Front Cover
 Title Page
 Table of Contents
 List of Figures
 Descrption of nearshore hydrodynamic...
 Description of sediment transport...
 Calibration of sediment transport...
 Model performance
 Inlet experiment
 Conclusion and recommendations...
 Biographical sketch

Group Title: Technical report – University of Florida. Coastal and Oceanographic Engineering Program ; 109
Title: Numerical modeling of nearshore morphological changes under current-wave field
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00075329/00001
 Material Information
Title: Numerical modeling of nearshore morphological changes under current-wave field
Physical Description: xi, 121 leaves : ill. ; 29 cm.
Language: English
Creator: Kim, Taerim, 1964-
Publication Date: 1995
Subject: Coastal and Oceanographic Engineering thesis, Ph. D
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis (Ph. D.)--University of Florida, 1995.
Bibliography: Includes bibliographical references (leaves 115-120).
Statement of Responsibility: by Taerim Kim.
General Note: Typescript.
General Note: Vita.
Funding: Technical report (University of Florida. Coastal and Oceanographic Engineering Dept.) ;
 Record Information
Bibliographic ID: UF00075329
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: aleph - 002056272
oclc - 33803986
notis - AKP4283

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Title Page
        Acknowledgement 1
        Acknowledgement 2
    Table of Contents
        Table of Contents 1
        Table of Contents 2
    List of Figures
        List of Figures 1
        List of Figures 2
        List of Figures 3
        List of Figures 4
        Abstract 1
        Abstract 2
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
    Descrption of nearshore hydrodynamic model
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
    Description of sediment transport model
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
    Calibration of sediment transport rate
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
    Model performance
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
    Inlet experiment
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
    Conclusion and recommendations for further study
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
    Biographical sketch
        Page 121
Full Text




Taerim Kim










I would like to express my sincere appreciation and gratitude to my adviser,

Professor Hsiang Wang, for his encouragement and guidance throughout my Ph.D.

program. He provided me the best environment for research and valuable experience.

I wish to extend my gratitude to Professor Robert G. Dean, Professor Daniel M.

Hanes and Professor Ulrich H. Kurzweg for serving as the members of my doctoral

advisory committee and to Professor Donald M. Sheppard for reviewing the disserta-

tion and attending the final exam. Thanks are also due to all other faculty members

in the department who taught during my graduate study. I would like to thank Dr.

Hans H. Dette, Leichtweib-Institute ffir Wasserbau, Technische Universitat Braunsh-

weig, Germany, and Prof. Alf T, Norwegian Hydrotechnical Laboratory, Trondheim,
Norway, for providing accommodations and computer and office equipment when I

visited the two institutions in mid 1994.

I am also grateful to Becky Hudson for providing me her generous hospitality,

Helen Twedell and John Davis for their efficiency and courtesy in running the archives,

and Mr. Subarna Malarka for computer help. Very special thanks go to Dr. Li-Hwa

Lin for his friendship, advice, and encouragement.

The experiments at the Coastal Laboratory have been conducted continuously as a

group project throughout my graduate study and have become part of my dissertation.

Thanks are given to Mr. Sydney Schofied, Mr. Jim Joiner, and other staff members

in the Coastal Laboratory for their help during the experiment. The endless sweat

during the shovelling on the artificial beach with group colleagues Santiago Alfageme

and Xu Wang will be kept as a precious memory.

The support of fellow Korean friends who finished their study ahead of me in the

department is warmly appreciated. The various topics discussed with them were one

of the great pleasures I had in the U.S.A. and gave me a way to appreciate many

experiences indirectly.

Finally, I would like to thank my parents who are always thinking and caring

about me. Their trust has always been a driving force and helped me through many

difficulties. I also thank my two elder brothers. Their sincere advice, encouragement,

and help were the foundation of this accomplishment. I hope my lost wing, my future

wife, can share this moment in the near future.


ACKNOWLEDGMENTS ................. ............ iii

LIST OF FIGURES .................... ............ vi

ABSTRACT .................................... x


1 INTRODUCTION ..................... .......... 1
1.1 Statement of Problem ................... ....... 1
1.2 Past Studies ................... ............. 5
1.3 General Description of the Model ...................... 8
1.4 Summary of Contents .................... ....... 10

2.1 Wave Model .................... ............ 11
2.2 Wave Breaking and Energy Dissipation ................. 14
2.3 Circulation Model .................... ......... 16
2.4 Undertow Current .................... ........ 17

3.1 Shear Stress under Wave and Current .................. 24
3.2 Shear Stress in the Surf Zone ...................... 26
3.3 Sediment-Threshold Theories in Waves and Currents ........ 28
3.4 Sediment Transport Formulae ...................... 29
3.5 Slope Effect .................... ............ 34
3.6 The Transition Zone ................... ....... 37
3.7 Cushioning Effect .................... ......... 40
3.8 Profile Change .............................. 43

4.1 Cross-Shore Transport Rate ....................... 46
4.2 Longshore Transport Rate ........................ 54

5 MODEL PERFORMANCE ......................... 70
5.1 Artificial Bar ................... ........... 70
5.2 Groins ..................... .............. 73
5.3 Breakwater .................... ............ 82

6 INLET EXPERIMENT .................... ........ 95

7.1 Conclusions .... ............................ 110
7.2 Future Study .................... ........... 112

BIBLIOGRAPHY ................................. 115

BIOGRAPHICAL SKETCH ................... ........ 121


1.1 Structure of nearshore morphodynamic model. . . 9

2.1 Distributions of a)Wave Height b)Discharge of Undertow Current,
and c)Mean Undertow Current in Different Input Wave Conditions. 20

3.1 Initiation of Motion and Suspension for Unidirectional Flow (from
van Rijn, L.C., 1989) ....................... 30

3.2 Type of Net Transport Rate Distribution (from Kajima et al., 1982). 32

3.3 Distributions of a)Wave Height b)Stress c)Sediment Transport Rate. 35

3.4 Distributions of Sediment Transport Rate with a)Different Slope
Affecting Coefficients b)Different Bottom Slope.. . ... 38

