A FEM model for the numerical simulation ofhydrodynamic transport phenomena: An effective toolfor the evaluation of human-induced impacts in coastal

areas of high environmental and economical value

I. Colominas1, F. Navarrina1, M. Casteleiro1, L. Cueto-Felgueroso2,H. Gomez1, J. Fe1, A. Soage1

1 Group of Numerical Methods in Engineering GMNIUniversidade da Coruna, SPAIN

2Aerospace Computational Design LaboratoryMassachusetts Institute of Technology, USA

Abstract

This paper presents a numerical model for the simulation of the hydrodynamic andof the evolution of the salinity in shallow water estuaries. The mathematical modelconsists of the equations to model the evolution of the depth and of the velocity field(“shallow water hydrodynamic equations”) and the equation that describes the evo-lution of the salinity level (“shallow water advective-diffusive transport equation”).Some important issues that must be taken into account are the effects of the tides (in-cluding the possible exposition of the seabed), the volume of fresh water provided bythe rivers and the effects of the winds. Consequently, different types of boundary con-ditions must be considered. The numerical model proposed for solving this complexproblem is a second-order Taylor-Galerkin Finite Element formulation.

The proposed formulation has been applied to predict effects of human actions onthe marine habitat in coastal areas and to evaluate their environmental impact underdifferent meteorological conditions. The example presented in this paper isLos Lom-bos del Ullawithin the Arousa Estuary in northwestern Spain, which is an area withhigh environmental, economical and social value.

Keywords: Shallow waters, advection-diffusion, salinity in estuaries, Taylor-Galerkin.

1 Introduction

Nowadays the numerical simulation of the hydrodynamic and transport phenomena inshallow waters estuaries has turned into a valuable tool for the prediction of possibleeffects of Civil Engineering public works and other human actions (such as dredging,building of docks, spillages, etc.) on the marine habitat. Furthermore, it is possible

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the evaluation of their environmental impact in areas with high economical and so-cial value, for example for the productivity of fish and of seafood. The knowledgeof these effects is essential in the decision about the different options that could beimplemented.

Figure 1: Stereographic polar image of Spain[Courtesy ofInstituto Nacional de Meteorologıa] andSatellite image of Galicia (the yellow circle indicates the location of the Arousa Estu-ary) [Courtesy of VideaLAB, ETSICCP–UDC].

An example of this necessity of prediction isLos Lombos del Ulla: a natural for-mation of sandbanks downstream the Ulla River, within the tidal Arousa Estuary (LaRıa de Arousa) in Galicia, Northwestern Spain (see figures1, 2, 3 and4). This is avery rich seafood area (specially in bivalves), being the major economic issue of theArousa Estuary (figure2) and the source of an extensive complementary industry.

In the past, sand was regularly extracted from the Ulla River in the area ofLosLombos. Since decades ago, this practice is strictly forbidden by the environmentallaws, and for this reason it could be producing an speed up of the accumulation ofsediments in the zone (figures3 and4).

The fishermen unions fear that the effects of the accumulation of sediments, thewinds and the high volume of fresh water provided by the river could be slowingdown the mixing and causing a stagnation of fresh water, and consequently a drop ofthe salinity level in the zone.

Likewise, the conclusions of biological studies in the area show that a slight drop inthe salinity level is associated to an expected fall in the shellfish productivity, both inquantity (for the death of most individuals in the bivalve colonies) and quality (for theless size of the survivors). So, the gradual accumulation of sediments inLos Lomboscould be causing a permanently low salinity level in the area, and the consequent hugeloss in the local shellfish industry.

In 2002 the Autonomous Government of Galicia started to design a project for

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Figure 2: Satellite image of the Arousa Estuary (Los Lombosare situated in the mouthof Ulla River, in the right-upper part of the image)[Courtesy of VideaLAB, ETSICCP–UDC].

Figure 3: Detailed image of the estuary of Ulla River (the sandbanks ofLos Lombosare visible in the right-upper part of the image)[Courtesy of VideaLAB, ETSICCP–UDC].

