are from
top to bottom 4, 6, and 9 groynes. ...................................................................................................... 39
Figure 25. Bed change [m] in Österdalälven around groynes after 1 year for Q=100 m3/s. The groyne
configurations are from top to bottom 4, 6, and 9 groynes. ................................................................... 40
Figure 26. Sediment yield at outlets for 1 year for configurations with and without groynes for Q=100
m3/s. The red bar marks the standard configuration. ............................................................................ 41
Figure 27. Velocity vector field on top of eddy viscosity [m2/s] for Q=100 m3/s with parabolic eddy
viscosity turbulence mode (left) and mixing length turbulence model (ri .............................................. 42
List of tables
Table 1. Annual suspended sediment yield and load for two measuring stations in Dalälven. The volume
of sediment is calculated using sediment density ρ=2650 kg/m3. .......................................................... 11
Table 2. Particle-size distribution from Klarälven. .............................................................................. 13
Table 3. Symbol explanations for equations 5-13. ............................................................................... 17
Table 4. Summary of boundary condition type for the model. .............................................................. 19
Table 5. Sediment size class and properties for the initial conditions for the sediment transport model. .. 20
Table 6. Regime coefficient for two stations in Dalälven. .................................................................... 20
Table 7. Comparison of sediment load calculated from the model result and sediment load calculated from
the regression curves. ........................................................................................................................ 21
Table 8. Simulation time and time step for the models. ........................................................................ 23
Table 9. Summary of simulation configurations. ................................................................................. 23
Table 10. Summary of the sediment transport modes and capacity formulas used in the simulations. ...... 23
Table 11. The three groyne configurations used for the simulations. ..................................................... 24
Table 12. Sediment yield at the west outlet after 1 year for the standard configuration for Q=100m3/s. ... 35
Table 13. Summary of sediment yield change at the west outlet for 1 year for different configurations. .. 35
Table 14. Change in sediment transport for groynes compared to no groynes, after 1 year for Q=100 m3/s.
........................................................................................................................................................ 41
vi
Table of contents Abstract ..............................................................................................................................................i
Sammanfattning ................................................................................................................................. ii
Acknowledgements ........................................................................................................................... iii
List of figures .................................................................................................................................... iv
List of tables ......................................................................................................................................v
1. Introduction ................................................................................................................................1
1.1. Background and problem statement .......................................................................................1
1.2. Aims ...................................................................................................................................5
1.3. Limitations ..........................................................................................................................5
2. Theoretical background ...............................................................................................................5
2.1. Flow and transport characteristics .........................................................................................5
2.2. Deposition mechanism in river bends ....................................................................................8
2.3. Modelling ............................................................................................................................8
2.4. River training.......................................................................................................................8
2.5. Groynes...............................................................................................................................8
3. Method .......................................................................................................................................9
3.1. Study Area ..........................................................................................................................9
3.2. Data collection ................................................................................................................... 11
1.2. CCHE modelling system .................................................................................................... 14
1.1. Model setup ....................................................................................................................... 16
1.2. The modelling approach in the CCHE system ...................................................................... 21
2. Result ....................................................................................................................................... 25
2.1. Standard configuration ....................................................................................................... 25
2.2. Application of groynes ....................................................................................................... 37
2.3. Turbulence model choice .................................................................................................... 41
2.4. Model validation ................................................................................................................ 43
3. Discussion ................................................................................................................................ 43
3.1. The implication of the results to the prevailing sedimentation problems ................................. 43
3.2. The possibility of mitigation measures................................................................................. 44
3.3. Model validity ................................................................................................................... 44
3.4. Sensitivity analysis............................................................................................................. 45
3.5. The study’s limitations ....................................................................................................... 46
vii
4. Conclusions .............................................................................................................................. 46
5. Bibliography ............................................................................................................................. 47
1
1. Introduction
This chapter describes the background of the problem, the current situation, and previous research on the
problem. Consequentially, it states the purpose and limitations of this study.
1.1. Background and problem statement
The river Österdalälven is a regulated morphologically active river with complicated flow and sediment
transport patterns that have a strong dynamic nature. During the past two decades, extensive sediment
transport problems have become noticeable along the river reach and at its entrance to the downstream
lake Siljan in Mora. Large quantities of fine sediment deposit along the shorelines and into the lake which
has caused severe navigation problems as well as significantly reduced the water storage capacity.
Österdalälven has a history of landslides and channelling north of Mora (SOU 2006:94). There are
significant unstable sediment deposits at the Österdalälven mouth in Siljan, of which a picture is shown in
Figure 1. Österdalälven deposits large quantities of fine sediments when passing the city of Mora,
resulting in a risk of eventually clogging the entry to the lake Siljan. The clogging of the river entry
elevates the risk of the river breaking through and forming a new channel. Current measures to mitigate
the problem are being undertaken in the form of dredging the river channel (Mora Municipality, 2006).
Areas with sedimentation problems are at the intersection of Oreälven and Österdalälven, in the straight
channel after this intersection, and in the main problem area: the outlets to Siljan, see Figure 2 and Figure
3. According to SMHI (2009), as cited by Mora Municipality (2017), the flow velocities in Österdalälven
are generally too low for erosion to occur. However, there is a risk for erosion at high flows by the
railway bridge, and at the bank at outer bends of the river. There is also a risk for sedimentation in all
inner banks of river bends.
A previous study covering Österdalälven by Dutto (2004) investigated how the river regulation had
influenced the sedimentation. The study concluded that the river sediment transport capacity along its
lower reaches (downstream of Mora) had experienced a significant decrease, compared to the conditions
before the river regulation. Consequently, since the regulation the suspended load in the reach has
increased from an estimated 40% to 60% of the total sediment load. It was also concluded that the
sedimentation rate in Mora harbour has increased significantly, as well as in most of the reaches of
Österdalälven upstream of Mora until Spjutmo, for location see Figure 6. As a result of this, the width of
the west inlet of Siljan has decreased between the years 1844 and 2000. The same study showed that the
regulation in Österdalälven caused an increase of the magnitude of normal discharges while there is a
considerable decrease in the magnitude of peak discharge values. One conclusion of the study is that the
regulation has resulted in reduced morphological activities.
The present project is an attempt to address some of the foregoing problems using a scientific approach.
2
Figure 1. Photos of the sandbanks by anonymous photographer (personal communication with B. Dargahi, 2018)
deposited on the island Sandholmen in Siljan. For the location of the island in the lake, see Figure 4.
3
Figure 2. Map retrieved from B. Dargahi (personal communication, 2018) of the reach showing depth (light to dark blue), areas where dredging (dashed red area), and beach protection have been performed (red dots). The volume of
removed sediment is marked with red writing.
4
Figure 3. Map of the areas with deposition and erosion in Mora. Adapted from Mora municipality (2006 & 2017).
(Esri, DeLorme, HERE & MapmyIndia)
5
1.2. Aims
The aims of the project are:
1. To investigate the nature of the flow and sediment transport in the river
2. To analyse the underlying causes of sedimentation
3. Investigate whether sediment mitigation measures can be applied
4. Explore the possibility of creating a working river numerical model despite a lack of relevant field data
1.3. Limitations
The project focus is on cause and effect investigations rather than seeking applicable mitigation measures
that would require extensive field data and more complex modelling approach that were possible within
the frames of the present limited study.
2. Theoretical background
This section gives a short account of different types of river and sediment transport characteristics as well
as modelling as a tool for hydraulic engineering and river training works.
2.1. Flow and transport characteristics
Flow can be characterised by the parameters time and distance. Flow division with respect to time is
steady: constant with time: or unsteady, variant with time. Flow division with respect to distance is
uniform: where the flow cross-section area is constant along the flow path, or non-uniform: where the
flow cross-section area changes. For steady state flow through a control volume, the mass influx equals
the mass efflux in a continuity equation. For unsteady state through a control volume, the mass influx
equals the mass efflux plus the mass change within the control volume. These continuity equations can
also be applied to change in momentum (Dey, 2014).
Fluid flows can also be characterized by the way they flow. Fluid flows can be laminar or turbulent.