3.5 a)Comparisons of Various Transition Length Formulas. b)Example
for Application of Transition Length Formula to the Turbulent
Shear Stress. ................... .......... 41

3.6 a)Distribution of Cushioning Effect. b)Evolution of Sediment Trans-
port Rate ............................ 44

4.1 Comparison between Computed and Measured Beach Profiles for
t= 62, 111, 273 minutes. Data from Dette and Uliczka (1986).. 47

4.2 Comparison of Cross-Shore Transport Rates between Experiment
and Present Model for t= 62, 111, 273 minutes. Data from Dette
and Uliczka (1986). ......................... 49

4.3 Comparison between Calculated and Measured Beach Profiles for
t= 1, 3, 5 hours. Data from Saville(1957). . . ... 51

4.4 Comparison of Cross-Shore Transport Rates between Experiment
and Present Model for t= 1, 3, 5 hours. Data from Saville(1957). 52

4.5 Comparison between Calculated and Measured Beach Profiles for
t= 10, 20, 40 minutes. Data from Air-Sea-Tank Experiment. 53

4.6 Comparison of Cross-Shore Transport Rate between Experiment
and Present Model for t= 10, 20, 40 minutes. Data from Air-Sea-
Tank Experiment. .......................... 55

4.7 a)Distributions of Longshore Transport Rate in Different Wave
Directions b)Comparison of Longshore Trasnport Rates between
CERC Formula and Present Model in Different Wave Directions. 58

4.8 Schematic Map of the Plain Beach Movable Bed Model for Normal
and Oblique Waves. ......................... 59

4.9 Photograph of a)Plain Beach Movable Bed Model and b)Resultant
Morphological Changes for Normal Incident Waves in the 3-D
Basin Experiment ................... ....... 61

4.10 Orthographic Plots of Bathymetric Change for Normal Incident
Waves in Plain Beach Movable Bed Experiment. . ... 62

4.11 Contours of Bathymetric Change for a Normal Incident Waves in
Plain Beach Movable Bed Experiment. . . .... 63

4.12 Comparison between Computed and Measured Beach Profiles for
t= 20, 40, 80 minutes. Data from Plain Beach Movable Bed Ex-
periment for Normal Incident Waves. . . . .... 64

4.13 Orthographic Plots of Bathymetric Change for Oblique Incident
Waves in Plain Beach Movable Bed Experiment. . ... 66

4.14 Contours of Bathymetric Change for Oblique Incident Waves in
Plain Beach Movable Bed Experiment. . . .... 67

4.15 Comparison between Computed and Measured Beach Profiles for
t= 20, 40, 80 minutes. Data from Plain Beach Movable Bed Ex-
periment for Oblique Incident Waves. . . .... 68

5.1 a)Inital and Quasi-Stable Profiles in 2 m Storm Surge and 2 m
Wave Height. b)Cross-Shore Transport Rate Distributions after 1
hour and 16 hours.................. ......... 72

5.2 a)Profile Change, and b)Cross-Shore Transport Rate Change for
Fixed Bar Case in 1 m Storm Surge and 2 m Wave Height .. 74

5.3 Profile Changes for a)Movable Bar, and b)Fixed Bar Cases in 1 m
storm Surge and 2 m Wave Height . . . .. 75

5.4 Profile Changes for a)Movable Bar, and b)Fixed Bar Cases in 2 m
Storm Surge and 2.5 m Wave Height . . . .... 76

5.5 a)Wave Crests, and b)Current Field on the Plain Beach with a
Single Groin for 0.5 m, 8 sec, and 10 degree Incident Waves. 78

5.6 Sediment Transport Field and Resultant Depth Changes a)with
and b)without Wave-borne Transport on the Plain Beach with a
Single Groin for 0.5 m, 8 sec, and 10 degree Incident Waves after
40 days .. . . . . . . . 80

5.7 Depth Changes after a)70 days, and b)140 days on the Plain Beach
with a Single Groin for 0.5 m, 8 sec, and 10 degree Incident Waves. 81

5.8 a)Wave Crests, and b)Current Field on the Plain Beach with Three
Groins for 0.5 m, 8 sec, and 10 degree Incident Waves. . 83

5.9 Depth Changes after a)70 days, and b)140 days on the Plain Beach
with Three Groins for 0.5 m, 8 sec, and 10 degree Incident Waves. 84

5.10 Sediment Bypassing Transport Rate for a)Single Groin, and b)Three
Groins on the Plain Beach for 0.5 m, 8 sec, and 10 degree Incident
W aves .. .. .. .. ... .. .. .. .. ... .. ... 85

5.11 a)Wave Crests, and b)Current Field on the Plain Beach with
Breakwater for 1 m, 6 sec, and Normal Incident Waves. . 87

5.12 Sediment Transport Field and Resultant Depth Changes a)with
and b)without Wave-borne Transport on the Plain Beach with a
Breakwater for 1 m, 6 sec, and Normal Incident Waves after 1 day. 88

5.13 Depth Changes after a)2 days, and b)7 days on the Plain Beach
with Breakwater for 1 m, 6 sec, and Normal Incident Waves. 90

5.14 a)Wave Crests, and b)Current Field on the Plain Beach with
Breakwater for 1 m, 6 sec, and 15 degree Incident Waves. . 91

5.15 Depth Changes after a)2 days, and b)7 days on the Plain Beach
with a Breakwater for 1 m, 6 sec, and 15 degree Incident Wave. 92

5.16 a)Wave Crests, and b)Current Field on the Plain Beach with a
Long Breakwater for 1 m, 6 sec, and Normal Incident Waves. 93

