Luận văn application of xbeach model to study sedimentation of lach van river mouth

6 Bathymetry of the small domain Figure 4.7: Wave field of the small domain, RSE wave scenano Figure 4.8; Flow field near the river mouth, H;3E Wave sC€IAHO...ciesiisvere Figure 4.9: Se

Declaration

1 hereby declare that is the research work by myself under the supervisions of

Dr Nguyen Quang Chien and Assoc Prof Dr Tran Thanh Tung The results and conclusions of the thesis are fidelity, which are not copied from any sources and any forms ‘The reference documents relevant sources, the thesis has cited and recorded as prescribed The matter embodied in this thesis has not been submitted by

ime for the award of any other degree or diploma

Hanoi, June 2018

Nguyen Quoc Anh

Acknowledgements

I would like to express my sincere thanks to professors and lectures at Department of Marine and Coastal Engineering of Thuy Loi University and professors and lecturers

of the Niche programme for supporting me throughout my study progress

Finally I would like to express my special appreciation to my friends and colleagues for their support, encourage and advices The deepest thanks are expressed to my family member and [lang Iu Chun for their unconditional loves

TABLE OF CONTENT LIST OF FIGURES

2.1 Numencal method cà iceoceiiiieeeeree

2.1.1 Overview of One-dimensional medelling

2.2 Computing sediment tansporl

2.2.1 Soulsby Van Rijn equation (1997)

2.2.3 Formulation in Delli3D model

2.3 Computing method of X-beach model

2.3.1 The Coordinate system and Grid setup

2.3 2 The short wave action balance

16

2.3.6 Bcd shoar stress cquations co ¬-

2.4 Selecting a Model for Lach Van river mouth sessesessesssneestnineeietnnetinee 31

CHAPTER 4 PROPOSED MODELING STUDY AND EXPRCTED ISSURS 41

4.6Hydrodynamie and morphological simulation in sinall doain 48

LIST OF FIGURES

Figure 2, 1 Blement volume on equilibrium beach profile .isenennninanninnnetneenane 8 Figure 2 2 Change in shoreline positions after simulations 1 (upper) and 2 (lower) in

Figure 2 3 Example of a curvilinear grid (Delft3D-ELOW User Manual, 2014) 13 Figure 2 4 Mapping of physical space to computational space (Delft31-FL_LOW User Mannal

+igue 2 5 Difference grid im x„y space (Ahmad, 8 1999) ccisenennninnemnnnenaneensne 4 Figure 2, 6Flow đỉagmm of Sonline” mọiphodynamic model selup (Roelvik, 2006), 16 Figure 2 7 The staggered grid showing the upwind mothod of setting bed load sediment

transport components at velocity points (G.R Lesser etal., 2004) cớ

Figure 2 8 Grid staggering, 3D view and top view (Delft3D-FLOW User Manual, 201 4) 22 Figure 2, 9 Rectangular’ Curvilinear coordinate system of XBeach (Xbeach manual, 2015) 23 Figure 2 10 Principle sketch of the relevant wave processes (Xbeach mammal, 2015) 21 Figure 3 1 Depth contours digitized from nautical chart (Chien 2017) 234 Figure 3 2 Beach profile constructed from various bathymetry data source (measured in

‘Vietnamese technical guideline for sea dike design STRM30, and GEBCO) (Chien N.Q, and

Figure 3 3 The position of points extracted wave in model WaveWatch

Figure 3 4 Wave roses of the periods Feb-2005 — Jan-2011 (left) and Eeb-:

Figure 3, 5 Relationship between wave height and peak period; separation between wind seas and swells is indicated (Color shades shows density of the data points.) (Chien and Tung

Vigure 4.2 Layout of the modeling domain

Figure 4 3 Jonswap wave speotnam for HO 1.28 rand 0.761 44

igure 4 4 Computed wave field in big domain for the case of ENE waves

Figure 4, 5 Computed wave field in big, domain for the casc oŸ ESE wavos Figure 1 6 Bathymetry of the small domain

Figure 4.7: Wave field of the small domain, RSE wave scenano

Figure 4.8; Flow field near the river mouth, H;3E Wave sC€IAHO ciesiisvere Figure 4.9: Sediment transport near the river mouth, ESE wave scenario

