1

Numerical Simulations of Morphological Changes in Coasts Induced by

Overflow and Overwash using a Supercritical Flow Model

Soumendra Nath Kuiry1, Yan Ding

2*, and Sam S. Y. Wang

3

1. Ph. D., Assistant Professor, Environmental & Water Resources Engineering Division,

Department of Civil Engineering, I.I.T. Madras, Chennai, Tamil Nadu, 600 036, INDIA,

Email: snkuiry@iitm.ac.in

2 Ph. D., M. ASCE, Research Associate Professor, National Center for Computational

Hydroscience and Engineering, The University of Mississippi, University, MS 38677, Email:

ding@ncche.olemiss.edu

3 Ph.D., P.E., F. ASCE, F.A.P. Barnard Distinguished Emeritus and Director Emeritus,

National Center for Computational Hydroscience and Engineering, The University of

Mississippi, University, MS 38677, Email: wang@ncche.olemiss.edu

Abstract

In this paper, an advanced explicit finite volume flow model in two-dimensions is

presented for simulating supercritical coastal flows and morphological changes in a tidal/coastal

inlet due to storm surges and waves. The flow model is coupled with a wave-action model and a

sediment transport model. It is capable of simulating flows induced by extreme conditions such

* Corresponding Author, Email: ding@ncche.olemiss.edu

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as river flood flows, storm waves, surge tides, winds, etc, and the morphological changes induced

by rapid coastal currents and waves. This supercritical flow model is based on the solution of the

conservative form of the non-linear shallow water equations with the effects of the Coriolis force,

uneven bathymetry, wind stress, and short wave averaged radiation stresses. The forward Euler

scheme is used for the unsteady term; and the convective term is discretized using Godunov-type

shock-capturing scheme along with the HLL Riemann solver on non-uniform rectilinear grids.

The accuracy of the developed model is investigated by solving an experimental dam-break test

case. Barrier island breaching, overflow and overwash due to severe storm attack are simulated

and the predicted morphological changes associated to the events are analyzed to investigate the

applicability of the model in a coast where all the physical forces are present.

Keywords: Coastal inlet; Wave model, Supercritical flow; Sediment transport, Overwash.

INTRODUCTION

During extreme hydrological conditions induced by a tropical storm or a hurricane, high

waves riding on the rising sea water, constantly pushing beaches and coastlines, may overflow,

overwash, and breach coastal levees and barrier islands. Due to wave runup and inundation of

flooding waters, strong currents together with storm surges may severely erode sand beach and

barrier islands, create deep local scouring around coastal structures, and make drastic shoreline

changes (e.g. Briaud et al., 2008). Hazardous coastal flood/inundation and morphological

changes due to surges and high waves can further cause property damages and loss of lives (e.g.

Fritz et. al., 2008). Due to strong currents and rapid changes in bathymetry, coastal flow may

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become complex and supercritical when it overwashes top of levees or barrier islands, or it surges

through a coastal/tidal inlet. For development of a resilient coastal community, better coastal

hazard management and designs of coastal structures are needed to consider such extreme

conditions in order to protect coastal zones from disastrous flooding/inundation and severe

morphological changes. For instances, extreme tropical storm hydrological conditions and their

impacts on morphological changes around coastal infrastructures were carefully studied for

planning the Lousiana coastal protection and restoration (e.g. LACPR, 2009) and the Mississippi

Gulf coast defense (e.g. MsCIP, 2010).

Coastal/tidal inlets along barrier islands are used to facilitate exchange of fresh and saline

water, navigation and pathway for sediments, nutrients, water-borne materials etc. Such inlets

and islands are often attacked by ocean waves, tides, and storm surges, result in significant

erosion, sediment movement, bed changes of inlet channel and instability of the shoreline at the

adjacent coasts. Militello and Kraus (2003) and Ding and Wang (2007) reported that

morphodynamic response of an inlet to tides and storm waves can lead to ebb and flood shoals

formation, navigation channel refilling, migration of the channel thalweg, skewing of ebb shoals,

development of tip shoals, beach erosion, and formation of scour holes inside the inlet and

adjacent to the jetty tips. The hydrodynamics and morphodynamics associated to these problems

may be investigated effectively and efficiently using process based numerical models.