5.17 Depth Changes after a)l day, and b)5 days on the Plain Beach
with a Long Breakwater for 1 m, 6 sec, and Normal Incident Wave. 94

6.1 Schematic Map of the Inlet Beach Movable Bed Model for Oblique
W aves . . . . .. .. . .. 97

6.2 Photograph of a)the Inlet Beach Movable Bed Model, and b)the
Resultant Morphological Changes for Oblique Waves in the 3-D
Basin Experiment ................... ....... 98

6.3 Orthographic Plots of Bathymetric Change for Oblique Incident
Waves in Inlet Beach Movable Bed Experiment. . ... 100

6.4 Contours of Bathymetric Change for Oblique Incident Waves in
Inlet Beach Movable Bed Experiment. . . .... 101

6.5 Calculated Wave Crests on the Initial Profile in Inlet Beach Mov-
able Bed Experiment for 8 cm, 1 sec, and Oblique Incident Wave. 102

6.6 Calculated Current Fields for a)Ebb, and b)Flood on the Initial
Profile in Inlet Beach Model for 8 cm, 1 sec, and Oblique Incident
W aves. .. .. .. .. ... .. .. .. .. .. .. .. ... 103

6.7 Calculated Sediment Transport Fields for a)Ebb, and b)Flood on
the Initial Profile in Inlet Beach Model for 8 cm, 1 sec, and Oblique
Incident W aves. ........................... 104

6.8 Orthographic Plots of Calculated Bathymetric Change for Oblique
Incident Waves in Inlet Beach Movable Bed Experiment. ...... 105

6.9 Contours of Calculated Bathymetric Change for Oblique Incident
Waves in Inlet Beach Movable Bed Model . . .... 106

6.10 a)Calculated Total Sediment Transport Field after 160 minutes
b)Comparison of Longshore Transport Rates between Inlet Exper-
iment and Numerical Model for 8 cm, 1 sec, and Oblique Incident
W aves. .. . .. .. . . . .. 108

6.11 Comparison of Bathymetric Changes after 160 minutes between
Experiment and Numerical Model for 8 cm, 1 sec, and Oblique
Incident W aves. ........................... 109

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy




August 1995

Chairman: Dr. Hsiang Wang
Major Department: Coastal and Oceanographic Engineering

The ultimate goal of this dissertation research is to develop a time-dependent

three-dimensional(3-D) nearshore morphological response model. This model predicts

the change of bottom topography, based on the sediment transport rates computed

in the nearshore wave and current field. The research effort consists of two major

aspects: numerical model development, and the model calibration and verification

through physical modeling.

The numerical model is developed by coupling a sediment transport submodel

with a depth-integrated nearshore hydrodynamic submodel. Modifications are made

in the model formulation to depict more realistically the hydrodynamics inside the

surf zone as a driving force for sediment transport. These include an undertow in the

shore normal direction and turbulent shear stress by wave breaking. This model also

considers the slope effect, wave-borne transport, and transition zone effect. These
effects are very important but largely have not been addressed in other sediment

transport models. A cushioning effect is introduced in the model which limits the

advection of turbulence generated by wave breaking from the surface to reach the

bottom. This mechanism enables the beach profile to approach an equilibrium state

under constant wave condition.

Calibration and verification of the numerical model concentrate mainly on the

sediment transport submodel utilizing a laboratory movable-bed physical model. The

experiment consists of a 2-D wave tank test using regular waves over a simple sloped

beach, and a 3-D basin test using normal and oblique waves over a uniformly-sloped

beach. The sediment transport submodel is calibrated separately for cross-shore and

longshore transport rates in each of the experiments. The numerical model is capable

of predicting the changes in bottom topography near structures such as artificial fixed

bottom bars, breakwaters, and groins. The verification of the numerical model is

carried out by comparing the results with available empirical transport formulas and

other experimental results. The numerical model yields a good prediction of sediment

transport over a uniformly-sloped beach with jetties and an inlet as compared with

the results from the inlet beach physical model test.


1.1 Statement of Problem

Generally speaking, natural beaches are more or less in dynamic equilibrium and

their changes due to changing wave climate are rather seasonal, featured by alternate

erosional and accretional cycles. However, once coastal structures are introduced, the

original sediment transport patterns are perturbed around the structures and perma-

nent topographic changes often take place rather rapidly. These changes are often

undesirable. Examples are downdrift beach erosion associated with the construction

of groins, tombolos formed behind offshore breakwaters, harbor siltation, erosion and

shoaling caused by jetties, and other engineering activities. Therefore, a predictive

capability of beach response is important for assessing the impact of coastal structures

and to improve their design. It is also useful for evaluating remedial and mitigation

measures. Physical modeling used to be the only viable tool to study beach response.

This tool is still being used but it does have its drawbacks such as high cost, limi-

tations on temporal and spatial scales, difficulty of modifying and duplicating, and,

the most serious one, on the question of scaling. Numerical modeling is clearly an

attractive alternative and is becoming increasingly viable with the advancement of

computational facilities and improved understanding of wave mechanics and sediment

transport processes.

Numerical modeling on nearshore morphological changes consists of two essential

elements, the prescription of nearshore hydrodynamics and computation of sediment

transport. At present, practically all the operational models are based on depth-

integrated 2-D hydrodynamic models and apply energetic approaches to calculate

sediment transport. It is recognized that nearshore coastal morphological changes

are dominated by the combined force of currents and waves. Therefore, in numerical

modeling it is essential to have an adequate wave-current field description, particularly

inside the surf zone where sediment transport is most active. Here, 2-D flow field de-

scriptions are clearly inadequate. At this stage, quasi-3D hydrodynamic models have

been developed and appear to be the state of the art. Fully 3-D coastal hydrodynamic

models with current-wave interaction have not been considered. There are still im-

portant consistency problems to be solved (De Vriend and Kitou, 1990). Even if one

attempted to construct one now, the model would be badly lacking the fundamentals

and too computationally intensive to be practical. Besides, there is hardly any 3-D
validation material available.

