Application of xbeach model to study sedimentation of lach van river mouth

51 Figure 4.9: Sediment transport near the river mouth, ESE wave scenario .... 55 Figure 4.13: Sediment transport near the river mouth, ENE wave scenario .... An application of one-line

Declaration

I 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

me 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 Hang Iu Chun for their unconditional loves

TABLE OF CONTENT

LIST OF FIGURES v

LIST OF TABLES vii

ABSTRACT 1

CHAPTER 1 INTRODUCTION 2

1.1 Research scope 3

1.2 Research Objective 3

1.3 Research content 3

1.4 Literature review 3

1.5 Research methods 5

CHAPTER 2 COMPUTING METHOD 7

2.1 Numerical method 7

2.1.1 Overview of One-dimensional modelling 7

2.1.2 One-line Model 8

2.1.3 Some limitations in considering changes in bottom topography when using One-dimensional model 10

2.1.4 Overview of multi-dimensional hydrodynamic modelling 10

2.1.5 Solution procedure 12

2.1.6 Modeling seabed change 14

2.1.7 Some limitations in considering changes in bottom topography when using multi-dimensional model: 16

2.2 Computing sediment transport 17

2.2.1 Soulsby–Van Rijn equation (1997) 17

2.2.2 Some problems need to consider when research sediment transport 19

2.2.3 Formulation in Delft3D model 20

2.3 Computing method of X-beach model 23

2.3.1 The Coordinate system and Grid setup 23

2.3.2 The short wave action balance 25

2.3.3 Wave breaking 26

2.3.4 The bottom friction element: 26

2.3.5 Shallow water equations: 27

2.3.6 Bed shear stress equations 28

2.3.7 Wind equations 29

2.3.8 Bottom updating equations 30

2.4 Selecting a Model for Lach Van river mouth 31

CHAPTER 3 DATA COLLECTION 33

3.1 Bathymetry data 34

3.2 Coastline identification 35

3.3 Wave Data 36

3.4 Wind Data 38

3.5 Tide and surge 39

3.6 Sediment data 40

CHAPTER 4 PROPOSED MODELING STUDY AND EXPECTED ISSUES 41

4.1 Sediment transport process 41

4.2 Grid setup 42

4.3 Model calibration 44

4.4 Modelling scenarios 46

4.5 Wave simulation in big domain 46

4.6 Hydrodynamic and morphological simulation in small domain 48

4.7 Result for ESE wave scenario 49

4.8 Result for ENE wave scenario 54

4.9 Discussion 57

CONCLUSIONS AND RECOMMENDATIONS 60

REFERENCE 61

LIST OF FIGURES

Figure1 1 Schematization of XBeach model 6

Figure 2 1 Element volume on equilibrium beach profile 8

Figure 2 2 Change in shoreline positions after simulations 1 (upper) and 2 (lower) in comparison with observed data 9

Figure 2 3 Example of a curvilinear grid (Delft3D-FLOW User Manual, 2014) 13

Figure 2 4 Mapping of physical space to computational space (Delft3D-FLOW User Manual, 2014) 13

Figure 2 5 Difference grid in x,y space (Ahmad, S 1999) 14

Figure 2 6 Flow diagram of “online” morphodynamic model setup (Roelvink, 2006) 16

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) 22

Figure 2 8 Grid staggering, 3D view and top view (Delft3D-FLOW User Manual, 2014) 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 manual, 2015) 24

Figure 3 1 Depth contours digitized from nautical chart (Chien 2017) 34

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 Tung T.T, 2018) 35

Figure 3 3 The position of points extracted wave in model WaveWatch 37

Figure 3 4 Wave roses of the periods Feb-2005 – Jan-2011 (left) and Feb-2011 – Jan-2017 (right) (Chien N.Q, and Tung T.T, 2018) 38

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 2018) 39

Figure 3 6 Typical astronomic tidal level of Dien Chau (Chien 2017) 39

Figure 4 1 Location of the study area, with basic modes of sediment transport (Chien and Tung 2018) 41