Los Lombos del Ullain order to protect the shellfish productivity and to improve thenavigation conditions in the area. The actions initially considered were the dredging

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Figure 4:Los Lombos del Ullacirca 1995,[Courtesy of VideaLAB, ETSICCP–UDC].

of a navigation channel in the direction of the main stream, and the dredging of thewhole area in order to increase the depth (in fact, this is an old and unyielding demandof the fishermen).

In this paper we show the main highlights of the numerical model developed inorder to evaluate the effect of the proposed actions on the salinity level inLos Lombos[1, 2]. This tool should provide valuable information about changes in the hydro-dynamics of the zone due to the possible actions, the stability of the sandbanks, thefuture possible accumulation of sand, and the environmental impact during the dredg-ing operations.

2 Mathematical model

Phenomena underlying the analysis of the evolution of the concentration of a productwithin a medium require to consider a hydrodynamic model and a convective-diffusivetransport model in order to obtain the velocity field and the product concentration, inthis case, the salt concentration. Furthermore, the model should take into acount thetidal effects in the area, the volume of fresh water of the Ulla River and the windeffect.

Hydrodynamics of the problem can be obviously studied by means of the shallowwater equations (SWE), since the depth of the Arousa Estuary is small in compari-son with the other two spatial dimensions [3, 4]. As it is known, the SWE is a 2Dmodel obtained by vertical integration of the Navier-Stokes equations [5], so the av-eraged velocity at each point is considered representative of the velocity field in thecorresponding vertical column of water.

Likewise, the averaged salinity at each point is considered representative of thesalinity field in the corresponding vertical column of water. So the transport of saltcan be adequately described by means of a SW transport model obtained by vertical

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integration of the advection-diffusion equations [3, 5, 6, 7, 8].

On the other hand, from the measured values of salt concentration inLos Lombos,it is concluded that the vertical distribution is almost uniform (and maybe with a veryweak stratification in the area of interest), so a single-layer model will be adopted inthis case.

Thus, for each pointxxxxxxxxxxxxxx = (x, y), at each time stept, the unknowns to be computedwill be

h: the depthh(xxxxxxxxxxxxxx, t) = z(xxxxxxxxxxxxxx, t) − zb(xxxxxxxxxxxxxx), wherez(xxxxxxxxxxxxxx, t) is the sea surface height andzb(xxxxxxxxxxxxxx) is the seabed height,

vvvvvvvvvvvvvv: the velocity vectorvvvvvvvvvvvvvv(xxxxxxxxxxxxxx, t) = [vx(xxxxxxxxxxxxxx, t), vy(xxxxxxxxxxxxxx, t)]T , and

c: the salinityc(xxxxxxxxxxxxxx, t).

The SWE in conservative form are given by [3, 5]

∂uuuuuuuuuuuuuu

∂t+

∂FFFFFFFFFFFFFF x

∂x+

∂FFFFFFFFFFFFFF y

∂y= RRRRRRRRRRRRRRS +

∂RRRRRRRRRRRRRRDx

∂x+

∂RRRRRRRRRRRRRRDy

∂y, uuuuuuuuuuuuuu =

h

hvx

hvy

hc

, (1)

whereRRRRRRRRRRRRRRS is the so-called “source” term

RRRRRRRRRRRRRRS =

0

fhvy + g(h − H) ∂∂x

H + τxρ−1 − n2gh−1/3 |vvvvvvvvvvvvvv| vx

−fhvx + g(h − H) ∂∂y

H + τyρ−1 − n2gh−1/3 |vvvvvvvvvvvvvv| vy

0

, (2)