The subject of sediment transport is one of great difficulties because of the vast

number of interacting parameters. The early work in theoretical and laboratory stud-

ies concentrated on steady flow over grains with uniform properties, and formulas for

practical use were mainly empirical relationships based on laboratory measurements

and limited field data. It is considerably more difficult to develop reliable formulas for

prescribing rates of sediment transport under the combined current-wave conditions.

Available formulas are scant and mostly based on grossly simplified assumptions.
These formulas are poorly verified for lack of data. Empirical coefficients are in-

troduced to account for all the unknown factors. One of the common practices in

surf zone modeling is to separate longshore and cross-shore sediment transport. The

computation of beach profile change is then based on cross-shore transport mecha-

nism only. This cross-shore transport mechanism and the resulting profile change are

then verified by physical experiments in 2-D flume tests on plane beaches. These

comparisons serve only to test the model's ability for describing the cross shore sedi-

ment processes under normal incident waves. The 3-D effects on cross-shore sediment

transport, such as a net through-flow due to a horizontal circulation (Hansen and

Svendsen, 1986) or the complications which arise when waves and currents interact

under an oblique angle (Davies et al., 1988), were all ignored. In nature, the coastal

profile is formed under the combined current and wave field caused by oblique waves.

It seems that the description of the cross-shore processes has reached a stage where it

is relevant to develop 3-D or 'quasi-3D' modeling of currents and sediment transport.

As mentioned earlier, most morphological numerical models utilize a 2-D depth-

integrated approach. Watanabe et al. (1986), for instance, developed a model based

on this approach and applied the model to several coasts in Japan with reasonable

success. The main advantage of a 2-D depth-integrated model is clearly the eco-

nomics in computational type. However, it precludes direct considerations on some

of the important effects due to vertical variations such as undertow current inside

the surf zone. More recently, quasi-3D models for wave transformation and wave-

induced currents have been developed. The application of this quasi-3D description

of nearshore hydrodynamics has just started in computing nearshore sediment trans-

port and assessing patterns of erosion and accretion in the coastal zone. Briand and

Kamphius (1993) constructed a numerical model combining a quasi-3D hydrodynamic

flow model and a sediment transport model and compared the results with laboratory

experimental data. Wang et al. (1991) applied a quasi-3D morphodynamic model

to simulate the evolution of a tidal inlet (disregarding wave effects). However, both

models ignored the wave-borne transport which is important in nearshore conditions.

The gravitational effects on sediment transport were also neglected. This down-slope

gravitational transport component is usually small as compared with the total trans-

port rate but is essential to the behavior of a morphodynamic system (De Vriend,

1986). Although this approach could depict the 3-D patterns of currents and sediment

transport, more coefficients are often required than 2-D approach. At present, these

coefficients are difficult to determine for lack of adequate experimental and field data.

Full 3-D model development is still at its infancy. An operational model of this kind

is unlikely to become available in the near future. Apart from the current compu-

tational limitations, the development is seriously hampered in lacking solid physical

foundations to formulate a sound model. This lack of basic knowledge can only be

remedied as more laboratory and field data become available.

Recognizing the difficulties and the current deficiencies of developing a full 3-D

operational morphological model, the present study takes the quasi 3-D approach. It

is aimed at developing an operational morphological evolutional model for engineering

application and strives to achieve the following capabilities:

1. Simulate the change of the beach profile shape and position in short-term pro-

cesses like storm-induced, cyclical daily, and seasonal changes and in long-term


2. Respond to changes in water level due to tides, storm surges, or long-term


3. Represent general boundary conditions and coastal structure configurations.

4. Approach an equilibrium bottom configuration under constant forcing and bound-

ary conditions.

The model development and some initial test results are presented in this dis-

sertation. It should be realized here that like other models of this kind, the model

presented here can not be claimed as an ultimate success but represents a step of

achieving such an ultimate goal.

1.2 Past Studies

In the nearshore zone, the bed material is almost always in motion under the
intense action of waves and currents. Beach stabilization and coastal protection in
this area are two major areas of concern in the field of coastal engineering. In the

past, the prediction of beach evolution was mainly conducted by relying on coastal

experience in similar cases and on the results of physical model tests. In recent years,

numerical models have been developed and applied for these purposes.

Coastal evolution processes are three-dimensional but many fundamental aspects
of the coastal behavior can be studied with models of lesser dimensions, either phys-

ical or numerical. This is because many of the physical changes associated with the

system that are of engineering interest such as profile evolution and shoreline mod-

ification often respond to essentially different length and time scales. Based on the
applicable ranges of temporal and spatial dimensions numerical models can be roughly

classified into three groups.

(1) Shoreline change model: This type of model such as the GENESIS (Hanson

et al., 1989) describes only the largest-scale behavior caused by longshore sediment
transport. Smaller scale effects are integrated over the typical temporal and spatial

dimensions of interests.

(2) Beach profile change model: This type of model such as by Kriebel (1985) and

Larson et al., (1989) ignores the longshore variation, but includes the vertical dimen-

sion of beach profile change. Since numerous physical experiments were conducted

in 2-D wave tanks on beach profile changes, models of this kind are generally more

mature and better calibrated.