In recent years numerical flow models have been increasingly developed and applied to

simulate coastal flows and morphological changes due to storm surge, wave or tsunami (e.g.

Lesser et al., 2004; Buttolph et al., 2006; Briaud et al., 2008; Ding and Wang, 2008; Kuiry et al.,

2010). Modelling the effects of these extreme events is important for design of coastal structures,

sediment management, shoreline protection, maintenance of navigation channel, etc. The

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numerical models can be used in a cost effective way comparing to physical model study in order

to refine and optimize designs of coastal structures.

In this study, a process-based supercritical coastal flow model is developed to simulate

overflow and overwash due to rapid surge currents through a coastal inlet, as well as

morphological changes in the inlet and the adjacent coastlines. The integrated model includes

three different submodels: (1) wave model, (2) wave-induced hydrodynamic model and (3)

sediment transport model. A phase-averaged wave model based on linear wave theory is used to

simulate wave transformation and deformation, and to calculate radiation stresses. Based on the

Godunov-type scheme along with the HLL Riemann solver (Harten et al., 1983), a supercritical

flow model is developed in this study to enhance the simulation capability of the integrated

coastal process model. The supercritical model solves the conservative form of the nonlinear

shallow water equations in which the effects of the Coriolis force, surface wind stress, bottom

roughness, uneven bathymetry and short wave-averaged radiation stresses are included. The

Godunov-type method represents physically correct propagation of information throughout the

flow field by solving a set of local Riemann problems. The radiation stresses are obtained by

simulating the wave field using the wave model and added as source term in the momentum

equations to represent the longshore current. The simulated flow field is used by the sediment

transport model and the bathymetry is updated at a given time interval. The developed coastal

process model calculates wave action, current, sediment transport, and morphological changes

sequentially under the combined conditions of surge tides and storm waves. The wave and

sediment transport models of the SMS (Surfacewater Modeling System) (Zundel, 2000) are

systematically used with the developed hydrodynamic model to simulate all the physical

processes. The flow model is validated carefully by simulating dam-break wave propagation over

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a triangular obstacle; and then the integrated model is applied to simulate hydrodynamic and

morphodynamic responses to a hypothetical surge tide and wave in a coast with barrier islands

and inlet. Barrier island breaching, overflow and over wash due to severe storm attack are

simulated and the morphodynamic changes associated to the events are analyzed to investigate

the applicability of the model in a coast where all the physical forces are present.

MODEL DESCRIPTION

The integrated model is developed based on the three other sub-models (a) wave model,

(b) wave-induced current model and (c) sediment transport and morphodynamic change model.

The first and third models are readily available in SMS (Buttolph et al. 2006) and the second

model is developed in this study and integrated with the other models so that all the three models

can be operated sequentially. Thus the coastal process model uses several differential equations

and they are solved in a decoupled way and the necessary values of the parameters are passed

from one model to another systematically. The wave model is a phase-averaged model and

computes radiation stresses. In the wave-induced depth-averaged current model radiation stresses

are included so that longshore current can accurately be represented. The cross-shore and

longshore sediment transport is calculated by a sediment transport model based on Lund-CIRP

total load formulation (Camenen and Larson, 2005). The models are briefly described below.

Wave Model

The CMS-Wave (Lin et al., 2008) takes into account the effect of an ambient horizontal

current or wave behaviour and solves the wave-action balance equation as

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2 2cos cos

2 2

y gxg y yy b

y

v N CCv N v NCC N N N R

x y

(1)

where N=E(σ,θ)/σ is the wave-action density to be solved and is a function of frequency and

direction . The spectral wave density ,E represents the wave energy per unit water

surface area per frequency interval. In Eq. (1), , gC C wave celerity and group velocity,

respectively; ,x y horizontal coordinates in two directions; , and x yv v v characteristic velocity

components with respect to , and x y ; ,y yyN N first and second derivatives with respect to

y , respectively; empirical constant representing the intensity of diffraction effect;

b parameterization of wave breaking energy dissipation and R source terms (e. g., wind

forcing, bottom friction loss, nonlinear wave-wave interaction term). The term needs to be

calibrated and optimized for structures. The velocity components in Eq. (1) are given by

cosx gv C u (1)

siny gv C v (2)

sin cosgC C C

vC x y

(3)

where ,u v depth-averaged horizontal current velocity components along x and y directions.