Figure 4.10: Seabed clevation change near the nyer mouth, ESE wave scenario

igure 4.11: Wave ñeld of the small domain, ENH wave soenario

Figure 4.12: Flow field near the river mouth, ENE wave scenario

Figure 413; Sediment transport near the river mouth, ENE wave 3GGIAL10 co igure 4.14: Seabed elevation change near the river mouth, INI wave scenario

vi

LIST OF TABLES

Table 3 | Extreme water level for location 19°01°N, 105°37°E

Table 4 1 Parameters of the big domain model

‘Table 4 2 Comparison between simulated result and observed cata

Table 4 3 Parameters of the small domain model

Table 4 4 The comparison of results

40

45

45

538

ABSTRACT

‘The deposition at the river mouth is a phenomenon interested in recent times on the world Because, it obstructs the economic activities, transportation of people living in

the vieinily

Nowadays, scientists have done a lot of research to find out the cause of sedimentation

at the river mouth They have carried out ficldwork and research methods on the model Lhe advantage of modeling is less costly to mvest Besides, updating situation changes and making status prediction by an image is very quickly and easily in interpreting the information With simple studies of the 11) model, researchers have produced results on shoreline dynamics, areas of flooding, ete Ilowever, recent studies using 2D models have made research results more meaningful This is due to the advantages in studying dhe lopography development, which based on the parameters of wind and sand There are many models used in the warld (Delft, Swan and XBeuch)

In the framework of the thesis, a Xbeach model is used to simulate the bottom

evolution of Tach Van river mouth in Dien Chau distinct, Nghe An proviec

Parameters aud results of the model will be tested with actual measurement data at the Tion Neu station; finally, the resulting of the bottom topography is stated through the sediment transport in here By using Xbcach model, the author wants to convey the advantages and disadvantages of the model, the ability to apply for specific conditions

CHAPTER 1 INTRODUCTION

Status of Lach Van river mouth:

Lach Van river mouth is located at (18.98°N, 105.62°F), belonging to Dien Chau

District, Nghe An province, Vietuain ‘this is a small and narrow river mouth (the mean width approximates 500 m), which is a final point of Bung river (a small river) This arca is a anchorage of 500 fishing boats, The anchoring, system for avoiding storms is built in 2003 ‘the river mouth has a part of navigation value, although not worthy because the river is 48 km long

Predicting the morphological change of Lach Van river mouth when the natural and human [actors affect to study area This posilion is an imerseciion of a small river and

sea, The river was named Bung and is being deposited at the river mouth, The two side

of the river mouth is a bow-shaped beach of 24k in length and blocked by 2 two rock

headlands

Ilowever, the deposition of Lach Van estuary has been complicated and has had a greal impact on the activities of the fishing Mcct of Dion Chau districl According Lo a

report in the Lao Dong newspaper [article posted on 18/4/2016], "Lach Van river

mouth increasingly exhausted, large fishing boats can not go in and small boats only

travel at high tide This has made it difficult for fishermen; many fishing vessels have

been stranded "Normally, the water level must be from 1.6 to 1.8 m, but now the

water level is just 1.2m" This topography situation is still ocourring in 2017 with the serious level of deposition

The cause of evolution in Lach Van river mouth:

According to the survey trom different sources from 2003 to 2009, the analysis

showed thal the nver mouth area has accretion - erosion silualions Wilh this river

1nouth, the main reason for sedimentation is due to the waves that cause the longshore

currents carrying sediment to the bottom sea Through the collection and processing of data, particularly data wave, stream sediment moves from north to south with a total

measurement about 10° m’/year

bà

Some factors related to economic activities such as the construction of inrigation reservoirs, upstream hydroelectricity, river works, aquaculture, river mouth tourism,

material exploitation, cic Tt also contributes to camplex developments,

Nowadays, the phenomenon of river mouth acoretion is complicated, many fishing

boals are sLuck This has great impacied the activities of Dien Chau distnet fishermen

‘rhus, a request to adjust the river mouth is very urgent,

- Analysis on the coastline evolution of Lach Van coal

- ‘he rationale and usability of XBeach model, for sediment transportation evolution and bed layout erosion

= Proposal of some scenarios about boundary conditions o computed

- Applying XBeach model to predict morphology changes

1.4 Literature review

The river mouth is where the sea and river meet There exists a complex dynamic rogime influcneed by inary faclors such as: waves, tidal, river flow snd the hunzan impact Thus, the sediment transport is difficult to estimate This leads to the fact that morphological changes carmot be accurately simulated

PA, Huong and V/T, Ca [1] showed calculation results identifying some hydrodynamic characteristics affevting Ihe morphology of Da Rang river mouth, Phu Yen province The hydrodynamic factors are dominated by:

= Flow regime from upstream river,

- The quantity and goological nature of sediment from the river to the sca through the river month, tidal cycle and amplitude, volume of tidal prism, coastal

currents duc to simultaneous ¢f{cets of waves and winds

In recent scientific studies, the researchers have made new strides in the simulation of natural phenomena by mathematical model combined with geographic fealures Delf31) model [2] analyzed dynamic factors and then verify the developmem of the river delta suggested by the geologists [3] In the case of the estuary, A Dastgheib et

al |4) have simulated many years of morphology for river mouth, tidal bay They used two-dimensional (2) model (Delft3L) + SWAN) to simulate the transformation of a sand spit toward the river mouth In addition, for the effects of the wind, Nardin and Fagherayyi [5] investigated the imleraction of external foree on the movement of sand

bar at the river mouth

Related to specific types of geomorphology, J.H Nicnhuis et al., [6] developed a computational model for straight coastlines, attached with a forecast of changes in the river moulh Besides, MD Hurst et al [7] has focused on modeling for concave

coastlines,

Today, the sediment calculation and morphology evolution have been performed by

many numerical models, including both 1D and 2D models Among them, 1D model

has one of the advantages in terms of time and money spent Ilence, the results of ID

is easily Lo consult in a simple way, and have a prediclable model even it, has some

wrong in calculation Reversely, although 2-dimensional model helps provide more specific detail in the plan view, but it is considered to be difficult to setup, time consuming (o Tun, have unstable and unreliable results [8]

In Vietnam, the studies in recent years show that scientists are using advanced methods which focused on quantilalive rather than qualilative, The numerical modeling is used in the study of sedimentation in the river mouth (Nguyen X Hien et

al [9]; Truong V Bon [10]; Vu T Thuy et al [11] Le D Thanh et al [12] has synthesized theoretical foundations and applied 2D model to calculate the geomorphological development of the three estuaries in central Vietnam (including:

Tu Hicn, My A, Da Rang.) In addition, Thuy loi university has many studies on the morphology of the coast zone Tran T Tung et al., [13] has studied the erosion -

slabihzation mecharism of extuanes Vu M Cat, Pham Q Sor [14] cvalualed the

change in shoreline shape during, the long period for many coast zone, river mouth in Vietnam Remarkably, In Lach Van nver mouth - study area Nguyen Q Chien Tran

T Tamg [15] used a one-hne model to estimale the change i local coasiimc

Tlowever, in fact, these studies are mostly interested in coastal erosion Conversely, there are vory little averotion estuaries are being studied and sought to overcome (am Quan river mouth, in Linh Dinh province) ‘thus, conducting research

for river mouths being accreted such as Lach Van is essential

15 Rescarch methods

© Collecting basic data at measuring station and natural characteristics

© Numerical Modeling; the use of XBeach model to predict morphography

evolulion

e Consulting experts

Conceptual framework of the study sedimentation of Lach Van river mouth:

Dox eollectan: E} „+ | Dananalyss => Gel | L— „7 |@atanhmaẻ Venkednai

¥igurel 1 Schematization of KBeach model

CHAPTER 2 COMPUTING METHOD

2.1 Numerical method

Numerical modeling is ari important Loot lo simulate the evolution of the shoreline in

general and the problem of sedimentation in particular In general, there are three types

of numerical models used:

- A shoreline model, in which shore location is monitored during the

simulation period

- A cosslal profile model, which model the crass-shore beach profile along anormal toa straight or gently ourving coastline

- A-coasial area model, in which the sea bed elevation in the break zone is

monitored and the shoreline interpolated on the ground surface as an elevation contour equal to the mean sea level (0 m)

The shoreline model is a one-dimensional model having a relatively simple structure

and resulting in faster and more direct results A long sequence of wave heights and directions is used as input Waves are refracted in from deep water to the surf zone, and cause longshore sediment transport al cach of points along the coastline Coastal profile models are more computationally demanding than shoreline model ‘This results

in an updated shape of cross-shore battom profile The process is repeated for each

successive wave voudilion The coastal area mode] not only uses the location of

shoreline, but also more detailed data is needed, especially topography parameters The morphodynamic evolution of the seabed is calculated by a two-dimensional sediment budget equation There are perspectives that recommend the use of coastal area models rather than shoreline madels, especially in the context of improved

topography data in recent years

21.1 Overview of One-dimensional modelling

The development of the ID morphology cquation assumes that a beach profile of constant shape slides along, a horizontal base located at closure depth d,, as in ligure