(3) Nearshore morphological evolution model: This type of model predicts nearshore

3-D topographical changes. This model (Watanabe et al., 1986) generally requires
formulas for estimating local sediment transport rates at each point and calculates

the morphological changes based on 2-D continuity equation. At present, models in

this category are generally suitable for intermediate temporal scales such as for storm

events and monthly or seasonal variations. Two distinct types can be found in this

group based on the approach concept. The first type combines the essential features

of the two types of models described in (1) and (2). The so called 3DBEACH (3-

dimensional decoupled model of beach change) by Larson et al. (1989) is a typical

one. It utilizes the profile change model, SBEACH, for calculating storm-induced

beach erosion and recovery and the shoreline change model, GENESIS, for calcu-

lating long-term change in shoreline position. The major advantage of this type of

model is that the submodels are individually calibrated and verified. Since the profile

model is based on equilibrium profile the combined model also maintains the ability

to approach an equilibrium bottom configuration under steady wave condition. This

is difficult to attain in the models of the second type. However, since the submodels

are all wave driven, combined current wave effect can not be directly addressed. This

severely limits the model's application as well as future improvement. Also, the defi-

ciency of a rational approach to attain a state of equilibrium gives rise to an ambiguity

of time scale which seriously affects the reliability of the predicted evolution.

The other approach computes nearshore topographic change based on local sed-

iment flux balance. This approach usually links a hydrodynamic submodel with a

sediment transport submodel. Models of this kind with varying degrees of sophisti-

cation have been developed. The sediment transport model developed by van Rijn et

al. (1989) seems to be representative of current level of effort. They estimated the

sediment transport rate by multiplying the wave-averaged mean vertical sediment

concentration by the wave-averaged local horizontal velocity. A logarithmic velocity

profile is assumed and the sediment concentration profile is obtained from the classic

approach of using a diffusion equation. In their model, the wave-borne transport

mechanism is not directly addressed.

A model developed by Ohnaka and Watanabe (1990), on the other hand, computes

the flow field with due considerations of current and wave interaction based on coupled
mild-slope wave equation and depth-averaged circulation equations. This computed

flow field then drives a sediment transport model. The sediment transport model,

however, is much simpler than that used by van Rijn et al. (1989). It calculates the

rate of sediment transport as the summation of two energetic mechanisms, one due

to the mean current and the other due to waves (Watanabe et al., 1986). The explicit

inclusion of a wave-induced transport is necessary in their model. This is because the

hydrodynamic model is depth integrated. Inside the surf zone, the current mechanism

alone will result in a zero cross-shore sediment transport which is, of course, not

true. A semi-empirical cross-shore transport formula based on wave energetic is,

therefore, introduced to correct this deficiency. The omission of important transport

mechanisms such as 3-D circulations and wave asymmetry are lumped together into

the empirical formula. Although this empirical approach restricts the applicability to

the area of validity of the empirical component such as uniform beach, this is one of

the few models that have reached a more or less operational stage, and the results

of various practical applications have appeared to be reasonable. Nadaoka et al.

(1991) developed a simple model to evaluate quasi-3D suspended sediment transport

in a non-equilibrium state. Katopodi and Ribberink (1992) included the influence of

waves to the wave-averaged concentration of suspended sediment by modifying the

sediment mixing coefficient and the boundary conditions near the bed.

Recently, the nearshore circulation model was improved by a 3-D approach, which

employed a combined depth-integrated current model and a vertical profile model(De

Vriend and Stive, 1987). This improvement when incorporated into the sediment

transport model enables one to more realistically represent the 3-D nature both in-

side and outside the surfzone. In a similar manner, Briand and Kamphius (1993b)

multiplied the time-averaged quasi-3D velocities to a time-averaged exponential sed-

iment concentration profile to achieve a 3-D sediment flux. This technique of com-

bining a quasi-3D velocity profile with a vertical distribution of suspended sediment

concentrations is a promising step to lead to full 3-D models in the future.

1.3 General Description of the Model

The model developed in this study consists of three submodels for calculation of

waves, nearhsore currents, and beach changes. At the first step, the initial beach

topography and the geometry of the structures for the study area are given as input

data. Next, the wave model determines the spatial distributions of radiation stresses
and near-bottom orbital velocities for a given incident wave condition. Then, the

circulation model computes the mean water surface level and the depth-averaged mean

currents using depth-averaged momentum and continuity equations with the radiation

stresses imported from the wave model as the driving force. The bottom friction,

advective acceleration, and lateral diffusion are also accounted for in the current

computations. Inside the surf zone, mean undertow current, transition zone length,

and cushioning effect are calculated based on the wave-current model results. Spatial

distribution of sediment transport fluxes are computed in the domain of interest

using separate transport equations within and outside the surfzone. Finally, bottom

topography changes are computed based on sediment mass conservation. The first

two models are fully coupled through interaction terms. The flow field at any point

of time is solved by iterations until both models converge. The change in bottom

topography will modify the flow field. Therefore, the hydrodynamic model needs to

be updated from time to time. The time intervals for such updating depend on the

application and the severity of the flow field. Figure 1.1 shows the computational

flow chart of the model.

Figure 1.1: Structure of nearshore morphodynamic model.

1.4 Summary of Contents

The following chapters document the development and the test of the numerical

model for nearshore morphological changes under waves and currents.

Chapter 2 describes the hydrodynamic model which provides inputs to drive the

sediment transport model. Wave, current, and wave-breaking models were reviewed

with simple derivation of equation for each model. The calculation of mean undertow

current based on the results of wave was derived. A comprehensive investigation of a

sediment transport model is documented in Chapter 3. Sediment transport formula,

bottom slope effect, sediment motion threshold theory, transition zone effect, and

cushioning effect are explained in separate sections. Chapter 4 details the calibrations

of cross-shore and longshore transport rates based on 2-D wave tank and 3-D basin

experiments. For the longshore transport, the numerical model result is compared

with empirical formula using different conditions. The performance of the model is

reported in Chapter 5. Topographic changes adjacent to the coastal structure such as

fixed bottom, breakwater, and groins are simulated. In Chapter 6, numerical results

simulating an inlet are compared with physical inlet model data. Finally, Chapter 7

presents the main conclusions of the present study and recommendations for future



2.1 Wave Model

Kirby (1984) derived a mild-slope wave equation for a wave-current coexisting
field, which is applicable to the computation of wave deformation due to combined
effects of wave shoaling, refraction, diffraction, and breaking. The governing equation
is written as