Flow Model

A depth and shortwave averaged form of the SWEs are used for simulating currents

induced by tides and waves (Ding and Wang, 2006). The governing equations in conservative

form can be written as follows:

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( ) ( )

( , , )x yt x y

U E U G US U (4)

in which,

;

H

Hu

Hv

U 2 21;

2

Hu

Hu gH

Huv

E

2 2

;

1

2

Hv

Huv

Hv gH

G

0

( )

( )

x y bx sx wx

x y by sy wy

Hu HuhgH f Hv D D

x x x y y

Hv HvhgH f Hu D D

y x x y y

S

where U vector of conserved variables; E and G convective fluxes in the x- and y-directions,

respectively; and S source term. In addition, h still water depth from a datum (see Figure 1);

deviation of the water surface from the still water level; H h total water depth; u

and v depth-averaged current velocities parallel to the x - and y -directions; g acceleration

due to gravity; f Coriolis force with 2 sinf , in which angular frequency of earth

rotation, and latitude. The other parameters in the x - and y -directions are: 0xS and

0 yS bed slopes; xD and yD diffusion coefficients; bx and by bed shear stresses; sx and

sy wave stresses; wx and wy surface wind stresses, respectively.

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Sediment Transport and Morphodynamic Change Model

The sediment transport model is based on the calculations of sediment transport rates and

resultant changes in water depth (bottom elevation) through gradients in transport rates as

proposed in Lund-CIRP formulations (Camenen and Larson, 2005). Bed level changes are

obtained from the sediment continuity equation:

1

1

bybxqqh

P Dt p x x

(5)

where ,bx byq q bed load transport rate in the x- and y-directions, respectively and p porosity of

sediment. The term bx byq x q y represents the bed load component and the term P D

corresponds to the suspended load component. While evaluating the bed changes by Eq. (5),

time-averaged transport rates are used ( ,bx byq q ). In this approach, instantaneous transport rates

are computed at a time interval of sedt and time-averaged transport rates and morphological

changes are calculated at a time interval of morpht . Also, the bed load components in Eq. (5) are

corrected for the slope effect as

bx bx s b x

hq q D q

x

(6)

by by s b y

hq q D q

y

(7)

where 2 2b bx byq q q . Finally, Eq. (8) is solved to compute depth changes at the time

interval morpht :

1

1

bybxqqh

P Dt p x x

(8)

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Camenen and Larson (2005) proposed a general transport formula for bed load under

combined effect of wave and current as

,350

exp1

bw crw net cw m

cw

qa b

s gd

(9)

,350

exp1

bn crn cn cw m

cw

qa b

s gd

(10)

where subscripts w and n represents wave direction and direction normal to the wave,

respectively; 50d median grain diameter; cr critical Shields parameter; s specific gravity;

,w na a and b empirical constants and , ,cw m cw mean and maximum Shields parameter

respectively. The quantities net and cn represent the net contribution of the shear stress to the

transporting velocity during a wave cycle in the direction parallel and normal to the waves,

respectively.

The suspended load qs is computed assuming an exponential concentration profile and a

constant velocity over the water column and can be expressed as

q u 1sw h

s R

s

c ew

(11)

where sw sediment settling velocity, Rc reference concentration and sediment diffusivity

(or turbulent mixing coefficient). The transport qs is considered to be taken place in the direction

of current because the waves are assumed to produce a zero net drift and do not contribute to the

suspended sediment transport.

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SOLUTION METHODS

In order to simulate coastal hydro and morphological processes, the governing partial differential

equations for the three submodels, i.e., the energy balance equation [Eq. (1)], the depth- and

wave-averaged continuity and momentum equation [Eq. (4)] and the seabed level evolution

equation [Eq. (8)] are solved numerically. The integrated model is developed on a non-uniform

rectangular Cartesian coordinate system. Though the wave and morphodynamic change models

are used directly from the SMS in the present study, a brief description of solution schemes of the

sub-models are presented in the following sections.