21

Figure 2 1 Element volume on equilibrium beach profile

Closure depth is the depth at which beach profiles are not changed by normally occurring wave conditions

2.1.2 One-line Model

Judgement on shoreline change can be made only after specifying an active profile

height (B + hx) Along the local coastline, where the beach consists of fine sand, a

typical berm height B ~ 0.5 m is observed with the closure depth (h+)

The coastline evolution is governed by the sediment balance:

An application of one-line model to study shoreline change near Lach Van River

mouth (N.Q Chien and T.T Tung [15]) is shown in Figure 2.2 The position of coastline is relative to initial position of zero The accretion on two sides the river

mouth is clear.

3p 2011 2012

Figure 2, 2 Change in shoreline positions after simulations 1 (upper) and 2 (lower)

in comparison with observed data

For Lach Van river mouth, the basic cause for sedimentation is due to waves causing

longshore current bringing sediment accretes at the river mouth,

The river outflow seems to play a minor role in local shoreline change, though infrequent river floods should cause short term changes of the coastline

The shoreline orientation at the river mouth is not accurate, hence the simulated change in coastline is not well represented The assumption of an identical beach

profile shape along the coast leads to errors in longshore transport (LST) calculation

One-line model (N.Q Chien and T.T Tung [15]) also accounts for the potential net

LST, which mostly directs southward with a rate of ~10° m*/yr This rate has

decreased during the years 2011-2016 If this amount of sediment (~10° m3/yr) is

completely deposited, then accretion at the river mouth (area~1 km?) will occur at a

rate of ~10 cm/yr

2.1.3 Some limitations in considering changes in bottom topagraphy when using One-dimensional model

‘The 1 modeling can perform well if the watercourse is simple, with limited topographic data and time-efficient solution algorithm IIowever, it has the following

limitation of computational Mexibility

Water level and discharge information is only available at points where cross

seclions are defined This 1s @ limilalion since distance belween cross sections

varies at different locations

1-D models do not perform well in areas where lateral flow plays an important role in (ood wave propagation Thus, i is difficult lo Ginding the exact palh of

flood wave

Model is nol capable of dealing with flooding and drying TL means drat the

researching arcas would be allowed to be flooded or remain dry, before

performing simulation

One-dimensional models must average properties over the two remaining directions Such as, the inability of one-dimensional unsteady models to

simulate supercritical flow

2.1.4 Overview of multi-dimensional hydrodynamic modelling

In many watercourses with complex bathymetry features, the long wave

propagation is not a one-dimensional phenomenon To accurately caplure the

effect, a two-dimensional modeling approach is needed

‘The following basic equations for the conservation of mass and momentum are

used to describe the flow and water level variations in two- dimensional model:

‘The continuity equation

a | op 3g

đt cử ủy -

X-momentum equation

Where: h(x,y.t) = Water depth (m)

Z(x,y,t) = Surface elevation (m)

p.q(zy.t) = Flux densities in x/y directions (m*/s/m)

(x,y) = Chezy resistance (m'/s)

g = Acceleration due to gravity (m/s*) fv) = Wind friction factor

Q(xy) = Coriolis parameter, latitude dependent (S*)

P,(@y.t) = Atmospheric pressure (kg/m/s*)

The model can be used for free surface flows, the simulation of hydraulic and related phenomena in rivers, lakes, estuaries, and coastal areas where the difference of characteristies holween water layers ean be neglecled Typical application arcas arc modeling of tidal hydraulics, wind and wave generated currents, storm surges, dam

break and flood waves

‘rhe model can simulate two types of flow regimes: subcritical and supercritical flow MIKE 21 requires at least two grid cells in the direction of flow to correctly resolve transition from sub- to supercritical flow at a control section such as a weir The water levels and flows are resolved by operation formulas on a rectangular grid covering the solution domain when provided with the bathymetry, bed resistance coefficients wind field, and hydrographic boundary conditions The modeling lool is capable of handling convective and cross momentum, bottom shear stress, wind shear stress at the surface, barometric gradients and Coriolis forces Therefore, it can deal with flooding and drying The modeling systema solves the fully lime-dependent non-linear equations of continuity and conservation of momentum The outcome of the simulation is the water

level and fluxes tn the computational domain

‘The hydrodynamic module resolves the unsteady shallow-water equations in two (depth-averaged) or three dimensions The system of cqwations consists of the

horizontal momentum equation, the continuity equation, the transport equation, and a

turbulence closure model The vertical momentum equation is reduced to the hydrostatic pressure relation as vertical accelerations are assumed to he small compared to gravitational acceleration and are not taken into account Hor example, the