FFFFFFFFFFFFFF x andFFFFFFFFFFFFFF y are the so-called “inviscid flux” terms

FFFFFFFFFFFFFF x =

hvx

hv2x + 1

2g(h2 − H2)

hvxvy

hcvx

, FFFFFFFFFFFFFF y =

hvy

hvxvy

hv2y + 1

2g(h2 − H2)hcvy

, (3)

andRRRRRRRRRRRRRRDx andRRRRRRRRRRRRRRD

y are the so-called “diffusive flux” terms

RRRRRRRRRRRRRRDx =

0

2hµρ−1 ∂∂x

vx

hµρ−1(

∂∂x

vy + ∂∂y

vx

)hγ ∂

∂xc

, RRRRRRRRRRRRRRDy =

0

hµρ−1(

∂∂x

vy + ∂∂y

vx

)2hµρ−1 ∂

∂yvy

hγ ∂∂y

c

, (4)

being

f : the Coriolis’ coefficient, which can be obtained from the latitude of the placeφand the angular velocity of rotation of the EarthΩ as

f = 2Ω sin(φ), (5)

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g: the gravity acceleration,

H: the average depth at each point (bathymetry),

ττττττττττττττ : the tangential stress due to the wind friction (ττττττττττττττ = [τx, τy]T ), which can be ob-

tained by means of the Ekman’s formula from the wind velocityvvvvvvvvvvvvvvw [4]:

ττττττττττττττ = κ|vvvvvvvvvvvvvvw|vvvvvvvvvvvvvvw, with κ = 3.2 10−3 N s2/m4, (6)

ρ: the water density,

n: the Manning’s coefficient (modeling the energy losses due to the seabed fric-tion),

µ: the dynamic viscosity, and

γ: the total diffusivity (that includes the combined effect of the molecular diffusion,the turbulent diffusion and the dispersive diffusion [6, 7]) can be obtained fromthe depthh and the velocityvvvvvvvvvvvvvv by means of the Elder’s formula [6, 7]:

γ = 0.6 h |vvvvvvvvvvvvvv|. (7)

Boundary conditions of the model must be imposed depending on the different typeof boundaries of the problem:

• In the part of the boundary that corresponds to the mouth of the Ulla River, theflow is super-critical, so the flux and the salinity must be prescribed:

h vvvvvvvvvvvvvvT nnnnnnnnnnnnnn = −hQR

A(h)and c = 0 on the river, (8)

beingQR the known volume of flow in the river,A(h) the area of the wet sec-tion of the river, andnnnnnnnnnnnnnn the external normal to the boundary. The salinityc isprescribed to be null, since the river flows fresh water into the estuary.

• In the part of the boundary that corresponds to the sea, the flow is sub-critical,so the depth and the salinity must be prescribed:

z = zS(t) + ∆zS and c = cS on the sea, (9)

being zS(t) the prescribed depth due to the tide harmonics, and∆zS the so-called “meteorological tide” (that is, the rise or the fall of the surface level duringa storm due to the wind effect on the whole fetch),

• In the part of the boundary that corresponds to the shore, the flux of water andthe flux of salt are prescribed null in the directionnnnnnnnnnnnnnn of the normal to the shore,what gives

h vvvvvvvvvvvvvvT nnnnnnnnnnnnnn = 0 and h gradgradgradgradgradgradgradgradgradgradgradgradgradgradT (c)nnnnnnnnnnnnnn = 0 on the shore. (10)

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3 Finite Element numerical model

The equations of this problem (1—4) can be numerically solved by the Finite ElementMethod by means of a second order Taylor-Galerkin (TG-2) approach [3, 5, 9, 10, 11].

The starting point of this approach is the Taylor’s expansion int of the unknownfunctionuuuuuuuuuuuuuu(xxxxxxxxxxxxxx, t)

uuuuuuuuuuuuuu∣∣∣t=tn+1

= uuuuuuuuuuuuuu∣∣∣t=tn

+ ∆t wwwwwwwwwwwwww∣∣∣t=tn

+ O(∆t3), (11)

where

wwwwwwwwwwwwww =

[∂uuuuuuuuuuuuuu

∂t+

∆t

2

∂2uuuuuuuuuuuuuu

∂t2

]. (12)

Now, if we isolate the term∂uuuuuuuuuuuuuu∂t

from the differential equation (1), we derive it againrespect the time coordinate in order to obtain∂2uuuuuuuuuuuuuu