D2+ D Vh(CCgVh) + (a2 k'CC) = -WD (2.1)
Dt2 Dt Dt
where t is the time, Vh is the horizontal gradient operator,

h i.+ Tj
= +

i and j are the unit vector in the x (cross-shore) direction and y longshoree) direction,
respectively, U is the depth averaged horizontal velocity vector, C is the phase velocity,
Cg is the group velocity, a is the intrinsic angular frequency, and 4 is the wave part
of the velocity potential at the mean water level. The last term in Equation (2.1)
is the energy dissipation term, where W is the energy dissipation coefficient. This
term has been added in order to handle the effect of wave decay and recovery after
breaking. Eventually the coefficient W is related to the energy dissipation due to
wave breaking following the work of Dally et al., (1984). The proper form of the
dispersion relationship is

a2 = gk tanh kh

where w is absolute angular frequency and g is gravity coefficient. The hyperbolic
Equation (2.1) can be reduced to an elliptic form based on the assumption that the

only time dependency of velocity potential 4 is in the phase,

Substituting the above equation into Equation (2.1), the following equation is ob-


-2iwU Vh + U Vh(U VhO) + (Vh U)(0 VhO) Vh ( CCqVhO) +

{a2 -2 k2CC iw(Vh. O)}q = iaWq (2.2)

where only the phase contribution to the horizontal derivative of 0 is retained in
obtaining the term on the right hand side of Equation (2.2). There are two major
computational drawbacks to numerically solving this elliptic equation. First, the
solution is required simultaneously for each grid in whole domain, which needs high
memory and take a very long time to run. Second, the boundary conditions must be

specified at all of the boundaries to solve the equation, which are difficult to attain

in many practical applications.

The parabolic approximation to the elliptic wave Equation (2.2) is derived by
the assumption that the direction of wave propagation is essentially along the x-axis

which is normal to the shoreline. For waves propagating at an angle to the x axis,

the proper form of 4 is

= A(x, y) ei(J kcosOdx+f ksinOdy)

and the proper form of the dispersion relationship is

w = a + kcosOU + ksinOV

where A is the complex amplitude and 0 is the angle of the wave propagation relative
to the x axis. By the assumption of small wave angle 0, sinO term can be neglected

and cosO is assumed to be unity. Then, the velocity potential q is approximated as

S= -A(, y) ei( kd)

The ei(f ksinOdy) part of the phase function is now absorbed into the amplitude function,
A. By substituting this 4 into Equation (2.2) and further assuming that the second
derivatives of amplitude A in the x direction are small compared to derivatives of
the phase function (i.e., that ikA, > 'A)), the following parabolic wave equation is
obtained (Winer, 1988),

a C cos 0 + U A + V, v V -
(C cosO + U)A,+ cos + A+VA+ ) A
2 ) 2 o- y

_i A W
-kc(1 cos2 O)A C ( + A= 0
2 a 2
where the subscripts x and y denote derivatives in the x and y directions, respectively.
Since the solution of a parabolic type of wave equation does not require a down-wave
boundary condition it does not have to be solved simultaneously for each grid in
the entire domain. The numerical solution can proceed grid-row by grid-row where
the solution at the new grid-row only uses the results from the previous grid-row.

Therefore, the only required boundary conditions are the conditions on the first grid-
row (usually the offshore boundary) and lateral boundary conditions which could
be open or closed. An open lateral boundary requires that waves pass through the
boundary without any reflection, whereas a closed boundary allows no flow. Since
only one grid row is solved at a time, the solution requires only that a tridiagonal
matrix equation be solved to obtain values for the grid-row. A Crank-Nicholson finite
difference scheme is employed to solve the complex wave amplitude (magnitude and
phase angle) and the wave direction. Details of the program can be found in Winer

2.2 Wave Breaking and Energy Dissipation

The surf zone is where the sediment transport is most active. Most of the incoming

wave energy is dissipated in this narrow region due to wave breaking. The resulting
intense turbulence causes large quantity of suspended sediment in this zone. The

suspended material is then transported by the currents. Unfortunately, the flow

inside the surf zone is extremely complex and the present knowledge on surf zone

dynamics is very limited. Grossly simplified models are used for modeling purposes.

The wave transformation model used in the present study follows the approach of

Dally et al., (1984) and is briefly described here.

The wave transformation model inside the surf zone is aimed at determining the

wave breaking location and the subsequent wave height decay. The earliest breaker

criterion was that of McCowan (1894), who asserted that a wave will break when its

height reaches a certain fraction of the water depth,

Hb = KhI (2.3)

where K was suggested to be equal to 0.78 and the subscript b denotes the value at

breaking. This criterion may be suitable for plane beach situation where the wave

breaks only once. On natural beach profiles where bars are present, it is not unusual

to see a wave break, reform, and break again. In this situation, criteria for wave

reform and successive breaks need to be developed.

Recently, wave breaking and transformation have been linked to the rate of wave

energy dissipation. These models can be classified into two groups; one is based on

the similarity between breaking waves and traveling bores and is therefore restricted

to the region of the surf zone far from the breakpoint where the breaker behaves like

a hydraulic bore (Battjes and Janssen, 1978). The formulation is rather complicated

(Sevendsen, 1984), requiring estimation on the geometry of the surface roller, and is

not practical for the present model. Another one consists of the energy dissipation
formulations using empirical equations that relate the change of energy flux to the

wave height change (Dally et al., 1984). In this approach, an empirical decay constant

is used to describe the decay of wave energy across the surfzone. This method can

incorporate terms to account for different forms of energy dissipation and allow the

reformation of a breaking.