DELFT3D-FLOW model is suitable for predicting the flow in shallow seas, coastal areas, and estuaries Jl aims to model Gow phenomena of which the horizontal length

and time scales are significantly larger than the vertical scales

In simulations including waves, some models c.g, Tielf3D have the hydrodynamic equations written and solved in a Generalized Lagrangian Mean (GLM) reference

Came

2.1.5 Solution procedure

Numerical modcls are bascd on finite difference or finite vohame methods, To discretize the shallow water equations in space, the model area is covered by a reclangular, curvilinear, or spherical grid TLis assumed that the grid is orthogonal and well structured In this arangement, the water level points (pressure points) are defined in the center of a (continuity) cell; the velocity components are perpendicular

to the grid cell faces where they are silualed

with the variables defined on a space staggered rectangular grid as shown in Figure

Figure 2 5 Difference grid in x,y space (Ahmad, S 1999)

A 'fractioned-step! technique can be combined with an Altemating Direction Implicit

(ADD algorithm is in the solution to avoid the iterative computations Second order accuracy is used through the centering in time and space of all derivatives to

appropriate evaluated At each time step, a solution is first calculated in the x-

momentum equations, and then a similar solution in the y-direction

2.1.6 Modeling seabed change

As a sediment balance equation, the Exner equation is used to simulate 2D evolution

Where n is the (constant) sediment porosity and q, and qy are the bed-load sediment

transport fluxes in the x and y directions

And then, in order to quantify the erosion, we also use the map of "elevation change"

compared to the original:

AE = Zaye — Fạq=m,

CO

Basic characteristic of a coastal morphodynamic in Kbeach model is a consideration

the bottom of research areas being invariant of sediment transport:

32s

‘Lhus, the bed load sediment is considered closed boundary, aloug, with the open boundaries Besides, the hydrodynamic processes impact to the sediment and make

change of the elevation of bed This change in turn affects the flow condition So that,

hydrodynamic and morphologic processes interact with each other

Tnteraction between hydrodynamic and morphological computation is constituled in the Xbeach model with a repetition circulatory The processes are the calculation of flow field taking place first and sequence, the rate of sediment transport is calculated

Then, using the Exrior equation Lo assess the balance of sediment, il can to estimate the

change in bed elevation (Az,) in an intemal time (At) ‘Ihus, the bed elevation is

changed to (2y + 42) which effects the flow depth h

This process is repeated to makes the iteration in model calculation However, the

bathymetry changes very small compared to change in flow So thal, il should caloulate the bathymetry once when model rens a number of flow timestep Sediment tansport, and bollom updating are calculated al the same time steps as the Mow field Besides, the bed clevation will update after scdiment accumulated m a number

timestep Then, the new update of bed elevation will change the characteristics of flow; take place a new balance of sediment transport and bogin a new cycle computation.

Transport Bed change

Figure 2 6 Tlow diagram of “online” morphodynamic model setup (Roelvink, 2006)

There is a difference in time scale between flow and morphology, a coefficient should

be considered the “morphological factor" So that, the change in bed level calculated in the model multiplied morphological factor by n ‘Ihis ‘online’ method has to make short-term processes such as inchiding various interactions between flow, sediment

‘unimportant’ terms or fluid properties), or the use of empirical correlation,

- ‘Two-dimensional models must assume depth average flow properties Such as, the ‘water-column’ effects of two-dimensional models

- Limitation in formulation is imposed because to estimate the forces acting on

each fluid component, such as viscous shear stresses and bed friction For example, the water column is affected by a viscosity caleulation when the vertical length scale approaches or cxeeeds the horizontal scale

A two dimensional model is different to implement a Manning’s roughness on the vertical bottom Commonly, roughness is only included on the plan of the

gird So thal, the changes of bottom shape and direction Additionally,

Manning’s xoughness coefficient was developed for one-dimensional flow

motion only

Many of the imitations imposed by ar on two-dimensional models are relaled

to depth, such as the hydrostatic pressure distribution or shear forces

2D information on surface elevation at each grid point is necessary

Due to detailed description of topography and fully two-dimensional equations

of continuity and momentum, 2-D models require significantly more time to setup and mun

A fine spatial resolution (dx) can be used that makes computing slow and requires a lot of computer memory