∂t2and both are substituted in (12), the

termwwwwwwwwwwwwww results in the form

wwwwwwwwwwwwww = bbbbbbbbbbbbbb −(

∂AAAAAAAAAAAAAAx

∂x+

∂AAAAAAAAAAAAAAy

∂y

), (13)

being

bbbbbbbbbbbbbb = RRRRRRRRRRRRRRS +∆t

2RRRRRRRRRRRRRR

S,

AAAAAAAAAAAAAAx =

[FFFFFFFFFFFFFF x +

∆t

2FFFFFFFFFFFFFF x

]−

[RRRRRRRRRRRRRRD

x +∆t

2RRRRRRRRRRRRRR

D

x

], AAAAAAAAAAAAAAy =

[FFFFFFFFFFFFFF y +

∆t

2FFFFFFFFFFFFFF y

]−

[RRRRRRRRRRRRRRD

y +∆t

2RRRRRRRRRRRRRR

D

y

] (14)

and where the dot-notation refers to the standard time-derivative (e.g.,RS =∂RRRRRRRRRRRRRRS

∂t).

Applying the Weighted Residuals Method in the spatial coordinates to (13) yields∫∫xxxxxxxxxxxxxx∈Ω

$

(wwwwwwwwwwwwww −

[bbbbbbbbbbbbbb −

(∂AAAAAAAAAAAAAAx

∂x+

∂AAAAAAAAAAAAAAy

∂y

)])dΩ = 0, (15)

for all members of a certain class of test functions$ defined onΩ. This variationalexpression can also be rewritten as∫∫

xxxxxxxxxxxxxx∈Ω

$ wwwwwwwwwwwwww dΩ =

∫∫xxxxxxxxxxxxxx∈Ω

$ bbbbbbbbbbbbbb dΩ −∫∫

xxxxxxxxxxxxxx∈Ω

$

(∂AAAAAAAAAAAAAAx

∂x+

∂AAAAAAAAAAAAAAy

∂y

)dΩ ∀$. (16)

Furthermore, and by applying the divergence-theorem, the second-term on the righthand side of this equation can be written as [11]∫∫

xxxxxxxxxxxxxx∈Ω

$

(∂AAAAAAAAAAAAAAx

∂x+

∂AAAAAAAAAAAAAAy

∂y

)dΩ =

∫xxxxxxxxxxxxxx∈∂Ω

$ AAAAAAAAAAAAAA˜ nnnnnnnnnnnnnn d∂Ω −∫∫

xxxxxxxxxxxxxx∈Ω

AAAAAAAAAAAAAA˜ gradgradgradgradgradgradgradgradgradgradgradgradgradgrad($) dΩ (17)

whereAAAAAAAAAAAAAA˜ andgradgradgradgradgradgradgradgradgradgradgradgradgradgradT ($) are given by

AAAAAAAAAAAAAA˜ =[AAAAAAAAAAAAAAx AAAAAAAAAAAAAAy

], gradgradgradgradgradgradgradgradgradgradgradgradgradgradT ($) =

∂$

∂x

∂$

∂y

. (18)

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Now, if we discretize the trial functions in the form

uuuuuuuuuuuuuu(x, y, t) =∑

I

uuuuuuuuuuuuuuI(t)φI(x, y), wwwwwwwwwwwwww(x, y, t) =∑

I

wwwwwwwwwwwwwwI(t)φI(x, y), (19)

and the test functions in the form

$(x, y, t) =∑

J

ββββββββββββββJ(t)$J(x, y), (20)

we obtain the discretized variational form∑I

[∫∫xxxxxxxxxxxxxx∈Ω

$J φI dΩ

]wwwwwwwwwwwwwwI =

∫∫xxxxxxxxxxxxxx∈Ω

[$J bbbbbbbbbbbbbb + AAAAAAAAAAAAAA˜ gradgradgradgradgradgradgradgradgradgradgradgradgradgrad($J)] dΩ

−∫xxxxxxxxxxxxxx∈∂Ω

$J AAAAAAAAAAAAAA˜ nnnnnnnnnnnnnn d∂Ω ∀J.