Laminar flows are predictable with slow mixing and can be described as layers of fluid flowing on top of
each other. Turbulent flows are unpredictable with fast mixing, chaotic flow directions and the forming of
eddy currents (Dey, 2014). Turbulence in fluid dynamics is described by different models, where the k-
epsilon the most common. The k-epsilon is a two-equation, linear eddy viscosity Reynold averaged
Navier Stokes approach. The k-epsilon 2-equation model has been shown to be a robust model. It can,
however, be sensitive to mesh quality (Autodesk, 2018). Other simpler turbulence models are the eddy
viscosity parabolic model and the eddy viscosity mixing length model. These two models can be more
stable than the k-epsilon model. The eddy viscosity model is best suited for flows with low velocity. The
mixing length model is not suited for flows with boundary layer separation or recirculation (Argyropoulus
& Markatos, 2014).
6
----------------------
The following two sections are reported directly from the book chapter Reservoir Sedimentation
by the permission of the author (Dargahi, 2012).
2.1 Sediment transport
The sediment transport process in a river is a result of a complex interaction between the various sediment
transport processes that prevail in the river and as well as the hydrodynamics of the river. To understand
the sedimentation process one must consider the process in two interrelated stages: (1) the motion of
sediment particles, and (2) the river channel sediment transport characteristics. All these processes are
controlled by a large number of flow parameters, soil or sediment properties, basin properties, and the
hydrological variables.
The motion of sediment particles is caused by the combined action of the gravity force working on the
sediment particles and the entrainment of sediment particles by flow forces. The latter are the
hydrodynamic forces that act upon the particle, producing drag and lift forces. The sediment particles
will remain in an equilibrium state as long as the critical particle shear stress is not exceeded. Under
increasing flow velocity the magnitude of the flow forces will exceed the critical shear stress and the
particles start to move. The critical shear stress (τcr) is commonly determined using the Shield (1936)
diagram that relates the shear stress to the particle Reynolds number ( u*Dm/ν). The relationship reads:
………………………………………………………….…………(5)
in which g=acceleration of gravity, ρs= sediment density, ρ=water density, u*=shear velocity
(hydrodynamic force), and Dm=characteristic sediment diameter. The critical shear stress can also be
written in terms of critical shear velocity as ρuc*2. Equation 5 is one of the most important relationships
2.2 River sediment transport processes
In their natural environment, all rivers display a number of classical features, among which are a
meandering of the river channel and the formation of different types of river beds (i.e., ripples, dunes, and
anti-dunes and the formation of various types of sand banks and bars. The river channel sediment
transport capacity is controlled by the hydraulics of the flow (applied shear stresses), the sediment
properties, and the hydrological variables. The available and supplied sediment to the river undergoes
different modes of transport during its path along the river. There are two major transport modes: bed load
transport and suspended load transport. Bed load transport is the movement of sediment particles in
contact with the bed by rolling, sliding and jumping. Suspended load is transported by the diffusion action
of turbulence. The origin of the transported materials is important. The transport that has its origin in a
river bed is known as bed-material transport. Here, the transport mode (either bed load or suspended load)
is determined by the bed sediment composition and flow conditions. The external supply of materials
)()(
*
m
s
cr Duf
g=
−
7
(surface erosion) is known as wash load and is not directly related with the river channel flow. Wash
loads are normally composed of very fine to coarse silt (4 µm - 60 µm) that is transported in suspension.
To distinguish between the two material origins is of importance for reservoir sedimentation. Wash load
is the main contributor from the river to the reservoir sedimentation. Surface erosion models are needed
to estimate the wash load. The annual suspended sediment yield of the major rivers in the world is
reported to be 20x109 tons (Holeman, 1968). Table 3 gives a summary of the annual sediment loads and
the sediment yields for 10 major rivers in the world (Allen, 1997). It is interesting to note that the
sediment yield from the Amazon River basin is relatively low compared to its drainage area and to other
major rivers such as the Colorado River and the Ganges River. A major part of the Amazon basin is
covered with dense tropical forest that limits the sediment yield from the basin.
Table 3 Annual sediment yield and suspended sediment for 11 major rivers (Allen 1997)
The three other important sources of sediment are riverbank erosion, landslides, and reservoir shoreline
erosion. In many cases, riverbank erosion is a natural process that is partly related to the meandering of the
river. Figure 2 shows an example of riverbank erosion in the upper river reach of Klarälven, which enters
Sweden in the north of the county of Värmland. Riverbank erosion can in some cases be the major
contributor to the total sediment load in a river.
River Drainage area
(km2)
Mean flow discharge
(m3/s)
Annual sediment
yield (t/km2 y)
Annual suspended
load (Mt/y)
Amazon 6 150 000 200 000 187 1150
Colorado
(CA)
640 000 32 234 150
Mississippi 334 400 18 400 120 125
St Lawrence 1 185 000 14 300 4 3
Rhien 225 000 2 243 0.72 17
Volga 1 350 000 8 400 26 19
Niger 1 112 700 6 020 32 29
Nile 2 715 000 317 46 125
Ganges 980 000 11 600 535 524
Yellow 980 00 2 858 120 122
8
2.2. Deposition mechanism in river bends
In a meandering river, and river bends in general, the flow is affected by the centrifugal acceleration
resulting in helical flow motion and a super-elevated surface in the transverse direction. Surface flow is
directed towards the outer bank and bed flow towards the inner bank. This phenomenon results in gradual
erosion of the outer bank and gradual deposit at the inner bank of the following river bend (Dey, 2014). It
should be noted that the sediment motion is statistical due to the fluctuating character of the acting forces.
2.3. Modelling
Hydraulic modelling is a tool to simulate natural processes, e.g. in rivers. It can be used to foresee
morphological evolution such as scouring or deposition of sediment. Creating a numerical hydraulic
model of an object can be easier than performing experiments on the real-world object. Valuable
conclusions can be drawn if the model is calibrated and validated with field data.
A numerical model can approximate the physical properties of a real-world object. By using time-step
solutions, the numerical problems can be solved so that a converged solution can be reached. A
representative numerical model run with good input data can provide meaningful numerical solutions.
However, all numerical models are approximations and are laden with a certain amount of error. These
errors are due to physical and mathematical approximations (Zang, 2006).
2.4. River training
River training is a method where one can change the courses of natural river processes by constructing
physical features that modify the flow characteristics. The goal of river training is to improve the state of
the river including its bottoms and banks, mitigate or prevent floods, reduce sediment transport and
erosion, and enable navigation and passing. There are many different kinds of physical river training
structures, which can be divided into two categories: longitudinal and transversal to the main flow
direction. Longitudinal structures are usually levees or different kinds of bank reinforcement. Transversal
structures can be check dams, sills, or groynes (Shresta, GC, Adhikary, & Rai, 2012). The choice and
design of a training structure depend on criteria such as purpose and effect, flow and bank characteristics,
available material, maintenance need, and costs (U.S. Army Corps of Engineers, 2002, 2006). A useful
and frequently employed river training method is morphological modification of a river reach using
groynes.
2.5. Groynes
Groynes (also referred to as groins, spur dykes, bendway weirs, etc.) are transversal structures for river
training. They are widely used for bank protection and erosion control. Groynes are direct erosion
mitigation measures that are constructed at an angle to the major flow direction, stretching from the banks
into the river. Groynes can be at angle towards upstream, downstream, or orthogonal to the flow direction
or the bank. Groynes can be permeable or impermeable. They can be constructed as submerged or
emerged structures, usually relative to the top of the bank. They can be constructed from rocks, concrete,
wood, sand, or other material. Groynes are often installed in groups consisting of several groynes installed
9
in a row with a certain distance between (U.S. Department of the Interior, 2015). The group of groynes is
referred to as groyne field or groyne system. Groynes can be used to prevent sediment accretion in areas
downstream of the groynes them (U.S. Army Corps of Engineers, 2008). By installing a group of groynes,
the major flow field is directed away from the bank. By creating a zone of lower velocity in the groyne
field, sediment can be deposited between the groynes on the upstream side of each groyne. Eddy currents
will form in the groyne field, and energy is dissipated. Some erosion may take place on the downstream
side of the groynes, as well as at the tips of the groins, forming so-called scour holes. The erosion is
usually initially large and diminishes with time (U.S. Department of the Interior, 2015).