The 2D Saint Venant equations are also commonly known as the shallow water equations, and are based on the assumplion that he horizontal Fength scale is

significantly greater than the vertical scale, implying that vertical velocities are

negligible, vertical pressure gradients are hydrostatic, and horivamtat pressure gradicnts are due to displacement of the free surface

2.2 Computing sediment transport

2.2.1 Soulsby—Van Rijn equation (1997)

A sediment budget reflects an application of the principle of continuity or conservation

of mass to coastal sediment The balance of sediment between losses and gains is

reflevted on Jocahzed erosion and deposition,

The sediment transport by wave and current with the long shore direction is the most dominant, Longshore sediment transport rale is usually given in unils of volume por time ‘There are four basic methods to use for the prediction of Longshore transport rate

at certain sile:

The best method is to adopt the best known date from a nearby site, with

modification based on local condition

7

- The second method is to compute the mass exchanged from data showing

historical changes in the topography of the littoral zone Some indicators of the

transport rate are the growth of a spit, shoaling patterns, deposition rates at an inlet

- The third method is to use either measured or calculated wave conditions to

compute a long shore component of wave energy flux (which related empirical curve)

- The last method is to estimate gross longshore transport rate from mean annual

near shore breaker height

Based on the wave and near shore current given in the collecting basic data part, some

formulas of empirical curve and the theory of sediment transports to calculate longshore transport rate:

Soulsby—Van Rijn [17] method is used in the calculation of sediment transport and distribution of suspended sediment based on the principle of instantaneously action of

sediment transport by wave and current combine with a bed slope

Where: qm? /s): Sediment transport unit discharge

Gee: Coefficient of verification

4z, A; Coefficient of bed load/ suspended load sediment transport

v (m/s) The long shore current velocity

D, Dimensionless factor of bed grain sediment

€ Coefficient of strength transport of sediment

% Coefficient of friction

A: The relative sediment density define by (A = fete)

Uy? The wave orbital velocity at the bed

er: The critical of wave velocity

2.2.2 Some problems need to consider when research sediment transport

Sediment transport is the essential link between the waves and currents and the morphological changes It is a strong and nonlinear function of the current velocity,

orbital motion and the sediment properties such as grain diameter bed roughness

Typically, transport is subdivided into bed load transport, which takes place just above

the bed and reacts almost instantaneously to the local conditions, and suspended load transport, which is carried by the water motion and needs time or space to be picked

up of to settle down

The useful morphological models can be made, because there are some general trends that are robust and lead to unambiguous morphological effects D Roelvink and A Reniers [18]

- Sand tends to go in the direction of the near bed current

- Ifthe current increases, the transport increases by some power greater than 1

- Ona sloping bed transport tends to be diverted downslope

19

- The orbital motion stirs up more sediment and thus increases the transport magnitude

- Tn shallow waler, the wave motion becomes asymmetric in various ways, which leads to a net transport texm in the direction of wave propagation or opposed to

it

Studies the coastal engineering for construction of coastal structures and coastline

protection need to consider:

- Long terms: Natural conditions such as marine dynamics, bed sediment composition, coastline composition, and coastal bathymetry are input data for sludying the developments of morphology of coast and river mouths

- Short terms: Geomorphology - morphodynamic is also responsible for the catastrophe caused by the charyge of the natural processes as the change of the

coastline by storms, floods or global sea level rise te

Wave breaking while propagating ta the coastal zone is the most violent process in coastal dynamic Wave breaking will produce cross shore and longshore current and sediment transport causing sea bed evolution At present, in regard to a formulation of

full motions of the fluid in the surf zone, there is not any function to model the motions, which are normally nonlinear and time depending Furthermore, water

particle acceleration in the wave motion in surf zone maybe larger than gravity

acceleration and orbital velocily is nol as small as phase velocity [19]

2.2.3 Formulation in Delft3D model

‘The quantity of each sediment fraction available at the bed is computed every half time slep using situply for the control volume of each computational cell This simple approach is made possible by the upwind shift of the bed load transport components

[20]

Suspended sediment transport

‘the net sediment changes due to suspended sediment transport is calculated as

fufows

As” = fyop (Sink — Source )At (2.12)

The correction for suspended sediment transported below the reference height, a, is taken into account by including gradients in the suspended transport correction vector,

Ao = is the area of the computational cell at location (m,n);