(21)

Finally, the selection of the Galerkin Method ($J(x, y) = φJ(x, y)) leads to thesecond-order Taylor-Galerkin expressions.

The TG-2 algorithm requires basically to solve at each time step the following LSE∑I

[MJI ] wwwwwwwwwwwwwwI(tn) = ffffffffffffffJ∣∣∣t=tn

, with

[MJI ] =

[∫∫xxxxxxxxxxxxxx∈Ω

φJ φI dΩ

]and

ffffffffffffffJ =

∫∫xxxxxxxxxxxxxx∈Ω

[φJ bbbbbbbbbbbbbb + AAAAAAAAAAAAAA˜ gradgradgradgradgradgradgradgradgradgradgradgradgradgrad(φJ)] dΩ −∫xxxxxxxxxxxxxx∈∂Ω

φJ AAAAAAAAAAAAAA˜ nnnnnnnnnnnnnn d∂Ω

,

(22)

and next the solution is updated (i.e., it is performed the time integration) by neglectingthird order errors, what gives the second order accurate expression

uuuuuuuuuuuuuuI(tn+1) = uuuuuuuuuuuuuuI(tn) + ∆t wwwwwwwwwwwwwwI(tn). (23)

In this project, the solution to (22) has been obtained by a diagonal lumping of themass matrix (22) [3], and the LSE has been solved by using a Diagonal PreconditionedConjugate Gradient algorithm without assembling the global matrix.

4 FEM discretization and Data of the model

The requirements of imposing the open-sea boundary conditions far away from thearea ofLos Lombos del Ullaand of taking into account the influence of the wholeestuary (Fig. 2) in the hydrodynamics force to consider all the estuary despite therelatively small size of the area of interest (Fig.3 and4).

The Finite Element discretization consists of a mesh of30970 isoparametric quad-rangular elements of 4 nodes, as it is shown in Fig.5 [12, 13, 14, 15]. This implies120424 degrees of freedom at each time step.

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The size of the finite elements gradually grows as we move away fromLos LombosFig. (5). The medium size of the elements vary from 25 m in the area of interest atLosLombosto 200 m in the open-sea zone of the estuary. Consequently,14979 elementsare placed inLos Lombos del Ulla(nearly half of the total elements) and are devotedto represent the approximate solution in the area of interest. The rest of elements arespread in the most extensive part of the estuary.

With this kind of discretization we also achieve two goals: obtaining the mostprecise results in the zone ofLos Lombos, and avoiding the stability conditions [3] tobecome excessively restrictive (because the largest elements are located in the deepestareas where the velocity of propagation of the gravity waves is higher). Thus, thesecond-order Taylor-Galerkin approach allows to obtain very good results for quitelarge time steps (close to the CFL limit) and to carry out long simulations.

Figure 5: GEN4U discretization of the whole estuary

In the analysis of this problem we have considered 3 different bathymetries of theRıa de Arosadepending on the possible actions:

• Theactualbathymetry of the whole estuary obtained from some measurementsspecifically made in the area ofLos Lombosduring 2002, from the nauticalcharts of the estuary and from the available topographic data of the shore [1](figures6, 7).

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Figure 6: 3D view of the Actual bathymetry of the wholeRia de Arosa.

Figure 7: Actual bathymetry inLombos del Ulla.

10

Figure 8: Bathymetry inLombos del Ullaconsidering thedredging of a navigationchannel.

• The bathymetry that corresponds to thedredging of a navigation channelinthe area ofLos Lombos(Fig. 8). This bathymetry is obtained from the actualbathymetry by dropping the corresponding values of the seabed height down tothe level−1.5 m (Total dredged solids:614, 651.24 m3).

• The bathymetry that corresponds to thegeneral dredgingin the area ofLos Lom-bos(Fig. 9). This bathymetry is obtained from the actual bathymetry by drop-ping the corresponding values of the seabed height down to the level−0.5 m,but limiting the drop to0.75 m in each point at the most [1]. (Total dredgedsolids:3, 876, 503.49 m3).