Groyne design has been conducted by engineering experience and rule of thumbs rather than by standard
design criteria, as this is yet to be conceived. There are, however, some existing guidelines where most
commonly used are the Coastal Engineering Manual (CEM), published by the U.S. Army Corps of
Engineers (U.S. Army Corps of Engineers, 2002, 2006) when local design standard are missing (Odén &
Johansson, 2005). Design characteristics of groynes include orientation angle, groyne length, spacing
ratio, permeability, width, and slope. The spacing ratio is defined as the ratio between the arc length
between groins and the longitudinal distance of the groyne, see Equation 1. According to CEM, a value of
2-3 is accepted as an initial value for groyne design.
𝑆 =𝐿𝑎𝑟𝑐
𝐿𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑖𝑛𝑎𝑙 (1)
A value of the spacing ratio close to 1 will render a single eddy current in the groin field, a value between
2 and 4 will render two currents, and a larger value than 4 will result in penetration of the main flow field
into the groin field (Youssef & de Vriend, 2010). According to Julien & Duncan (2003), the spacing
should not exceed 4 as this will decrease the size of the low-velocity zone.
3. Method
This section includes a description of the study area and the complete approach to set up and run the
model, as well as a general description of the modelling system CCHE2D.
3.1. Study Area
Österdalälven is a 300 km long section of Dalälven between Idre and Djurås, where it combines with
Västerdalälven forming Dalälven. As the river Österdalälven reaches the city of Mora, it flows into the
lake Siljan. The upstream lake Orsasjön is connected to Siljan with the river Oreälven. The location and
extensions of the rivers and lakes are presented in Figure 4.
Österdalälven is a regulated river with six hydropower dams, including the largest dam in Sweden,
Trängslet. The regulation implies that the magnitude of the flow is regulated and can, in this case, vary
between 0 and 250 m3/s. However, a minimum flow magnitude of 21m3/s is set to imitate the natural
conditions (Hedström-Ringvall et al., 2017).
10
Figure 4. Study area location in Europe and Sweden with marked rivers, lakes and islands (Esri, DeLorme, HERE
& MapmyIndia).
11
3.2. Data collection
3.2.1. Hydrological data
The available hydrological data for the analysis were:
• Daily discharge values measured at Spjutmo station in Österdalälven ranging from 1996 to 2017.
• Daily discharge values measured at Skattungen station in Oreälven ranging from 1931 to 2017
(SMHI, 2018a).
• A bathymetry map of the reach, see Figure 5.
The locations of the measuring stations are marked in Figure 5 and Figure 6.
1.1.1. Sediment data
In a project conducted by SMHI, sediment data was measured between the years 1967 and 1993 in two
stations in Dalälven. The stations were located at the station Vikbyn in Dalälven, approximately 110 km
southeast of Mora, and at the mouth of Dalälven in the Bothnian sea in Älvkarleby. Analyses of these
measurements show that the amount of suspended and soluble solids was correlating well with the flow
magnitude in between the years of 1967-1993 (Brandt, 1996). For this project, the average flow and annual
sediment yield, listed in Table 1, have been produced from the measured data in these two stations. These
stations are located downstream of this project’s study area.
Table 1. Annual suspended sediment yield and load for two measuring stations in Dalälven. The volume of sediment
is calculated using sediment density ρ=2650 kg/m3.
Measuring
station
Drainage
area
[km2]
Mean flow
discharge
[m3/s]
Annual
suspended
sediment yield
per km2
[tonnes/km2 y]
Annual suspended
sediment yield
[ktonnes/y]
Annual
suspended
sediment
yield [m3]
Vikbyn 25 950 312 3.8 99 37 470
Älvkarleby 28 959 347 1.8 53 19 830
Apart from the limited and general data from Dalälven listed in Table 1, no field data concerning
sediment load or sediment size distributions in Österdalälven were available to this study. It is known
from previous studies (Dargahi, 2006) in morphologically similar river that the sediment consists mostly
of sand. Sediment data which was available was field measurements from the lower reaches of Klarälven
which is a relatively large river flowing south-west of Dalälven. The soil types in the watersheds of
Klarälven and Dalälven are similar (SMHI, 2018b).
The field sediment data from Klarälven consists of various soil samples in the form of particle -size
distributions in graph form (Dargahi, 2006). One sample is presented in Table 2, where the values have
been noted in the table by the author. The average size of this material sample is of the category fine sand.
12
Figure 5. Bathymetry map for the reach. The depth is ranging from 0-2 (light) to 10-12 (dark) ( (SMHI, 2000).
13
Figure 6. Map showing the two SMHI measuring stations for hydrological data in Österdalälven (Spjutmo) and
Oreälven (Skattungen) (Esri, DeLorme, HERE & MapmyIndia).
Table 2. Particle-size distribution from Klarälven.
Grain size
[mm]
% less than indicated size
2 100
1 90
0.6 45
0.3 5
0.125 1
0.08 0
14
1.2. CCHE modelling system
The CCHE modelling system used in this study is a system for modelling free surface flows, sediment
transport, and morphological processes. This modelling system was chosen since it is well suited for the
aim of the study of modelling hydraulic and sediment transport mechanisms.
The system includes three parts: a structured mesh generator CCHE-MESH, the CCHE2D flow and
transport model, and a graphical user interface CCHE-GUI. The software is developed by the National
Center for Computational Hydroscience and Engineering (NCCHE) (Zang, 2006). The most important
features of this software for this study are described below. Full documentation of the CCHE modelling
system can be found in the CCHE documentation (Zang, 2006). CCHE-MESH is a software for
generating structured meshes in 2D. Topography databases are used to generate algebraic and numerical
meshes. The software can also be used to create the topography databases needed for the mesh generation.
The CCHE2D model is a depth-averaged two-dimensional numerical model for hydrodynamic and
sediment transport modelling in unsteady open channel flows over loose beds (Zhang & Jia, 2009).
1.2.1. Hydrodynamic model and governing equations
The governing equations for solving an initial boundary value problem in the hydrodynamic model are
the depth-averaged Navier-Stokes equations for continuity (Equation 2) and momentum in two
dimensions (Equations 3-4):
Continuity equation:
𝛿𝑍
𝛿𝑇+
𝛿(ℎ𝑢 )
𝛿𝑥+
𝛿(ℎ𝑣)
𝛿𝑦= 0 (2)
Momentum equations:
𝛿𝑢
𝛿𝑡+ 𝑢
𝛿𝑢
𝛿𝑥+ 𝑣
𝛿𝑢
𝛿𝑦= −𝑔
𝛿𝑍
𝛿𝑥+
1
ℎ[
𝛿(ℎ 𝜏𝑥𝑥)
𝛿𝑥+
𝛿(ℎ𝜏𝑦𝑥)
𝛿𝑦] −
𝜏𝑏𝑥
𝜌ℎ+ 𝑓𝐶𝑜𝑟𝑣 (3)
𝛿𝑣
𝛿𝑡+ 𝑢
𝛿𝑣
𝛿𝑥+ 𝑣
𝛿𝑣
𝛿𝑦= −𝑔
𝛿𝑍
𝛿𝑦+
1
ℎ[
𝛿(ℎ𝜏𝑦𝑥)
𝛿𝑥+
𝛿(ℎ𝜏𝑦𝑦)
𝛿𝑦] −
𝜏𝑏𝑦
𝜌ℎ+ 𝑓𝐶𝑜𝑟𝑢 (4)
, in which u and v are the depth-integrated velocity components in the x- , and y- directions, g is the
gravitational constant, Z is the water surface elevation, h is the local water depth, 𝜏𝑥𝑥 , 𝜏𝑦𝑥 , 𝜏𝑥𝑦 , 𝜏𝑦𝑦 are
the depth-integrated Reynolds stresses, 𝜌 is the water density, 𝜏𝑏𝑥 and 𝜏𝑏𝑦 are the bed surface shear
stress, and 𝑓𝐶𝑜𝑟 is the Coriolis’ parameter (Zang, 2006).