Figure 4 2 Layout of the modeling domain 43

Figure 4 3 Jonswap wave spectrum for Hm0 = 1.28 m and 0.76 m 44

Figure 4 4 Computed wave field in big domain for the case of ENE waves 47

Figure 4 5 Computed wave field in big domain for the case of ESE waves 47

Figure 4 6 Bathymetry of the small domain 48

Figure 4.7: Wave field of the small domain, ESE wave scenario 50

Figure 4.8: Flow field near the river mouth, ESE wave scenario 51

Figure 4.9: Sediment transport near the river mouth, ESE wave scenario 52

Figure 4.10: Seabed elevation change near the river mouth, ESE wave scenario 53

Figure 4.11: Wave field of the small domain, ENE wave scenario 54

Figure 4.12: Flow field near the river mouth, ENE wave scenario 55

Figure 4.13: Sediment transport near the river mouth, ENE wave scenario 56

Figure 4.14: Seabed elevation change near the river mouth, ENE wave scenario 57

LIST OF TABLES

Table 3 1 Extreme water level for location 19°01’N, 105°37’E 40

Table 4 1 Parameters of the big domain model 45

Table 4 2 Comparison between simulated result and observed data 45

Table 4 3 Parameters of the small domain model 49

Table 4 4 The comparison of results 58

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 vicinity

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

at the river mouth They have carried out fieldwork and research methods on the model The advantage of modeling is less costly to invest 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 1D model, researchers have produced results on shoreline dynamics, areas of flooding, etc However, recent studies using 2D models have made research results more meaningful This is due to the advantages in studying the topography development, which based on the parameters of wind and sand There are many models used in the world (Delft, Swan and XBeach)

In the framework of the thesis, a Xbeach model is used to simulate the bottom evolution of Lach Van river mouth in Dien Chau district, Nghe An province Parameters and results of the model will be tested with actual measurement data at the Hon Ngu station; finally, the resulting of the bottom topography is stated through the sediment transport in here By using Xbeach 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°E), belonging to Dien Chau District, Nghe An province, Vietnam 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 area 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 factors affect to study area This position is an intersection 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 24km in length and blocked by 2 two rock headlands

However, the deposition of Lach Van estuary has been complicated and has had a great impact on the activities of the fishing fleet of Dien Chau district According to 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 1.2 m" This topography situation is still occurring in 2017 with the serious level of deposition

The cause of evolution in Lach Van river mouth:

According to the survey from different sources from 2003 to 2009, the analysis showed that the river mouth area has accretion - erosion situations With this river mouth, 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 105 m3/year

Some factors related to economic activities such as the construction of irrigation reservoirs, upstream hydroelectricity, river works, aquaculture, river mouth tourism, material exploitation, etc It also contributes to complex developments

Nowadays, the phenomenon of river mouth accretion is complicated, many fishing boats are stuck This has great impacted the activities of Dien Chau district fishermen Thus, a request to adjust the river mouth is very urgent

- Analysis on the coastline evolution of Lach Van coast

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

- Proposal of some scenarios about boundary conditions to 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 regime influenced by many factors such as: waves, tidal, river flow and the human impact Thus, the sediment transport is difficult to estimate This leads to the fact that morphological changes cannot be accurately simulated

P.T Huong and V.T Ca [1] showed calculation results identifying some hydrodynamic characteristics affecting the morphology of Da Rang river mouth, Phu Yen province The hydrodynamic factors are dominated by:

- Flow regime from upstream river;

- The quantity and geological nature of sediment from the river to the sea through the river mouth, tidal cycle and amplitude, volume of tidal prism, coastal currents due to simultaneous effects 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 features Delft3D model [2] analyzed dynamic factors and then verify the development 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 (2D) model (Delft3D + SWAN) to simulate the transformation of a sand spit toward the river mouth In addition, for the effects of the wind, Nardin and Fagherazzi [5] investigated the interaction of external force on the movement of sand bar at the river mouth

Related to specific types of geomorphology, J.H Nienhuis et al., [6] developed a computational model for straight coastlines, attached with a forecast of changes in the river mouth Besides, M.D 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 Hence, the results of 1D

is easily to consult in a simple way, and have a predictable 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 to run, have unstable and unreliable results [8]

In Vietnam, the studies in recent years show that scientists are using advanced methods which focused on quantitative rather than qualitative 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 Hien, 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 - stabilization mechanism of estuaries Vu M Cat, Pham Q Son [14] evaluated the change in shoreline shape during the long period for many coast zone, river mouth in Vietnam Remarkably, In Lach Van river mouth - study area –Nguyen Q Chien, Tran

T Tung [15] used a one-line model to estimate the change in local coastline

However, in fact, these studies are mostly interested in coastal erosion Conversely, there are very little accretion estuaries are being studied and sought to overcome (Tam Quan river mouth, in Binh Dinh province) Thus, conducting research for river mouths being accreted such as Lach Van is essential