SE as See = are the suspended sediment correction vector components in the

uand v directions at the u and v velocity points

Ax) Aye = are the widths of cell (mn) in the x and y directions,

respectively

Bedload sediment transport

Similarly, the change in bottom sediment due to bed load transport is calculated as:

beạà ““ÍMoR gựmA=ĐẠx (a1) _ gh) atom) Acmn)

(2.14)

Where $;"\/.; Sy = the bed load sediment transport vector at the u and v velocity

points, respectively

To ensure stability of the morphological updating procedure, it is important to ensure a

one-to-one coupling between bottom elevation changes and changes in the bed shear

stress used for bed load transport and sediment source and sink terms This is achieved

by using a combination of upwind and downwind techniques as follows:

- Depth in water level points is updated based on the changed mass of sediment

in each control volume

- Depth in velocity points is taken from upwind water level points

- Bed shear stress in water level points (used for computing bed load sediment

transport and suspended sediment source and sink terms) is taken from

downwind velocity points

- Bedload transport applied at velocity points is taken from upwind water level

points

Key

Vetoctty point Death point edt! tacspont

Figure 2 7 The staggered grid showing the upwind method of setting bed load

sediment transport components at velocity points (G.R Lesser et al., 2004)

Figure 2 8 Grid staggering, 3D view and top view

(Delft3D-FLOW User Manual, 2014)

n

2.3 Computing method of X-beach model

2.3.1 The Coordinate system and Grid setup

© The orientation of girds:

‘XBeach uses a coordinate system where the computational x-axis is always oriented

towards the coast, approximately perpendicular to the coastline, and the y-axis is

alongshore This coordinate system is defined in world coordinates The grid size in x-

and y-direction may be variable but the grid must be curvilinear Alternatively, in case

of a rectangular grid (a special case of a curvilinear grid) the user can provide

coordinates in a local coordinate system that is oriented with respect to world

coordinates (Xw, Yw) through an origin (Xeris Yori) and an orientation (a) as depicted in

Figure 2.11 The orientation is defined counter-clockwise w.1.t the xy-axis (East)

© The type of grid cells:

The grid applied is a staggered grid, where the bed levels, water levels, water depths

and concentrations are defined in cell centers, and velocities and sediment transports

are defined in u- and y-points at the cell interfaces In the wave energy balance, the

energy, roller energy and radiation stress are defined at the cell centers, whereas the

radiation stress gradients are defined at u- and v-points

Velocities at the u- and v-points are denoted by the output variables (uy) and (vy)

respectively, velocities u and v at the cell centers are obtained by interpolation and are for output purpose only The water level, (z,), and the bed level, (z,) are both defined

positive upward (uy) and (vy) are the u-velocity at the v-grid point and the v-velocity

at the u-grid point respectively These are obtained by interpolation of the values of the

velocities at the four surrounding grid points

The model solves coupled 2D horizontal equations for wave propagation, flow,

sediment transport and bottom changes, for varying (spectral) wave and flow boundary

conditions

Short wave envelope

Figure 2, 10 Principle sketch of the relevant wave processes (Xbeach manual, 2015)

Important to note that all times in XBeach are prescribed on input in morphological

time If you apply a morphological acceleration factor all input time series and other

time parameters are divided internally by morfac This way, you can specify the time

series as real times, and vary the morfac without changing the rest of the input files

2.3.2 The short wave action balance

The wave forcing in the shallow water momentum equation is obtained from a time dependent version of the wave action balance equation The directional distribution of the action density is taken into account The wave action balance is then given by:

OA ôc,A ôcyA AcgA_ Dy, + Dy + Dy

Where Dw, Ds Dy= is the dissipation processes of wave breaking, bottom

friction and vegetation

Cy, Cg = is The wave action propagation speeds in x, y, @

8 = the angle of incidence with respect to the x-axis

Sw = the wave energy density in each directional bin

h = the local water depth

k = the wave number

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2.3.3 Wave breaking

In both the mstationary or stationary case the total wave dissipation is distributed

proportionally over the wave directions with the formulation:

Hmms = the root-mean-square wave height

@ =is applied as wave dissipation coefficient

h =the water depth

2.3.4 The bottom friction element:

The short wave dissipation by bottom friction is modeled as:

3

(@.21)

Where: fy = the short-wave friction coefficient

Tyox= the mean period of primary swell waves

p= the water density

(fw) represents the water density only affects the wave action equation and is

unrelated to bed friction in the flow equation Studies conducted on reefs indicate that (fw) should be an order of magnitude (or more) larger than the friction coefficient for

flow due to the dependency of wave frictional dissipation rates on the frequency of the

motion

2.3.5 Shallow water equations:

A depth-averaged Generalized Lagrangian Mean (GLM) momentum equation is given:

Tox»Tsy = Wind shear stresses

Tyas Thy = Bed shear stresses

n= The water level

E,E.— — Thewavo Induced siressos

H;„ = The stresses induced by vegetation

‘Yo account for the wave induced mass-flux and the subsequent flow these are cast into

a depth-averaged Generalized Lagrangian Mean (GLM) formulation In such a framework, the momentum and continuity equations are formulated in terms of lhe

Lagrangian velocity (aÙ) which is defined as the distance a water particle travels in

one wave period, divided by that period

2.3.6 Bed shear stress equations

The bed Iiction associated with mean curenls and long waves is included via Lic formation of the bed shear stress ‘The bed shear stress is calculated with:

The = Gv (L161;m)2 — (+ rr)?

Thy — ŒØVzvj(1.160yme)2 — (Hy + tr}?

436)

Where: tq, by = the Eulerian velocity in x- and y- direction respectively (the

shorl wave averaged velocity observed al a fixed point)

¢y = the dimensionless bed friction coefficient

There are four ways to calculate (rp) implemented in XBeach:

- The dimensionless friction coefficient can be calenlated from the Chézy value

‘ with equation A (ypical Chévy value is in the order o[ 55 (m2 /S]:

tr sen

3 3 3

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- From the Manning coefficient (72), it can be seen as a depth-dependent Chézy value and a typical Manning value would be in the order of 0.02 (s/m!)

- From the grain size (Dgo) This formulation is based on the relation between the

(Dgo) of the top bed layer and the geometrical roughness

(2.30)

2.3.7 Wind equations

These forcing terms due to the wind are formulated as;

Tex = ‘sx = Pala PaCaW Hi | h (231)

Ty sy = Pala = PaCaW |W, | y | (232)

Where: T,= Wind stress

Pa= Density of air C4 the wind drag the coefficient

W= the wind velocity

‘The wind stress is tuned off by default, and can be tumed on by specifying a constant

wind velocity or by specifying a time varying wind file

2.3.8 Bottom updating equations

As recommend, the Exner equation is used to calculate the changes of the sediment transport due to sediment fluxes at the bed level

If calculation is applied for short-term simulations with extreme events, a morphological factor (fyor) Will be multiplied to all input time series and other time

parameters are divided internally by (finee):

2 _ _oh _ for (2x , Ody

(2.33)

This approach is only valid as long as the water level changes that are now accelerated

by morfac do not modify the hydrodynamics too much

If a scenario has an alongshore tidal current, as is the case in shallow seas, the morphological factor (fmor) Will be applied without modifying the time parameters

This means all the unchanged hydrodynamic parameters are left and just exaggerate

what happens within a tidal cycle

Besides, avalanching is a process to account for the slumping of sandy material from the dune face to the foreshore during storm-induced dune erosion is introduced to update the bed evolution, Avalanching is introduced via the use of a critical bed slope for both the dry and wet area It is considered that inundated areas are much more prone to slumping and therefore two separate critical slopes for dry and wet points are used When this critical slope is exceeded, material is exchanged between the adjacent

cells to the amount needed to bring the slope back to the critical slope

30

(2.34)

2.4 Selecting a Model for Lach Van river mouth

Base on the detail of collected data, the author chooses to perform simulations based

on the XBeach model because of the following advantages:

- ‘Two-dimensional hydraulic models are commonly used for modelling of floodplains, coastal and marine situations, where the flow path is poorly

- Model has many funotions that are resalved are wave propagation, directional

sproading, shoaling, telraclion, bottom dissipation and wave breaking, and a

roller model is included,

- These situations are usually dominant in nearshore areas of limited extent The

mean relum flow duc lo mass Mux and roller is included in the mode) and

affects the sediment transport, leading to an offshore contribution, ‘'o balance this, effects of wave asymmetry and skewness are included as well Bed slope

effects can further modity the cross-shore behavior

- ‘The transport formulations implemented into XBeach distinguishes bed load and suspended load transport It is possible to in- and exeinde these transports components here is also a possibility to compute the total bulk transport

rather than bed and suspended load separately The bed load will be calculated

if it is suspended transport On top of that this switch will have impact on how the bed slope effect will be calculated

- Lach grid cell in XBeach holds its own sediment distribution and the sediment

trausporl formulations are used differentiale between fractions Therefore, the

distribution of sediment may change over time and processes like armoring and

31