The available turbulence models are two eddy viscosity models: the depth-integrated parabolic model and
the mixing length model, and the 2-equation k-epsilon model.
15
1.2.2. Sediment transport model
The CCHE2D sediment transport model employs a non-equilibrium model for both bed and suspended
load. Using a non-equilibrium model has been shown to be needed for cases with strong deposition,
especially under unsteady flow conditions.
The CCHE2D sediment transport model has the option of treating either combined sediment transport or
transport separated as bed load or suspended load. The user can choose from three types of transport
modes:
1. Total load as suspended load plus bed load
2. Total load as suspended load
3. Total load as bed load.
All three transport modes take both suspended load and bed load into consideration. However, the two
latter modes compute the total load but with either suspended load or bed load as the dominant transport
mode. For these two transport modes, four transport capacity formulas are available:
• Wu et. al.
• Modified Engelund& Hansen
• Modified Ackers& White
• SEDTRA module
The governing equations for sediment transport and bed deformation for the three transport modes are
presented below. Symbol explanations are listed in Table 3. For full documentation and all derivations,
the reader is directed to the CCHE2D sediment transport model manual by Wu (2001).
Total load as suspended load plus bed load
Bed load and suspended load transport are given by equations 5&6 respectively:
𝛿(𝜹𝑐̅𝑏𝑘)
𝛿𝑡+
𝛿𝑞𝑏𝑘𝑥
𝛿𝑥+
𝛿𝑞𝑏𝑘𝑦
𝛿𝑦+
1
𝐿𝑡
(𝑞𝑏𝑘 − 𝑞𝑏∗𝑘 ) = 0 (5)
𝛿(ℎ𝐶𝑘)
𝛿𝑡+
𝛿(𝑈ℎ𝐶𝑘)
𝛿𝑥+
𝛿(𝑉ℎ𝐶𝑘 )
𝛿𝑦=
𝛿
𝛿𝑥(𝜀𝑠 ℎ
𝛿𝐶𝑘
𝛿𝑥) +
𝛿
𝛿𝑦(𝜀𝑠 ℎ
𝛿𝐶𝑘
𝛿𝑦) + 𝐸𝑏𝑘 − 𝐷𝑏𝑘 (6)
Bed deformation is computed from the equation 7 or the sediment continuity equation 8:
(1 − 𝑝′)𝛿𝑧𝑏𝑘
𝛿𝑡= 𝛼𝜔𝑠𝑘 (𝐶𝑘 − 𝐶∗𝑘 ) +
(𝑞𝑏𝑘−𝑞𝑏∗𝑘)
𝐿𝑡 (7)
(1 − 𝑝′)𝛿𝑧𝑏𝑘
𝛿𝑡+
𝛿(ℎ𝐶𝑡𝑘 )
𝛿𝑡+
𝛿(𝑞𝑏𝑘𝑥+𝑞𝑠𝑘𝑥)
𝛿𝑥+
𝛿(𝑞𝑏𝑘𝑦 +𝑞𝑠𝑘𝑦 )
𝛿𝑦= 0 (8)
16
Total load as bed load
Bed load transport is given by equation 9:
𝛿(ℎ𝐶𝑡𝑘)
𝛿𝑡+
𝛿(𝛼𝑡𝑥𝑞𝑡𝑘)
𝛿𝑥+
𝛿(𝛼𝑡𝑦 𝑞𝑡𝑘)
𝛿𝑦+
1
𝐿𝑡
(𝑞𝑡𝑘 − 𝑞𝑡∗𝑘 ) = 0 (9)
Bed deformation is computed from the sediment continuity equation 10 or equation 11:
(1 − 𝑝′)𝛿𝑧𝑏𝑘
𝛿𝑡+
𝛿(ℎ𝐶𝑡𝑘 )
𝛿𝑡+
𝛿(𝑞𝑏𝑘𝑥+𝑞𝑠𝑘𝑥)
𝛿𝑥+
𝛿(𝑞𝑏𝑘𝑦 +𝑞𝑠𝑘𝑦 )
𝛿𝑦= 0 (10)
(1 − 𝑝′)𝛿𝑧𝑏𝑘
𝛿𝑡=
(𝑞𝑡𝑘−𝑞𝑡∗𝑘)
𝐿𝑡 (11)
Total load as suspended load
Suspended load transport is given by equation 12:
𝛿(ℎ 𝐶𝑡𝑘)
𝛿𝑡+
𝛿(𝑈ℎ 𝐶𝑡𝑘 )
𝛿𝑥+
𝛿(𝑉ℎ𝐶𝑡𝑘)
𝛿𝑦=
𝛿
𝛿𝑥(𝜀𝑠ℎ
𝛿𝐶𝑡𝑘
𝛿𝑥) +
𝛿
𝛿𝑦(𝜀𝑠ℎ
𝛿𝐶𝑡𝑘
𝛿𝑦) + 𝛼𝜔𝑠𝑘 (𝐶𝑡∗𝑘 − 𝐶𝑡𝑘 ) (12)
Bed deformation is computed from the sediment continuity equation 13:
(1 − 𝑝′)𝛿𝑧𝑏𝑘
𝛿𝑡= 𝛼𝜔𝑐𝑘 (𝐶𝑡𝑘 − 𝐶𝑡∗𝑘 ) (13)
1.1. Model setup
1.1.1. Conceptual model
The model area will include a bend of Österdalälven which intersects with Oreälven in Mora, the section
of Oreälven between the lake Orsasjön and Siljan, the mouths of Oreälven and Österdalälven into Siljan,
and the most northern part of Siljan. The outlet at Siljan is divided into two by the islands Klubbholmen
and north and south Gotholmen. There is also another island, Sandholmen, in the southern part of the
outlet. The location of the lakes, the rivers, and the island are marked in Figure 4. The inlets are referred
to as Oreälven inlet and Österdalälven inlet. The outlets are referred to as the south and west outlet. These
inlets and outlets define the model’s two boundary conditions. A conceptual representation of the model
is shown in Figure 7.
The boundary conditions at the inlets define the water and sediment discharge. The water surface
elevation is defined by the boundary conditions at the two outlets. The bed and banks of the river are no-
flow boundaries, i.e. the groundwater exchange is negligible.
17
Table 3. Symbol explanations for equations 5-13.
Ratio between near-bed concentration
and depth-averaged concentration
Lt Adaptation length of bed-material load
tx Direction cosine of total load transport 𝑝’ Porosity of bed material
𝐶𝑘 Depth-averaged suspended-load
concentration
𝑞𝑏𝑘 Bed load transport rate of the k:th sediment
size class
𝐶𝑡𝑘 Depth-averaged concentration of the
total load
𝑞𝑏∗𝑘 Bed load transport of the k:th sediment size
class at the interface between the suspended-
load zone and bed-load zone
𝐶𝑡∗𝑘 Depth-averaged transport capacity of
total load
𝑞𝑏𝑘𝑥
𝑞𝑏𝑘𝑦
Bed load transport in the x or direction of the
k:th sediment size class
𝐶∗𝑘 Depth-averaged concentration under
equilibrium conditions
𝑞𝑠𝑘𝑥
𝑞𝑠𝑘𝑥
Suspended load transport rate in x-, or y,
direction
𝑐�̅�𝑘 Average concentration of bed load at
the bed-load zone
𝑞𝑡𝑘 Actual transport rate of the k:th sediment size
class of bed-material load
𝜀𝑠 Eddy diffusivity of sediment 𝑞𝑡∗𝑘 Actual transport capacity of the k:th sediment
size class of bed-material load
Thickness of bed load zone U, V Depth-average flow velocities in x- or y-
directions
𝐸𝑏𝑘 Entrainment flux of the k:th sediment
size class at the interface between the
suspended-load zone and bed-load
zone
𝜔𝑠𝑘 Settling velocity of the k:th sediment size class
Dbk Deposition flux of the k:th sediment
size class at the interface between the
suspended-load zone and bed-load
zone
𝑧𝑏𝑘 The thickness of bed over datum
h Local water depth
1.1.1. Initial conditions for the hydrodynamic model
Initial conditions include conditions for the flow and the bed. The initial conditions for the flow are initial
water surface elevation and bed elevation which were inferred from the bathymetry map in Figure 5. The
initial conditions for the bed include bed roughness, erodibility, max deposition thickness, max erosion
thickness, layer thickness, and layer sample number. These parameters were unknown in this study. The
bed roughness was estimated to n=0.025. The maximum deposition and erosion thickness were set so that
deposition and erosion thicknesses were unlimited. The remaining parameters were left as the default
values provided by the modelling system.