1.5 Research methods

• Collecting basic data at measuring station and natural characteristics

• Numerical Modeling: the use of XBeach model to predict morphography evolution

• Consulting experts

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

Figure1 1 Schematization of XBeach model

CHAPTER 2 COMPUTING METHOD

2.1 Numerical method

Numerical modeling is an important tool to 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 coastal profile model, which model the cross-shore beach profile along

a normal to a straight or gently curving coastline

- A coastal 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 at each of points along the coastline Coastal profile models are more computationally demanding than shoreline model This results

in an updated shape of cross-shore bottom profile The process is repeated for each successive wave condition The coastal area model 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 models, especially in the context of improved topography data in recent years

2.1.1 Overview of One-dimensional modelling

The development of the 1D morphology equation assumes that a beach profile of constant shape slides along a horizontal base located at closure depth dc, as in Figure 2.1:

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 + h∗) 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:

0 1

+

∂

∂

q x

Q h

B t

(2.1)The sediment source or sink, q, is omitted for open coasts in which zero net cross-shore transport

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

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 ~105 m3/yr This rate has decreased during the years 2011–2016 If this amount of sediment (~105 m3/yr) is completely deposited, then accretion at the river mouth (area∼1 km2) will occur at a rate of ~10 cm/yr

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

The 1D modeling can perform well if the watercourse is simple, with limited topographic data and time-efficient solution algorithm However, it has the following limitation of computational flexibility:

- Water level and discharge information is only available at points where cross sections are defined This is a limitation since distance between cross sections varies at different locations

- 1-D models do not perform well in areas where lateral flow plays an important role in flood wave propagation Thus, it is difficult to finding the exact path of flood wave

- Model is not capable of dealing with flooding and drying It means that the researching areas 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 capture 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:

- X-momentum equation:

- Y-momentum equation:

(2.4)

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

z(x,y,t) = Surface elevation (m) p,q(z,y,t) = Flux densities in x/y directions (m3/s/m)

c(x,y) = Chezy resistance (m1/2/s)

g = Acceleration due to gravity (m/s2)

f(v) = Wind friction factor Ω(x,y) = Coriolis parameter, latitude dependent (S-1)

Pa(x,y,t) = Atmospheric pressure (kg/m/s2)

= Density of water (kg/m3)

x,y = Space coordinates (m)

= Components of effective shear stress

v,vx,vy (x,y,t) = Wind speed and components in x,y direction (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 characteristics between water layers can be neglected Typical application areas are modeling of tidal hydraulics, wind and wave generated currents, storm surges, dam break and flood waves

The 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 tool 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 system solves the fully time-dependent non-linear equations of continuity and conservation of momentum The outcome of the simulation is the water level and fluxes in the computational domain

The hydrodynamic module resolves the unsteady shallow-water equations in two (depth-averaged) or three dimensions The system of equations 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 be small compared to gravitational acceleration and are not taken into account For example, the DELFT3D-FLOW model is suitable for predicting the flow in shallow seas, coastal areas, and estuaries It aims to model flow phenomena of which the horizontal length and time scales are significantly larger than the vertical scales

In simulations including waves, some models e.g Delft3D have the hydrodynamic equations written and solved in a Generalized Lagrangian Mean (GLM) reference frame

2.1.5 Solution procedure

Numerical models are based on finite difference or finite volume methods To discretize the shallow water equations in space, the model area is covered by a rectangular, curvilinear, or spherical grid It is assumed that the grid is orthogonal and well structured In this arrangement, 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 situated

Figure 2 3 Example of a curvilinear grid (Delft3D-FLOW User Manual, 2014)

Figure 2 4 Mapping of physical space to computational space (Delft3D-FLOW User

Manual, 2014)

Model simulates unsteady 2-D flows in one layer (vertically homogeneous) fluids The continuity and momentum equations are solved by implicit finite difference techniques

with the variables defined on a space staggered rectangular grid as shown in Figure 2.4

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

A 'fractioned-step' technique can be combined with an Alternating Direction Implicit (ADI) 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

Interaction between hydrodynamic and morphological computation is constituted 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 Exner equation to assess the balance of sediment, it can to estimate the change in bed elevation in an internal time ( ) Thus, the bed elevation is changed to (Zb + ) 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 that, it should calculate the bathymetry once when model runs a number of flow timestep Sediment transport and bottom updating are calculated at the same time steps as the flow field Besides, the bed elevation will update after sediment accumulated in 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 begin a new cycle computation