On the other hand, and regarding the general data of the model we have consideredthe following values for the physical constants of the problem:Ω = 2π/86164.09 rad/s,φ = 43o 35′ 58′′ (the latitude of theVilagarcıa de Arousaharbour),g = 9.81 m/s2,ρ = 103 Kg/m3, n = 0.0425 s/m1/3, cS = 0.035 andµ = 50 Kg/ms. and the tideeffect has been modeled by adding up the first 10 harmonics (n = 9) of the corre-sponding Fourier series, as

zS(t) =n∑

i=0

Ai cos(ωit + ϕi), (24)

where the amplitude (Ai), the angular frequency (ωi) and the phase (ϕi) of each har-monic (i) have been obtained from the Spanish seaports authority website [11, 16]

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Figure 9: Bathymetry inLombos del Ullaconsidering ageneral dredgingof the area.

5 Results and discussion

In the project we programmed two types of numerical simulations[1, 11]:

• 28 days simulations in Normal Conditions (NC). In these simulations, the resultsobtained with the actual bathymetry are compared with each one of the twopossible actions (dredging a navigation channel and dredging the whole areaof Los Lombos) in the case ofnormal meteorological conditions. From theaccurate analysis of these results we obtained an important conclusion, sincethe dredging of the whole area ofLos Lomboshad to be discarded.

• 2 days simulations in Exceptional Conditions (EC). In these simulations, theresults obtained with the actual bathymetry are compared with the results pre-dicted if a navigation channel is dredged inLos Lombosin the case of differentexceptionalmeteorological conditions.

“Normal Conditions” correspond to the average volume of water (QR = 56 m3/s)in the Ulla River, and the average velocity wind (vW = 4.8 m/s) blowing in thedominant direction in the area (202o S–SW) without meteorological tide (∆zS = 0 m).

On the other hand, we consider the following 5 different types of “Exceptional Con-ditions” depending on the velocity of the wind (vW ), its direction, the meteorologicaltide (∆zS) and the volume of water in the Ulla River (QR):

• Southwest storm (EC#1):vW = 15.0 m/s, blowing210o SW,∆zS = +0.15 m,QR = 56 m3/s,

• Flood condition (EC#2):vW = 4.8 m/s, blowing202o S–SW,∆zS = 0 m,QR = 300 m3/s,

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• Southwest storm and flood condition (EC#3):vW = 15.0 m/s, blowing210o SW,∆zS = +0.15 m, QR = 300 m3/s,

• Northeast storm and flood condition (EC#4):vW = 15.0 m/s, blowing30o NE,∆zS = −0.15 m, QR = 300 m3/s,

• Northeast storm (EC#5):vW = 15.0 m/s, blowing30o NE, ∆zS = −0.15 m,QR = 56 m3/s.

From the 28 days simulations in Normal Conditions considering the actual bathy-metry, it is possible to observe that the salinity level inexorably falls during the neaptide cycles due to the continuous contribution of fresh water from the river, while it isfully recovered during the spring tide cycles due to the emptying of most of the basinand to the periodic contribution of salt water from the sea. This periodic emptying ofthe area ofLos Lombosdue to the low tide during the spring tide cycles is essential inorder to maintain the average level of salinity (figure10).

The opposite sitation to this one would corresponds to the general dredging. In thiscase, the stagnation of fresh water during the neap tide cyles remains during the springtide cycles since there is not an important contribution of salt water from the sea in thearea ofLos Lombosin any moment. This action would cause an important decrease inthe average salinity level in all the area (figure11). So we absolutely advised againsta general dredging ofLos Lombos.

On the other hand, the dredging of a navigation channel in the direction of the mainstream should not significantly modify the average salinity level inLos Lombos(figure12). From the numerical simulations, it is possible to observe two opposite effects thatcancel one to other: an improvement in the salinity level during the spring tide cyclessince the channel would facilitate the emptying and the filling of the basin, versusa certain decrease in the average salinity level during the neap tide cycles. So, theshellfish production of the area would not be substantially affected by the dredging ofa channel, while the navigation conditions in the area could be significantly improved.