18
Figure 7. A conceptual model showing the discharge and water surface elevation boundary conditions. The boxes represent inlets and outlets, and the arrows represent the flux direction. The dashed line marks the model domain.
BC: Boundary Condition (Esri, DeLorme, HERE & MapmyIndia).
19
1.1.2. Boundary conditions for the hydrodynamic model
The setup of the boundary conditions is listed in Table 4.
Table 4. Summary of boundary condition type for the model.
Hydrodynamic model Sediment transport model
Inlet boundary Österdalälven
Oreälven
Water discharge:
Steady inflow or hydrograph
Sediment discharge
(bed load and suspended
load):
Steady inflow or hydrograph
Outlet boundary Siljan Water surface elevation:
Constant value or rating
curve
The discharge data used here for the Oreälven inflow is collected upstream in the river at the measuring
station Skattungen upstream of Orsasjön as marked in Figure 6. Oreälven is the only main tributary to
Orsasjön and can, therefore, be used as the outflow discharge of Orsasjön.
Since water surface elevation data for the outlet at northern Siljan was unavailable, steady-state
simulations with varying flow discharges were done to obtain a rating curve for the outlet boundaries.
The used flow discharges were ranging between 30 and 200 m3/s in Österdalälven. Simulations were
performed until converged solutions were reached. Two linear rating curves were estimated from these
simulations, one corresponding to a higher water surface elevation and one to a lower. However, a range
of different rating curves could be fitted, as the model would converge with different outlet surface
elevations for the same flows. The rivers and lakes are regulated meaning several discharges can
correspond to a single water level and vice versa. The resulting rating curves were Equation 14 for high
water surface elevation and Equation 15 for low water surface elevation, where y is the water surface
elevation in meters above a datum of 149.7 m a.s.l. and Q the water discharge in m3/s.
𝑦 = 0.0035𝑄 + 11.361 (14)
𝑦 = 0.005𝑄 + 10.169 (15)
The rating curves were developed for the sake of this project only and should not be seen as a
representative rating curve for other applications outside of this project.
1.1.3. Parameters and initial conditions for the sediment transport model
The sediment material properties of size class and porosity are listed in Table 5. The simulations were
done with a uniform material sediment load. The number of bed layers was set to one for simplicity. The
minimum mixing layer thickness was left as the default value. The foregoing choices were the result of
unavailable field data.
20
Table 5. Sediment size class and properties for the initial conditions for the sediment transport model.
Size class Mean diameter [mm] Fraction Porosity
1 0.36 1 0.4
The transport mode for the sediment transport can be set to three transport modes: bed load only,
suspended load only, and total transport mode, as described in section 1.2. The majority of the
simulations were run with the total load mode.
1.1.4. Boundary conditions for the sediment transport model
The boundary conditions for the sediment model are suspended and bed load sediment discharge at inlets,
see Table 4. Because the sediment loads were unknown, the sediment load discharge was initially
calculated using the Van Rijn 1984a formula for total load transport, with the help of a program
developed by B. Dargahi (personal communication, 2018). The loads were calculated using the result of
the hydrodynamic model at one flow section at each inlet using the rating curve in equation 14. This was
done for a low, medium, and high flow relative to the Österdalälven flow.
Dargahi (1984) produced two regression curves for the Vikbyn and Älvkarleby stations in Österdalälven,
see equation 16 and Table 6 for regime coefficients:
𝑄𝑆 = 𝐴𝑄𝐵 (16)
, where Qs is the solid discharge expressed in tonnes/month, Q discharge in m3/s and A, B are regime
coefficients.
Table 6. Regime coefficient for two stations in Dalälven.
A B r
Year 1979/1980 1979/1980 1979/1980
Vikbyn 0.04/0.51 1.98/1.52 0.79/0.56
Älvkarleby 0.01/0.05 2.06/1.82 0.82/0.65
The sediment load calculated by these regression curves were included for the sake of comparison with
the calculated sediment transport loads from the model result, see Table 7.
Sediment rating curves were developed from the loads calculated with the Van Rijn formula. The
sediment curves for the two inlets are as shown in equations 17 and 18, in which Qs is in kg/s, and Q is in
m3/s.
Österdalälven: 𝑄𝑠 = 0.0001𝑄 − 0.0032 (17)
Oreälven: 𝑄𝑠 = 0 (18)
21
Table 7. Comparison of sediment load calculated from the model result and sediment load calculated from the
regression curves.
Measuring
station
Q
[m3/s]
Van Rijn
sediment
load
[kg/s]
Vikbyn
1979
Regression
result
[kg/s]
Vikbyn
1980
Regression
result
[kg/s]
Älvkarleby
1979
Regression
result
[kg/s]
Älvkarleby
1980
Regression
result
[kg/s]
Österdalälven 50 0.0032 0.035 2.1 0.012 0.024
100 0.0057 0.14 11 0.050 0.083
150 0.014 0.31 29 0.12 0.17
Oreälven 20 0.00 0.0057 0.24 0.0018 0.0044
25 0.00 0.0089 0.41 0.0029 0.0066
30 0.00 0.013 0.63 0.0042 0.0093
The calculated sediment loads shown in Table 7 were low so that for simplicity, the inlet boundary of
sediment discharge was set to zero.
1.1.5. Groyne design
The groynes were defined in CCHE2D as thin walls along the selected grid lines. No characteristics such
as width or side slopes can be defined, as the structures are single mesh line structures. Different
arrangements of groynes were tested. The varied parameters were the number of groynes and their
longitudinal length.
1.2. The modelling approach in the CCHE system
The modelling approach is described below in this section. Creating the models was an iterative process
where parameters such as mesh size and boundary conditions were altered, and the model was rerun
several times.
1.2.1. Mesh creation from the bathymetry map using CCHE-MESH
A topography database was created in CCHE-MESH by mapping the elevation lines from the bathymetry
map in Figure 5. An algebraic mesh was then created, in order to create the final numerical mesh, which
is shown in Figure 8. Finally, the topography was interpolated using triangulation interpolation. The mesh
quality was evaluated from the parameters smoothness and orthogonality. Several numerical methods are
available for generating the numerical mesh. The numerical method which generated the most satisfactory
result in terms of the evaluated parameters was chosen which was the numerical RL orthogonal mesh with
smoothness control [1]. This numerical method is also recommended by Zhang & Jia (2009) for natural
rivers with irregular boundaries.
Triangulation interpolation was chosen as it rendered results that were the most concordant with the
bathymetry in between data points. The interpolated bed topography was smoothed in some areas. The
mesh was later refined in order to be able to capture flow directions at certain points such as bends, the
22
island, and around the groynes. The final mesh size was I*J= 81*301, where I stretches in the north-south
and direction and J in the west-east direction.
1.2.2. The building of a hydraulic model in CCHE2D and hydrodynamic simulations
The mesh was imported into CCHE-GUI, where the hydrodynamic model was set up by defining the
boundary and initial conditions. Some initial conditions were unknown in this study; thus, they were
estimated in the initial simulations.
The model was run for steady flow discharges in Österdalälven of 50, 100, 150, and 200m3/s. The
Q=100m3/s roughly corresponds to the mean flow in Österdalälven at the Spjutmo measuring station
(which is 90 m3/s), for location see Figure 6. The corresponding discharge in Oreälven was inferred by
calculating the average flow in Oreälven corresponding with the stated discharges in Österdalälven.