In the present model, the second approach was chosen for its simplicity, flexibility

and overall efficiency in predicting wave height decay in the surf zone. In this simple

approach, the energy dissipation rate, DE, is expressed as

DE = k[ECg E,Cg]

Once waves start to break based on the criterion in Equation (2.3), the rate of energy

dissipation is assumed to be proportional to the difference between the local wave

energy density and a designated energy density value associated with the stable wave,

E,, that the breaker is striving to attain. The local stable wave energy density E8 is

calculated using Horikawa and Kuo's (1966) empirical equation

E, = pg(rd)2

where (rd) represents the stable wave height a breaking wave tends to reach on a

constant depth bottom. Values for parameters k and T were determined by best fit

with Horikawa and Kuo's laboratory results for plane beaches. The parameters were

found to be not particularly sensitive to beach slope and offshore wave steepness so
that for natural beaches, the values (k = 0.17 and T = 0.4) suggested by Dally et al.

(1984) are used. Dally et al.(1984) showed their model to yield good results for wave

height decay over the entire surf zone for a wide range of beach slopes and incident

wave conditions.

2.3 Circulation Model

In this study, the two-dimensional time-averaged and depth- integrated horizontal
(2-DH) circulation model is used to provide current field for sediment transport.
This model is based on time-averaged and depth-integrated equations of motion for

incompressible and homogeneous fluid. This approach is widely used and is considered

adequate beyond the surf zone. Within the surf zone, modifications are necessary.
The governing equations are given by (Ebersole and Dalrymple, 1979)

dU a9U aU a 1 1 1 (SZX 9S,, .la ,
+ U +V + + ---- --7 + + + 0
at ox ay ox pD pD pD \ x Oy P py

49V OV V V 0 1 1 1 _S, as,, 19 7n
+ U +V +g + -- + + + =0
at x x y +gy pD pD pD + x by ) px

+ (UD) + (VD)= 0
at Ox Oy

where t is the time; x and y are the cartesian coordinates in a horizontal plane; U and
V are the corresponding velocity components of the nearshore current; D = h + i;

h is the still water depth; r is the elevation of the mean water level due to wave set

up/set down; ri is the lateral shear stress due to turbulent mixing; ,2 and by are the

bottom shear stresses; T,, and r, are the surface shear stresses; and S,., Sy, and Sy
are the radiation stress components which arise from the excess momentum flux due
to waves. The radiation stress terms are forcing terms, whereas the bottom friction

terms and the lateral mixing terms represent flow impedances. These equations are

obtained by integrating the local x and y momentum equations and the continuity

equation over the depth of the water column and then time-averaging the results. The
governing equations in the circulation model are solved by a matrix analysis using
the alternating direction implicit (ADI) scheme (Winer, 1988). In order to treat the

wave-current interaction, waves and currents are calculated alternatively.

2.4 Undertow Current

Inside the surf zone, the 2-D model is inadequate as the model will yield null

current in the cross-shore direction, consequently, zero net cross-shore transport. In
reality, the current inside the surfzone is highly three dimensional. Field and labo-

ratory observations of surf zone flow show the existence of current that is directed

offshore on the bottom, balanced with the onshore flow of water carried by the break-

ing waves. This offshore-directed steady current near the bed, commonly referred to

as undertow, is known to be the most important mechanism causing profile erosion
and bar formations during strong wave conditions. This undertow is mainly driven

by an imbalance between the excess momentum flux induced by the breaking wave

and the pressure gradient produced by the local mean water difference, or "set up".

The driving mechanism of undertow current by these local imbalances was orig-

inally postulated by Nielsen and Sorensen (1970) and later analytically formulated

by Dally et al. (1984). Svendsen (1984) developed a theoretical model using the first

order approximation technique in describing breaking waves.

The two dimensional conservation of mass equation in the x z plane is

8u 9w
+ =0

Integrating over depth and applying Leibniz rule of integration, the integrated conti-

nuity equation is rewritten as

S_ udz [u W], + [UO + wh = 0
TX f h x X?

Further simplification will result through the use of boundary conditions in two di-

mensions. The kinematic boundary conditions at surface is

at az

The bottom boundary conditions for a fixed bottom is

[u + w]_h = 0

Substituting these conditions into the vertically integrated continuity equation yields

arl i9 n ,
+ udz =0
at ox J-h

Now let the turbulent-averaged velocity vector, U(u, w), be decomposed into mean

velocity and wave fluctuation, which will be distinguished by the subscript c and w,


U = Uc+U,

77 = r/c + 7w,

where Uc and r7c are the time-averaged value of velocity and free surface displacement.

U, and rw are the residual wave fluctuation which can be removed through the process

of wave-averaging.

The wave components are given in terms of wave characteristics such as wave

height, wave number and frequency by linear wave theory as follow:

r77 = -Hcos(kx at)
H coshk(h +z)
u, = -- cos(lckz at)
2 sinhkh

Substituting these into the integrated continuity equation,

+ T f h(uc + uI)dz = 0,
9t Ox _-h

then expanding in a Taylor series at 7 = Ic, which is a mean water surface level, and

taking the time-average,

-+ (/ u + u(wdz) + ,i w,, =0
__t TX -h

Removing the wave fluctuations, this equation can be simplified as

at c 9____
-t- + udz + (--)z= 0

Here, (-u),, can be expressed as the mass flux of x and y components as followings,

M = (wUw), =g H2 k

This mass transport is contained primarily in the crest of waves above the mean water

level and included to satisfy the mass conservation. Finally, we get

Qr/c a [a 9M,
a+ a n udz + a =
at +x J-h ax

Assuming a steady motion, the integrated continuity equation becomes

({Q. + M,) = 0


QX = UCdz

Therefore, the depth-integrated discharge of x component by undertow current, Q,,

can be expressed by the onshore mass flux since the depth-integrated total mass flux

has to be zero in the steady state. That is,

Q. = -M,

The mean undertow velocity is simply estimated as fi = Qh/(7 + h), which is directed

offshore. Figures 2.1 and 2.2 show the distributions of wave height, set up, discharge,
and mean velocity of undertow current for different incident wave height conditions.
The discharge by undertow current gradually increases as the wave shoals, shows the

maximum value near the breaking point, and rapidly decreases after the breaking

point. The mean velocity of undertow also shows a similar trend with discharge,
except for another increase near the shoreline because of the very shallow water

a) Wave Height and Set Up

- '...............