Wave Model

The energy balance Eq. (1) is solved by means of parabolic approximation, in which the

waves are assumed to have a principal propagation direction from offshore to onshore. Therefore,

the computations are carried out line by line from offshore to onshore. The first term of Eq. (1) is

discretized by forward difference scheme, second and third terms are discretized by QUICK

scheme (proposed by Leonard, 1979), diffraction term is discretized by central difference scheme

and the source term is obtained by solving algebraic equations. Consequently, Eq. (1) is

expressed in a finite difference form and is solved explicitly. The implementation of the

numerical scheme is described in detail in Mase (2001) and Mase et al. (2005).

Hydrodynamic Model

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A cell centered finite volume method is used to discretize Eq. (4) over a non-uniform

rectangular control volume in a Cartesian grid with the assumption that the dependent variables

are represented as piecewise constants. It is useful to rewrite Eq. (4) as

( , , )x yt

UF U S U (12)

in which, ( , )F E G is the flux tensor, in order to introduce integral form of the equations over a

fixed control volume :

d d dt

U

F S (13)

In the 2D approach, a discrete form of Eq. (13) is applied to each cell with dimension

( ,x y ) so that the volume integrals represent integrals over the area of the cell and the surface

integrals represent the total flux through the cell boundary . Assuming U as the average value

of conservative variables over the volume at a given time, from Eq. (13) and applying Gauss

divergence theorem to the second integral, the conservation equation can be written as

A d At

U

F n S (14)

where A is the cell area and n is the unitary outward normal.

A two-dimensional discrete finite volume formulation of system of Eq. (14) with explicit

scheme, which applies forward Euler discretization to time derivative, on a non-uniform

rectilinear grid with spacing ( ,x y ), leads to the inherently conservative method:

1 * * * *, , 1 2, 1 2, , 1 2 , 1 2 ,

n ni j i j i j i j i j i j i j

t tt

x y

U U E E G G S (15)

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in which * * *1 2 1 2 1 2,i i i F E G numerical convective flux functions through the cell interfaces

1 2,i j and , 1 2i j (Figure 2) respectively; t time step size and ,i j S a discretization of the

source term. In this study, HLL Riemann solver (Harten et al., 1983) is chosen for convective

flux ( *F ) computation.

Sediment Transport and Morphodynamic Change Model

In the present study the Lund-CIRP model available in SMS is used to compute bed

evolution. In this sub-model, the sediment transport properties and transport rates are calculated

at the cell centers. After transport rates are calculated by the Lund-CIRP formulae for all the cells

in the domain, they are mapped back to the cell faces such that x-directed rate is located on the

left face center and the y-directed rate is located on the bottom face center. These instantaneous

transport rates are calculated at the sediment transport time step sedt and instantaneous rates

averaged over the morphologic change time step are evaluated at the time step morpht . The Eq.

(8) is then solved for every cell by means of forward Euler scheme to compute the bed changes

over the time period morpht . The implementation of the model is explained in Buttolph et al.

(2006).

MODEL APPLICATION

Since the wave and sediment transport models are verified and validated before (Ding and

Wang, 2006), accuracy of the hydrodynamic model is investigated here and presented below.

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Then the coupled model is applied to a severe storm surge attacking a hypothetical coast with an

inlet.

Flow over a Triangular Obstacle

This test is carried out to examine the ability and accuracy of the hydrodynamic model to

simulate flows over a dry and irregular bathymetry. The experiment was conducted under the

supervision of J. M. Hiver at the Laboratoire de Recherches Hydrauliques at Châtelet together

with the University of Bruxelles (Belgium) (see Brufau et al, 2004). The physical experiment

includes complex hydraulic properties like a dam break flow, transitions between wet and dry

beds and hydraulic jump flows over an obstacle. The channel geometry is illustrated in Figure 3.