A steady-state boundary condition hydrodynamic model was built and ran until a converged solution was
found. Convergence is here defined to when the solutions are independent of time. The simulation time
was 48 hours divided into two simulation intervals, see Table 8. The time step was chosen so that the
model was stable and converging, while not requiring unnecessary long simulation times.
When using a mesh with external boundaries corresponding to the extension of the bathymetry map, the
initial simulations showed that the water was flowing in the wrong direction at the Oreälven inlet. The
problem was due to the flat bed slope and shallow areas in the river. To overcome this problem, the model
was elongated in an upstream direction with a constant depth channel. This moved the boundary further
away from the actual model area. This modification gave a reasonable flow condition corresponding to an
inward direction of the water flow at this boundary in accordance with the physics.
1.2.3. Sediment transport simulation
The sediment transport model was run coupled with the hydrodynamic model. The simulation time was
one year divided into three simulation intervals, see Table 8. The simulations were done under a steady
state inflow.
Simulations with several different setups of both the hydrodynamic and sediment transport model were
done. The setup with which the simulations for various discharges were made will be referred to as
“standard configuration”. The other configurations were done with Q=100 m3/s, for solely comparison.
The turbulence model, wall slip coefficient, Manning’s roughness coefficient, mesh size, and sediment
size were varied one at a time in the purpose of a sensitivity analysis to the choice of these parameters.
Values of boundary conditions and the transport mode choice were calibrated against the measured
volume of transported sand at the outlets which are marked in Figure 2, as well as varied for being
included in the sensitivity analysis. The sensitivity analysis was done by comparing the model response to
the varied input in comparison to that of the standard configuration in a one-at-a-time approach.
23
Table 8. Simulation time and time step for the models.
Model Simulation time
[s]
Time step
[s]
Runs
[-]
Total run time
[days]
Hydrodynamic 100 000 100 2 2
Sediment transport 1 544 500 10 3 365
Table 9 summarizes the different simulation configurations used in this study. The configurations for the
sediment transport modes and capacity formulas are listed by Table 10.
Table 9. Summary of simulation configurations.
Parameter Standard
configuration
Setup Variations
Turbulence
model option
K-epsilon model Parabolic eddy
viscosity model
Mixing length
model
Wall slipness
coefficient [-]
0.5 0 1
Outlet water
surface elevation
for Q=100m3/s
[m]
10.8,
rating curve in
equation 14.
11.8, rating curve in equation 15.
Manning’s
roughness
coefficient [-]
0.025 0.02 0.03
Mesh Size [I*J] 81*301 49*293
Sediment size
[mm]
0.036 0.6
Table 10. Summary of the sediment transport modes and capacity formulas used in the simulations.
Standard
configuration
Setup variations
Transport
mode
Total load as
suspended and
bed load
Total load as suspended load
Total load as bed load
Transport
capacity
formula
Wu et. Al. Modified
Ackers and
White
Modified
Engelund and
Hansen
SEDTRA
Simulations with groynes
Groynes were added to the model at the Österdalälven reach near the inflow boundary. The location is
marked in Figure 8. Three different configurations were examined, see Table 11, and simulations were
done for a simulation time of 1 year for Q=100 m3/s. The spacing ratio was set to 3.
24
Table 11. The three groyne configurations used for the simulations.
Groyne configurations
no/ longitudinal length
[m]
4/70 6/45 9/30
Figure 8. The final mesh split in two parts where the left part is the north part and the right the south part . The
black dotted line marks the I-line from which result was extracted. The red dashed box marks the area where the
groynes were located.
25
2. Result
This section will cover the main result of some of the simulations, i.e. velocity vectors, shear stress
distributions, bed level changes, and sediment transport characteristics. The result is mainly from the
simulations with the standard configuration and groyne configurations for Q=100 m3/s.
2.1. Standard configuration
2.1.1. Result from the hydrodynamic model
The simulated water surfaces at the inlets are 10.9m which means there is a difference of 0.1m between
inlets and outlets, resulting in a slope of the water surface elevation of 10-5. The water surface elevation is
shown in Figure 9. The flow division between the west and south outlet is 36% at the west outlet and 64%
at the south outlet in average from simulations with Q=50, 100, 150 and 200m3/s at the Österdalälven
inlet.
The flow velocity vector field is presented in Figure 10 for Q=100m3/s. From this result, it can be seen
that the flow velocity in area a is low. The flow velocity in area b is higher, especially at the outer part of
the river bend. Circulation occurs in area c at the flow intersection region of the two river branches, see
Figure 11. There is also circulation in area e where the flow divides to the two outlets, and after the island
Sandholmen. Sections with reversed flow occur on the east bank in areas d and e, see Figure 11 and
Figure 12. The flow is subcritical throughout the model, i.e. the Froude number is less than 1. As can be
seen in Figure 11, the eddy viscosity is large in areas with circulation.
26
Figure 9. Water surface elevation [m]for one of the groyne configurations 45/6 (left) and standard configuration
(right) for Q=100m3/s.
27
Figure 10. Simulation results showing the uniformly scaled velocity vector field [m/s] for the standard configuration
for Q=100 m3/s marked by regions a-f.
28
Figure 11. Velocity field in area e, with overlaid eddy viscosity layer [m2/s] for the standard configuration for
Q=100 m3/s. Circulation and reversal flow regions are apparent.
29
Figure 12. Velocity vector field [m/s] with reverse flow in east side of the channel in area d for the standard
configuration for Q=100m3/s.
Distribution of bed shear stresses
The values of the bed shear stresses are large in areas b, c, and d, see Figure 13, in comparison with the
other regions of the model. The bed shear stress correlates well with the velocity field, i.e. the shear
stresses are large in areas with high velocity and vice versa, as it can be seen in Figure 14, Figure 15, and
Figure 18. The results in these figures are extracted along an I-line of which the location is marked in
Figure 8. The marked I-line stretches along the modelled river reach in the middle of the river channel
from the intersection of the rivers to the south outlet through areas c-f.
30
Figure 13. Distribution of bed shear stress [N/m2] for the standard configuration for Q=100 m3/s
31
Interdependency of velocity, flow pattern, and shear stress on the flow discharge
The magnitude of the velocity and shear stress distribution throughout the model is generally higher for a
larger flow discharge. Figure 14 and Figure 15 show the variation of shear stress and velocity magnitude
extracted along the mesh I-line. The distributions of the velocity magnitude and shear stress and the flow
pattern generally look the same despite varying flow discharges, although their magnitude changes. For
the highest flow, Q=200 m3/s, the west eddy at the bifurcation disappears, see Figure 16.
Figure 14. Velocity variation for varying flow discharges in Österdalälven along the constant I-line marked in Figure 8 for the standard configuration.
Figure 15. Shear stress variation for varying flow discharges in Österdalälven along the constant I-line marked in
Figure 8 for the standard configuration.
0
0.2
0.4
0.6
0.8
130 150 170 190 210 230 250 270 290
Velo
cit
y [
m/s
]
J-line
Q=200 m3/s Q=150 m3/s Q=100 m3/s Q=50 m3/s
0
0.5
1
1.5
2
130 150 170 190 210 230 250 270 290
Sh
ea
r st
ress
[N
/m2
]
J-line
Q=200 m3/s Q=150 m3/s Q=100 m3/s Q=50 m3/s
32
Figure 16. Velocity field [m/s] in area e, for the standard configuration for Q=200 m3/s.
33
2.1.2. Result from the sediment transport model
The sediment transport simulation results are presented in terms of suspended and bed load transport rate
along the reach, bed level changes, and sediment yield at the outlets.
Sediment transport
The sediment transport rate along the I-line is shown in Figure 17. Along the mesh line, the suspended
load transport rate is generally higher than that of the bed load. The normalized sediment transport rate is
shown in Figure 18, with the variations of the normalized shear stress and velocity magnitude. It’s clear
that the transport rate correlates with the shear stress.
Figure 17 Sediment transport rate for the suspended load and bed load for the standard configuration for
Q=100m3/s along the I-line marked in Figure 8.
Figure 18. Normalized sediment transport rate, shear stress, and velocity magnitude for the standard configuration
for Q=100m3/s along the I-line marked in Figure 8.