Figure 2 6 Flow 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 This ‘online’ method has to make short-term processes such as including various interactions between flow, sediment and morphology [16]

2.1.7 Some limitations in considering changes in bottom topography when using multi-dimensional model:

- The model lacks the capability to model the complex flow patterns within the hydraulic jump

- All numerical models are required to make approximations These may be related to geometric limitations, numerical simplification (i.e omission of

‘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 calculation when the vertical length scale approaches or exceeds 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 that, the changes of bottom shape and direction Additionally, Manning’s roughness coefficient was developed for one-dimensional flow motion only

- Many of the limitations imposed by or on two-dimensional models are related

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 run

- 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 assumption that the horizontal length scale is significantly greater than the vertical scale, implying that vertical velocities are negligible, vertical pressure gradients are hydrostatic, and horizontal pressure gradients 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 reflected on localized erosion and deposition

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

at certain site:

- The best method is to adopt the best known date from a nearby site, with modification based on local condition

- 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

: Coefficient of bed load/ suspended load sediment transport (m/s) : The long shore current velocity

: Dimensionless factor of bed grain sediment : Coefficient of strength transport of sediment

: Coefficient of friction

∆ : The relative sediment density define by ( )

: The wave orbital velocity at the bed

: 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

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

- On a sloping bed transport tends to be diverted downslope

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

- In shallow water, the wave motion becomes asymmetric in various ways, which leads to a net transport term in the direction of wave propagation or opposed to

- Short terms: Geomorphology - morphodynamic is also responsible for the catastrophe caused by the change of the natural processes as the change of the coastline by storms, floods or global sea level rise etc

Wave breaking while propagating to 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 velocity is not 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 step using simply 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 follows:

(Sink Source) t f

s sus m n = MOR − ∆

∆ ( , )

(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,

S cor, as follows:

) , ( )

, ( ) , ( , )

1 , ( ) 1 , ( ,

) , ( ) , ( , )

, 1 ( ) , 1 ( , )

,

(

n m n

m n m vv cor n

m n

m vv cor

n m n m uu cor n

m n m vv cor MOR n

m

cor

A

t x

S x

S

y S

y S

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

; = are the suspended sediment correction vector components in the

u and v directions at the u and v velocity points

∆x(m,n); ∆y(m,n) = are the widths of cell (m,n) in the x and y directions, respectively

• Bedload sediment transport:

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

(2.14) Where ; = 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

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)

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 (x w , y w ) through an origin (x ori , y ori) and an orientation (α) as depicted in

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

Figure 2 9 Rectangular/ Curvilinear coordinate system of XBeach (Xbeach manual,

2015)

• 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 v-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 (u u ) and (v v) respectively; velocities u and v at the cell centers are obtained by interpolation and are

for output purpose only The water level, (z s ), and the bed level, (z b) are both defined

positive upward (u v ) and (v u) 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

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:

Where: Dw, Df, Dv = is the dissipation processes of wave breaking, bottom

friction and vegetation

cx, cy, = is The wave action propagation speeds in x, y,

t = time

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

= the wave energy density in each directional bin

h = the local water depth

k = the wave number

Where: Trep = the representative wave period

Hrms = the root-mean-square wave height

α = 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:

(2.21) Where: = the short-wave friction coefficient

= the mean period of primary swell waves

= the water density ( ) 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 ( ) 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:

(2.22)

(2.23)

(2.24)Where: uL, vL: The Lagrangian velocity in x- and y- direction respectively

= Horizontal viscosity = Coriolis coefficient = Wind shear stresses

= Bed shear stresses

= The water level

= The wave induced stresses

= The stresses induced by vegetation

To 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 the

Lagrangian velocity (u L) 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 friction associated with mean currents and long waves is included via the formulation of the bed shear stress The bed shear stress is calculated with:

(2.25)

(2.26) Where: = the Eulerian velocity in x- and y- direction respectively (the

short wave averaged velocity observed at a fixed point)

= the dimensionless bed friction coefficient

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

- The dimensionless friction coefficient can be calculated from the Chézy value with equation A typical Chézy value is in the order of 55 :

- From the Manning coefficient ( ), it can be seen as a depth-dependent Chézy value and a typical Manning value would be in the order of 0.02 (s/m1/3):

= Density of air = the wind drag the coefficient

W = the wind velocity The wind stress is turned off by default, and can be turned 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 (f mor) will be multiplied to all input time series and other time

parameters are divided internally by (f mor)

(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 (f mor) 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