The experiment consists of a reservoir with water up to 0.75 m contained by a dam at 15.5x m

and a dry bed downstream within a rectangular channel of length 22.5 m. A symmetric triangular

obstacle (6 m long, 0.4 m high) is situated with its peak located at 14 m downstream the dam. A

number of gauge points located on the bed of the channel at different distances from the dam are

also shown in Figure 3 and are at 4 m (G4), 10 m (G10), 11 m (G11), 13 m (G13), and at 20 m

(G20). The gauge point G13 is located at the vertex of the obstacle and therefore is a critical

point. At these gauge points water depth evolutions are measured. The fixed boundaries are walls

except the free outlet and the Manning’s roughness coefficient is taken as 0.0125 -1 3m s , a value

which has been supplied by the experimentalists (Brufau et al, 2004). In the computation, 0.1 m

square size grids and 0.01t s are used. The water depth variations with respect to time at the

four gauge points are shown in Figure 4 (a-e). It can be seen that the water depth evolution and

the prediction of arrival time of the wave to the corresponding gauge points are quite comparable

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with the experimental observations. The prediction of the transitions from wet to dry at the gauge

point G13 is also well predicted. Thus it can be concluded that the present model accurately

simulates the flow characteristics observed in complex laboratory experiments.

Short-Term Morphodynamic Simulation Driven by Storm Surges and Waves through an

Tidal Inlet Channel in A Coast

During severe storm or hurricane, the barrier islands along a coast get seriously affected.

The barrier island may be over washed and/or breached. Inlet channel may be developed through

the breached area. The flood water passes through inlets and floods the bay area. At the same

time morphology of the coast also changes drastically. This may result in undermining the

foundation of coastal structures, ebb and flood shoal formation. Sometimes existing navigation

channel is refilled by migrated sediments. The study of hydraulics of such flow field and

morphological changes are important for engineering design of inlet structures. The present

model is applied to such an idealized coast with an inlet of 30 m wide. The coast is designed in

such a way that it represents the basic geometry, inlet entrance configuration, offshore slope,

wave and storm forcings at a medium size inlet. Figure 5 shows the flow domain with bathymetry

varying from 30 m at offshore to dry bay.

The inlet channel section is enlarged and is shown separately in the same Figure 5. The

wave-current-morphodynamic processes in the coast are investigated when a severe storm surge

attacks the coast. A rectangular mesh grid is generated for the flow domain with the help of SMS

grid generator with resolution 25 m in the channel and 50 m in the offshore. The three processes

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are simulated sequentially by the steering option of the SMS package. An irregular spectral wave

with significant wave height 3.5 msH , a peak period 9 spT , and mean incident angle 30

(JONSWAP spectrum 3.3 ) is imposed at the offshore boundary. Superimposed into a M2

tide with amplitude of 0.5 m above the mean sea level, a storm surge shown in Figure 6 with a

peak of 10.0 m is also imposed at the offshore boundary. The other ocean boundaries are

specified as free flow boundaries. The radiation stress gradients calculated from the specified

wave is updated at an interval of 3 hrs. The uniform median grain size (d50) in the coast is

specified as 0.2 mm. The Lund-CIRP formulations as presented before are used to compute the

total sediment transport rate and the bed evolution is calculated using Eq. (8).

In Figures 7 and 8, the results are reported at two time intervals at 19 hrs and 27 hrs, respectively.

At 19 hrs, flood tide passes through the inlet, at 27 hrs ebb tide leaves the bay back to the sea.

Both the flood and ebb tides induce strong velocities. Figure 7(a) shows the morphological

changes and (b) velocity vectors with streamtraces at 19 hrs (flood tide) for a coastal area around

the inlet. Figure 8(a) shows the bed elevation changes and (b)velocity vectors with streamtraces

during the ebb tide at 27 hrs (ebb tide). The strong velocities cause significant erosion and

develop scour hole at the entrance of the inlet and deposition at the bay side. Thus a flood shoal

can be created in the bay which is frequently observed in a real coastal inlet. At 27 hrs, during

the ebb tide, flow passes from the bay to the offshore direction. At this instant, bed erosion takes

place at the entrance of ebb tide in the bay side and deposition takes place along the inlet channel.