Bed change
Simulated bed level changes were used to recognize the sedimentation and erosion regions in the model.
The strongest deposition area is located at the bifurcation in the lower part of area d and in area e. The
largest magnitudes of bed change are around 5m for deposit and -2m for erosion. Erosion occurs at the
outer bend of area b. There is also deposition in area c at the intersection.
0
0,001
0,002
0,003
0,004
0,005
0,006
0,007
130 150 170 190 210 230 250 270 290
Sed
imen
t tr
an
spo
rt r
ate
[kg
/s/m
]
J-line
Suspended load
Bed load
0
0.2
0.4
0.6
0.8
1
130 150 170 190 210 230 250 270 290
J-line
Shear Stress Velocity Magnitude Suspended Load Transport Bed Load Transport Rate
34
Figure 19. Bed level changes [m] for the standard configuration Q=100 m3/s after 1 year.
Sediment transport rate at the outlets
The sediment transport rate is presented in terms of annual sediment yield. The sediment yield at the
outlets depends on the flow rates, see Figure 20. The sediment yield at the south outlet is low for all
values of flow discharge. The sediment yield varies with the choice of sediment transport mode and
sediment transport capacity formula, see Figure 21. The total mode transport model renders the highest
yield, whereas using the capacity formulas Engelund & Hansen or the SEDTRA module result in
practically zero yields. Using the total load transport mode, the annual sediment yield at the west outlet is
approximately 2600 tonnes for Q=100m3/s for the standard configuration whereof the suspended load is
1800 tonnes, see Table 12 . The annual suspended sediment yield is lower than at the two stations
downstream, listed by Table 1. The yield at the downstream stations are larger by 30-55 times
(Älvkarleby respectively Vikbyn).
35
As can be seen from Figure 22, the sediment yield also varies with the choice of certain parameters such
as the water surface elevations at the outlets, Manning’s roughness coefficient, and size of sediment
diameter. It’s less sensitive to the choice of turbulence model, wall slip condition, and grid size. The
results of the sensitivity analysis to these variations are summarized in Table 13.
Figure 20. Sediment yield at outlets after1 year for the standard configuration for varying discharges.
Table 12. Sediment yield at the west outlet after 1 year for the standard configuration for Q=100m3/s.
Sediment
transport mode
Annual sediment
yield [m3]
Annual sediment
yield [tonnes]
Suspended load 675 1790
Bed load 310 820
Table 13. Summary of sediment yield change at the west outlet for 1 year for different configurations.
Change in parameter Change
[%]
Transport
mode
Transport capacity
formula
Change
[%]
Standard - Total load -
Parabolic eddy viscosity 5 Total load as
suspended
load
Wu. Et. Al. -27
Mixing length 1 Ackers&White -64
Wall slip = 0 35 Engelund&Hansen -100
Wall slip = 1 -24 SEDTRA -100
WSE = 11.8 m -100 Wu. Et. Al. -3
n = 0.02 -64 Total load as
bed load
Ackers&White -62
n = 0.03 102 Engelund&Hansen -95
d = 0.6 mm -81 SEDTRA -100
Coarser grid 25
0
500
1000
1500
2000
2500
3000
3500
0 50 100 150 200
Sed
imen
t y
ield
at
the
ou
tlet
s
[m3
]
Q [m3/s]
West Outlet
South Outlet
36
Figure 21. Sediment yield at west outlet for Q=100m3/s after 1 year with variations in transport capacity formula.
The red bar marks the standard configuration.
Figure 22. Sediment yield at west outlet Q=100m3/s after 1 year for variations in the configuration.
0
200
400
600
800
1000
Sed
imen
t y
ield
at
wes
t o
utl
et
[m3
]
Total load
Total load as suspended load
Total load as bed load
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Sed
imen
t yie
ld a
t w
est
ou
tlet
[m3
]
37
2.2. Application of groynes
2.2.1. The influence on the flow field
All three configurations, as listed by Table 11, resulted in the formation of secondary eddies to various
extents within the groyne spacing. The eddies can be seen by the reverse flow in between the groynes in
Figure 23. The groynes did not give rise to secondary eddies within all of the groyne spacing. In some
areas in the groyne field, no additional eddies were formed because of penetration of the main flow field
into the groin field. The groynes resulted in the main flow path being deflected away from the outer river
bank into the channel. The flow field after the last groyne structure is extended out into the main channel.
The main flow path of Oreälven is outgoing into the east side the channel which results in a higher
velocity at the river bend after the flow intersection region. The flow velocities in the reach downstream
of this intersection are lower than without groynes. The groyne field results in a backwater effect
upstream of the groynes. The water surface elevation is locally elevated by 1 to 6 cm, depending on the
constellation of groynes. The water surface elevation downstream is unaffected, see Figure 9.
Bed shear stress
At the inlet at Österdalälven, the field of high shear stress is deflected away from the wall and into the
main channel, see Figure 24. There is an increase in shear stress at the intersection of the rivers. The
magnitude of shear stress downstream of this is similar to the one without groynes.
2.2.2. The influence of groynes on erosion and sedimentation patterns
The groynes significantly affect the magnitude and location of bed changes. Sedimentation occurs
between the groynes in the groyne field as shown in Figure 25. The groynes give rise to distinctive scour
holes at the tips and in the main channel. Both erosion and sedimentation are occurring at the flow
intersection region.
The sediment transport was simulated with the total load model in the groyne simulations. The presence
of groynes decreased the volume of sediment that was transported out of the west outlet by 21-34% and
15-23% at the south outlet, see Figure 26 and Table 14.
38
Figure 23. Uniform vector velocity field [m/s] for configurations with groynes for Q=100 m3/s. The groyne
configurations are from top to bottom 4, 6, and 9 groynes.
39
Figure 24. Bed shear stress [N/m2] in Österdalälven for Q=100 m3/s. The groyne configurations are from top to
bottom 4, 6, and 9 groynes.
40
Figure 25. Bed change [m] in Österdalälven around groynes after 1 year for Q=100 m3/s. The groyne
configurations are from top to bottom 4, 6, and 9 groynes.
41
Figure 26. Sediment yield at outlets for 1 year for configurations with and without groynes for Q=100 m3/s. The red
bar marks the standard configuration.
Table 14. Change in sediment transport for groynes compared to no groynes, after 1 year for Q=100 m3/s.
No./ longitudinal length [m] Decrease in sediment transport
[%]
West outlet South outlet
6/45 -34 -23
4/70 -31 -15
9/30 -21 -15
2.3. Turbulence model choice
The choice of turbulence model affected the distribution and magnitude of eddy viscosity. The k-epsilon
turbulence model renders a high value of eddy viscosity where the flow forms eddies which can be seen
in Figure 11. The other models: the parabolic eddy viscosity model and the mixing length model neglect
this which can be seen in Figure 27. Using these models, the eddy viscosity is low in areas with
circulation.
0
200
400
600
800
1000
No groynes 4/70 6/45 9/30
Sed
imen
t y
ield
at
wes
t o
utl
et
[m3
]
42
Figure 27. Velocity vector field on top of eddy viscosity [m2/s] for Q=100 m3/s with parabolic eddy viscosity turbulence mode (left) and mixing length turbulence
model (ri
43
2.4. Model validation
The model validation was done by comparing the total simulated load with field data and the known
characteristics of the sedimentation and erosion patterns.
The problem areas for sedimentation and erosion are marked in Figure 2 and Figure 3. The model
successfully captured important aspects of sediment transport, such as the strong areas of deposition in
areas c and d/e in agreement with the field data and observations. According to Figure 2, there is a large
problem of erosion in area b. The model did not capture this. The erosion in area e corresponds well with
the problem statement that erosion occurs at the railway bridge at high flows. According to Figure 2,
10 000 m3 sand was removed from the west outlet between the years 1999-2000. The model result renders
a yearly sediment yield of 1000 m3 for the standard configuration which is considered to be a reasonable
yield in relation to the stated sediment removal.
The suspended load in the reach makes up 60% of the total load according to Dutto (2004). The average
suspended load percentage of the total load along the examined mesh line is 74% which implies that the
model successfully models the ratio of suspended and bed load transport.