From the comparison of results of the numerical simulations by using the actualbathymetry and by using the bathymetry with the dredging of a navigation channel inthe five cases of exceptional conditions considered we can conclude that there are nosignificantly differences in both situations (figures13,14,15,16,17). In any case, it ispossible to observe a litle improvement in the second case for the channeling effectproduced.

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Figure 10: Salinity level inLos Lombosunder Normal Conditions: actual bathymetrycase [Intertidal zones: yellow, salt water: green, fresh water: blue]

Figure 11: Salinity level inLos Lombosunder normal conditions: general dredgingcase [Intertidal zones: yellow, salt water: green, fresh water: blue]

Figure 12: Salinity level inLos Lombosunder normal conditions: channel dredgingcase [Intertidal zones: yellow, salt water: green, fresh water: blue]

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Figure 13: Comparison of the salinity level at a same time inLos Lombosconsid-ering the Condition EC#1 between the actual bathymetry case (left) and the channeldredging case (right) [Intertidal zones: yellow, salt water: green, fresh water: blue].

Figure 14: Comparison of the salinity level at a same time inLos Lombosconsid-ering the Condition EC#2 between the actual bathymetry case (left) and the channeldredging case (right) [Intertidal zones: yellow, salt water: green, fresh water: blue].

Figure 15: Comparison of the salinity level at a same time inLos Lombosconsid-ering the Condition EC#3 between the actual bathymetry case (left) and the channeldredging case (right) [Intertidal zones: yellow, salt water: green, fresh water: blue].

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Figure 16: Comparison of the salinity level at a same time inLos Lombosconsid-ering the Condition EC#4 between the actual bathymetry case (left) and the channeldredging case (right) [Intertidal zones: yellow, salt water: green, fresh water: blue].

Figure 17: Comparison of the salinity level at a same time inLos Lombosconsid-ering the Condition EC#5 between the actual bathymetry case (left) and the channeldredging case (right) [Intertidal zones: yellow, salt water: green, fresh water: blue].

Finally, it is important to remark that the numerical results of the model have beencompared with data given by the experts in the hydrodynamics of the area, with mea-surements performed during the project and with computed results obtained with sim-pler models. The results agree with the available data and the model predicts correctlythe main hydrodynamical phenomena that are observed in the estuary and reported byfishermen and the regional coastal authorities [[11]].

6 CONCLUSIONS

A numerical model for the simulation of the hydrodynamic and of the evolution of thesalinity in shallow water estuaries have been presented in this paper. The mathemati-cal model consists of the SW-hydrodynamic equations and the SW-transport equation,and include the most relevant issues, such as the tidal effect, the volume of fresh waterprovided by the rivers and the effects of the winds. The numerical model proposedis a Second order Taylor-Galerkin Finite Element formulation. The presented modelprovides useful and accurate numerical information for the prediction of the possible

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effects of Civil Engineering public works and other human actions and the evalua-tion of their environmental impact. Furthermore, it contributes to knowing better themarine habitat by showing how important are the different processes involved in thehydrodynamics of an estuary, while the obtained numerical results can be used forother practical purposes (i.e.: for predicting the migration of the shellfish coloniesdepending on the salinity level and on the currents).

Acknowledgments

This work has been partially supported by theConsellerıa de Pescaof theXunta deGalicia by means of a research contract between theFundacion CETMARand theFundacion de la Ingenierıa Civil de Galicia, by Grants # PGIDIT05PXIC118002PNand # PGDIT06TAM11801PR of the DXID–CIIC of theXunta de Galicia, by Grant# DPI-2004-05156 and # DPI2006-15275 of the SGPI–DGI of theMinisterio de Edu-cacion y Ciencia, and by research fellowships of theUniversidade da Corunaand theFundacion de la Ingenierıa Civil de Galicia.

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