Thus the scour hole created during the flood tide is refilled and ebb shoal is formed at the

offshore side (see the offshore in Figure 7(a)). The computed bed profiles at different times along

a transect A-A, shown in Figure 5, is plotted in Figure 9. It is clearly shown that the severe

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erosion happens in the entrance of the inlet and a scour hole is formed; the flood shoal and the

ebb shoal are developed in the channel and the entrance of this tidal inlet. Though the results

shown in this study need further investigations to determine the accuracy of the model, it can be

stated that the present model can be applied to study wave-current-morphodynamic processes.

The shock capturing property of the hydrodynamic model helps to simulate the complex flow

scenario in the inlet when attacked by a severe storm.

Overflow and Overwash Driven by Storm Surges and Waves In a Coast with an Inlet

A coast is generally protected by levees or barrier islands and storm surges are allowed to

pass through the inlet channel. However, during extreme hydrological conditions, the inlet

channel may not be able to divert excessive flow and hence water may overflow the levees or

barrier islands. During overflow, the top portion is over washed by currents induced by storm

surges. As a result, levee crests may be eroded by the overwash flow. Such flow condition and

the corresponding morphological change are simulated herein. The flow and wave conditions are

kept same as the previous example only the geometry is modified to represent levee in between

ocean and bay (Figure 10). To demonstrate an overwash current by the surge tide as shown in

Figure 6, the crest level of the levees adjacent to the inlet was lowered to approximate 2.0 m

above the mean sea level, which is higher than the flood tide level (i.e. 0.5 m above the mean sea

level). It is assumed that the levee is formed by coastal sands with the same grain size as that on

the sea bed (i.e. d50 = 0.2mm). As the computed morphological changes around the coast and the

inlet are presented in Figure 11, the storm surge and waves are allowed to overflow the levees,

erode the levee crest, and deposit the sands to the toe of the levee at the bay side. This pattern is

clearly seen at t = 19 hrs in Figure 11 (a). At t = 27 hrs, a small portion of the sediments are

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carried back to the ocean side but the transport rate is not significant (Figure 11 b). Since the

overflow and overwash happen over the levees, the flows through the inlet become weaker than

those in the above-mentioned case (e.g. Figures 7 and 8) in which neither overflow nor overwash

occur over the crest of the levees. Therefore, the rate of erosion and deposition in the inlet

channel in this is not as significant as the previous one. Inside the inlet channel, both sides of the

inlet are eroded. After the ebb tide, an ebb shoal appears at the ocean side close to the entrance of

the inlet channel (Figure 11(b)). The computed bed profiles are observed during the simulation at

three transects shown in Figure 10 and are plotted in Figures 12 (a-c). The bed profiles along

transects A-A and C-C shown respectively in Figure 12 (a) and (c) indicate that by the overflow

and overwash the erosion on the levee crests and the depositions at the toe of the levee are

developed in both the north and south sections of the levee. Inside the inlet channel (Figure 12

(b)), the bed elevation changes show that a small flood shoal and an ebb shoal are created by the

storm surges and waves. The bed morphology pattern predicted by the model is qualitatively

representative. However, the model should be validated with real world data.

CONCLUSIONS

A numerical model for systematically simulating wave-current-morphodynamic processes

in two-dimensions with a focus on modeling overflow and overwash, as well as the

corresponding morphological changes is developed. The two-dimensional shallow water

equations are solved by shock-capturing finite volume method considering the effects of short

wave-averaged radiation stress, wind stress, Coriolis force and strong bottom irregularities. The

hydrodynamic model is coupled with CMS-Wave (Lin et al., 2008) and morphodynamic models

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of SMS package (Zundel, 2000; Buttolph et al., 2006) in order to simulate wave deformation,

transformation and morphological changes in coastal/tidal inlets and their adjacent coasts. The

accuracy of the presently developed hydrodynamic model is investigated by solving an

experimental test case in which a dam-break flow was generated and an overflow over an

obstacle in stream was measured. The model results closely follow the experimental observations

on the propagations of the supercritical dam-break flow and the overflow over the obstacle. The

applicability of the model is tested by simulating a storm surge attacking a medium size idealized

coast with an inlet. The successful simulations show that the storm surge causes significant bed

erosion, deposition, overflow, over wash and formation of flood and ebb shoals. The overall

results seem to be satisfactory and representative for preliminary investigation of applicability of

such a process based numerical model and further study is required to examine the predictive

accuracy of the model.