There is a point of singularity in the model in Oreälven inlet where the model simulates high values for
the water surface, shear stress and consecutive the bed changes relative to the result in the rest of the
model. It can be seen as a point of high shear stress in Figure 13. The point of singularity is due to the
local quality of the mesh. This point of singularity does not significantly affect any result downstream and
is neglected in the result.
3. Discussion
3.1. The implication of the results to the prevailing sedimentation problems
As the reason for this project states, there are sedimentation problems in the Österdalälven river mouth in
Siljan lake in Mora. A previous study (Dutto, 2004) has concluded that the sediment transport capacity in
the lower reaches of Österdalälven has decreased since the regulation of the river. Activities in the form
of dredging the sandbanks and depositions are being undertaken to mitigate the problem.
This project has successfully created a 2D depth-averaged numerical model which has been used to map
the flow field, shear stress distribution, and erosion and sedimentation patterns, of which a part is shown
in the result section. The result indicates that erosion occurs in areas where the flow velocity is high, i.e.
the shear stress is high. Sedimentation occurs in areas with secondary flow, e.g. circulation regions, and
low velocities. The amount of sediment that is transported out of the west outlet depends directly on the
magnitude of the flow. This study shows that the sediment yield at the west outlet is low compared to
downstream regions, which implies that the sediment transport rate is lower as well.
As can be seen in Figure 19, the bed level changes are large, with maximum values of -2m respectively
5m in some areas of the model. The model ran with the discharge of Q=100 m3/s for 1 year.
44
The simulations were done for this long period of time with a steady inflow to model the accumulated
erosion and sedimentation patterns. However, the actual duration of the flow Q=100m3/s is however not 1
year. To capture the magnitude of the bed change and sediment transport rate more realistically, the
simulations should be done with unsteady boundary conditions corresponding to the actual flow patterns
in Österdalälven.
3.2. The possibility of mitigation measures
According to the result, mitigation of the sedimentation problem is possible. This study has successfully
shown that by applying groyne structures to the model, the amount of sediment that is regularly
transported into Siljan could be decreased. However, modification of the river reach with physical
structures may give rise to other problems. In the present application, the groynes cause erosion outside
and downstream of the groyne field, and a backwater effect upstream in the upper reach of Österdalälven.
If groynes are used, they should be constructed in such a way that they do not cause unnecessary new
problems elsewhere. In addition, there may be other river training structures that are more suitable to
mitigate this problem.
3.3. Model validity
The validation of the model was done from the simulated result of the erosion and sedimentation patterns,
as this was the main purpose of the project. The result was compared with the available field data
regarding both the location and magnitude of the sedimentation regions.
As stated, the model did not capture all of the recorded characteristics of the erosion and sedimentation
patterns, e.g. sedimentation did not occur in places that were marked as problem areas. A numerical
model is only a representation of the real-world object, and as mentioned is laden with a certain amount
of error. However, it should be noted that there might be a significant inaccuracy regarding the recorded
field observations especially considering the magnitude of the long-term sediment transport. The other
shortcoming in the study was the lack of field data that hindered detailed calibration and validation.
Despite these shortcomings, the proposed model performed well by the reasonable predictions of
sediment transport patterns and the recognition of problem areas.
The majority of the model runs was done with a water surface elevation at the outlet boundary condition
that was lower than the average water state in Siljan. This was done in order to highlight the sediment
transport patterns. However, this resulted in a too low water surface elevation throughout the model
where parts of the banks were dry. Because of the dry banks, no sediment transport could occur there
which explains why there is no sedimentation in the banks of the west outlet, although it is marked as an
area with sedimentation problems.
The performance of the present model can be refined by collecting relevant field data for more accurate
and reliable mapping of the sediment and erosion patterns and the suggestions of possible mitigation
measures for the sedimentation problem in the reach.
45
3.4. Sensitivity analysis
When creating the hydrodynamic and sediment transport model, one can choose between different ways
to represent the physical object and the ongoing processes. The model sensitivity to a selection of these
parameters has been tested. These parameters were choice of turbulence model, wall slip condition,
Manning’s roughness coefficient, grid size, and sediment transport model.
The input parameters have been varied in their expected or plausible range or implementation possibility
(grid size). The percentage change of each parameter varies, i.e. they are not varied by an equal relative
magnitude. The resulting sensitivity thus depends on the magnitude of change in each parameter. The
sensitivity analysis also includes the variation of auxiliary models and grid size, of which a change cannot
be quantified. The sensitivity analysis, therefore, shows how sensitive the result is to the variation of input
within its expected range, and not the input parameter’s relative sensitivity to each other.
The sensitivity of the model is evaluated based on the sediment transport through the west outlet for
Q=100m3/s for 1 year of simulation, expressed as annual sediment yield. The scale for determining the
sensitivity of the model to the change of input will range from 0-33% as less sensitive, 34-67% as
sensitive, and 68-100% as more sensitive. The scale is based on that those parameters to which the
sensitivity of the result is less than 34% are here accepted as not to have a significant impact on the result.
Those parameters of which the sensitivity is more than 67% are accepted to have a significant impact.
It can be concluded that in terms of sediment transport, the model is less sensitive to the choice of
turbulence model. The sensitivity varied from 1-5%. However, if one is interested in mapping secondary
flow conditions, the 2-equation k-epsilon performed best of the three tested models in terms of eddy
viscosity distribution. In terms of wall slip, the sensitivity was in the range of less sensitive to sensitive.
For a viscous flow, zero wall slip can often be assumed. The model results were not sensitive to the
decrease in grid size. However, the grid size is of importance. The model of this project either did not run
or did not give reasonable results in terms of the hydraulics of the river. For instance, the coarser grid did
not capture some elements of the flow field such as secondary regions of circulation or reverse flow. The
model was more sensitive to the magnitude of Manning’s roughness coefficient. This parameter needs to
be measured or calibrated to field data in order to make a reliable model.
The model was sensitive to the choice of transport model; total load mode, bed-load mode or suspended-
load mode, and to the choice of transport rate formula which defines the two latter modes as described in
section 1.2.2. The volume of sediment transported through the west outlet in one year for the different
modes and transport rate formulas varied up to 100% compared to the total load mode. The Engelund &
Hansen and SEDTRA modules did not perform well in this study in the sense that they computed loads
that were significantly lower than field data stating the magnitude of the sediment yield. The conditions of
this project are within the applicability ranges of these formulas. However, the rate of sediment loads is
low in the river as indicated in previous sections which can be a reason why some formulas perform
poorly.
46
In the present study, it cannot be stated which transport mode or transport capacity rate formula is “best”.
However, by calibrating against field data, the mode that is best suited for this particular case can be
chosen.
The model was more sensitive to the choice of rating curve, i.e. the water surface elevation at the outlets
as well as the sediment diameter. These parameters are field data and by collecting these data, the model
can produce results that could be truer to reality.
3.5. The study’s limitations
The most important limitation of this study is the lack of field data. Discharge and sediment rating curves
and sediment diameter for allocating boundary conditions were unavailable. Thus, the study focus has
been on the mechanisms behind the prevailing problem and not on quantifying the sedimentation or
erosion rates.
4. Conclusions
The present study has successfully developed a 2D depth-averaged numerical model for combined flow
and sediment transport to address the sedimentation problems in the lower reach of Österdalälven. The
main objectives of the study of understanding the morphological characteristics of the river reach and
suggestion possible mitigation measures were achieved. A summary of the main conclusions is:
• The model is sensitive to the choice of boundary conditions, Manning’s roughness coefficient,
and sediment transport mode and transport capacity formula. The main conclusion is that
collecting field data is crucial to refine the model so it can be useful for quantifying hydrological
and morphological characteristics of the studied reach.
• The study shows that creating a working numerical river model based on the physical
understanding of the flow and sediment transport features despite the lack of field data is
possible.
• High shear stress and flow circulation regions are correlated with an increased rate of sediment
transport.
• The total sediment transport rates at the mouth of Österdalälven in Siljan can be decreased by
applying river training structures, e.g. groynes.
47
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