ACKNOWLEDGEMENTS

This work was a product of research partially sponsored by USACE-ERDC’s Coastal and

Hydraulics Laboratory (CHL) under contract No. W912HZ-06-C-0003 and the National Center

for Computational Hydroscience and Engineering (NCCHE) at the University of Mississippi,

USA. The first author had conducted this study in the NCCHE from 2008 to 2010.

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Figure 1. Definition sketch for bed topography, water depth and water surface elevation

Figure 2. Discretization of a finite volume cell: (a) Interfaces (b) numerical fluxes

x

y 1 2,i j

, 1 2i j

1 2,i j

, 1 2i j

,i j

x

y *1 2,i jE

*, 1 2i jG

*1 2,i jE

*, 1 2i jG

,i j

(a) (b)

23

Figure 3. Geometry and gauge locations for the experimental and model set up

24

Figure 4. Computed and measured water depth variations at stations (a): G4; (b): G10;

(c): G11; (d): G13; and (e): G20

G4 G10

G11 G13

G20

25

Figure 5. Idealized coast with initial bathymetry

Ocean Bay

Inlet

26

Figure 7: Computed results at t = 19 hrs (a) Bed elevation change (b) Velocity vectors

(a) (b)

Figure 6: Storm surge imposed at offshore boundary

27

Figure 9: Computed bed profile along A-A at different times

-14

-12

-10

-8

-6

-4

-2

0

2

4

3500 4000 4500 5000 5500 6000 6500 7000 7500

Be

d e

leva

tio

n a

lon

g A

- A

[m

]

Distance [m]

Arc 1 Datasets\Simulation, Bed at 15 hrs

Datasets\Simulation, Bed at 20 hrs Datasets\Simulation, Bed at 25 hrs

Datasets\Simulation, Bed at 30 hrs Initial Bed

(a) (b)

Figure 8: Computed results at t = 27 hrs (a) Bed elevation change (b) Velocity vectors

(a) (b)

28

Figure 10: Idealized coast with initial bathymetry

Ocean Bay

Inlet

29

(a)

(b)

Figure 11: Bed morphological changes at (a) a flood tide, t = 19 hrs, and (b) at an ebb

tide, t = 27 hrs

Deposition

Erosion

Ebb Shoal

30

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4600 4800 5000 5200 5400 5600 5800 6000

Be

d e

leva

tio

n a

lon

g A

- A

[m

]

Distance [m]

Arc 1 Datasets\Simulation, Bed profile at 15 hrs

Datasets\Simulation, Bed profile at 20 hrsDatasets\Simulation, Bed profile at 25 hrs

Datasets\Simulation, Bed profile at 30 hrs Initial Bed

(a) A-A

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

4000 4500 5000 5500 6000 6500 7000

Be

d e

leva

tio

n a

lon

g B

- B

[m

]

Distance [m]

Arc 2 Datasets\Simulation, Bed profile at 15 hrs

Datasets\Simulation, Bed profile at 20 hrsDatasets\Simulation, Bed profile at 25 hrs

Datasets\Simulation, Bed profile at 30 hrs Initial Bed

(b) B-B

31

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4600 4800 5000 5200 5400 5600 5800 6000

Be

d e

leva

tio

n a

lon

g C

- C

[m

]

Distance [m]

Arc 3 Datasets\Simulation, Bed profile at 15 hrs

Datasets\Simulation, Bed profile at 20 hrsDatasets\Simulation, Bed profile at 25 hrs

Datasets\Simulation, Bed profile at 30 hrs Initial Bed

(c) C-C

Figure 12: Computed bed profiles at different times along transects (a) A-A, (b) B-B,

and (c) C-C as shown in Figure 10