H = 0.5m
S-5- H = 1.0m
........ H= 1.5m
...... H=2.0m
-10 -'''
0 50 100 150 200 250

b) Undertow Current

.... "-- - --. ....... .....~.....
E -0.5 ........

"-H = 0.5m \ .
.c -1 H=1.0m \. ."
S......... H=1.5m
...... H=2.0m
-1.5 '
0 50 100 150 200 250

c) Undertow Current

1-0.5 .

S\1H = 0.5m
0 -1 -H = 1.0m
S........ H = 1.5m
> ...... H= 2.0m

0-1 50 100 150 200 250

Figure 2.1: Distributions of a)Wave Height b)Discharge of Undertow Current, and
c)Mean Undertow Current in Different Input Wave Conditions.


The submodel for sediment transport and beach profile change is described in

this chapter. Depending upon the degree of details involved in problem formulation,

there are three basic approaches to model sediment transport in the coastal zone:

global, intermediate, and detailed approaches. The global approach estimates the

total sediment transport rate in simple terms of total magnitude and mean direction.

Empirical formulas of simple forms relating the gross properties of transport rate to

environmental factors are used. The global longshore transport formulations such as

given in Komar and Inman (1970), SPM (1984), and Kamphuis (1991a) are typical

examples. Such global expressions were derived for beaches with straight and parallel

contours and single-peaked sediment transport profile. Such conditions usually are

not met in a real situation (Kamphius, 1991b). The most common global cross-shore
transport expressions are derived on the concept of 'equilibrium profile' (Bruun, 1954;

Dean, 1977). The global approach is widely used in one line or multi-line models.

Models of this type are incapable of describing bar formations.

The intermediate approach considers the sediment transport as a combined phe-

nomenon of flow and sediment entrainment, and each can be separately influenced

by environmental factors. The equations employed in this type of model usually are

of global nature but are separate for the flow and for the sediment. As an example,

an intermediate approach to longshore sediment transport can be accomplished by

using the longshore velocity formula derived by Longuet-Higgins (1970) combining

with an exponential-type sediment entrainment expression. This approach allows for

improvement or modification on the two elements separately. For instance, various

modified formulas were proposed to compute sediment transport to account for vary-

ing degrees of current-wave interactions such as by Bijker (1966) and Willis (1979).

Owing to the complicated nature and the inherent non-linear behavior of the trans-

port process, none of the proposed expressions appeared to be clearly superior than

the others (Kamphius,1991b).

The detailed approach, as the name implies, computes sediment transport with

detailed consideration on local sediment transport rates. The transport rate across a

vertical cross-section is then obtained by formally integrating over water depth and

wave period as follows,

1 T 0o
Qai =T uTJ (z,t)C(z,t)dzdt

where Q,i is the local rate of sediment transport rate in coordinate direction i. In

principle, this approach is certainly correct. In practice, this full 3-D formulation

is still beyond the state of the art both in terms of fundamental knowledge and

computational ability. The so-called quasi-3D model developed by De Vriend and

Kitou (1990) that provides a 3-D flow profile represents a step toward the development

of such a model. Clearly, there is no operational model of this kind at present.

In the present study, a model of compromised nature is developed. The approach

is actually a mixture of all three types. The rate of sediment transport is treated as

the summation of bed load transport and suspended load transport. Both types of

transport are based on energetic formulation. In the bed load transport, combined

velocity due to mean current and wave orbital motions is incorporated into the for-

mula. The suspended load transport, which dominates inside the surf zone, takes into

consideration the current profile variations inside the surf zone, in other words, the

undertow current profile.

Energetic approach is a popular choice among morphological modelers because

the resulting equations are relatively simple and seemed to yield reasonable results

based on some, though limited, verifications. The concept was introduced by Bagnold

(1963) (see also Bailard, 1981; Bailard and Inman, 1981) and asserts that the sediment

transport rate is directly related to the local energy spent. For bed load transport

this leads to a simple formula equating the transport rate to bottom tangential stress

multiplied by a transport velocity. All other unknown factors are lumped into a sin-

gle empirical coefficient. Due to the time-averaged and depth-integrated nature of

the energetic model, the principal assumption is that the instantaneous sediment

transport rate responds to changes in the near bed velocity immediately. This as-

sumption was pointed out as a limitation of energetic method along with the lack of

the threshold condition for initiation of sediment movement. When applied to the

surf zone, Bailard and Inman (1981) also pointed out another limitation with the lack

for consideration of breaking induced turbulence; all the energetic power is assumed

to be related to the bottom shear stress induced turbulence alone. For suspended

load transport, the energetic concept can also be applied. The cross-shore surf zone

transport mechanism proposed by Dally and Dean (1984), for instance, represents an

alternative view of energetic approach.

In the present model, as will be explained later, a more consistent energetic ap-

proach is used to derive both bed load and suspended load transport formulas. This is

accomplished by introducing the added effect of breaking induced turbulence into the

basic energetic formula. In this fashion, the suspended load inside the surf zone can

now be directly related to the shear stress and a transport velocity computed from

an undertow current. The forms of bed load and suspended load transport formulas

are now consistent.

3.1 Shear Stress under Wave and Current

One of the long-established maxims of the coastal engineers is that 'waves dis-

turb, currents transport'. When waves are superimposed on currents, it is clear from

field observations that the increase in sediment transport is drastic (Owen and Thorn,

1978). Inman and Bowen (1963) and Bijker et al. (1976) also observed enhanced up-

stream sediment transport above the roughness elements at the bottom when a weak

current was superimposed on waves. Authors of existing sediment transport formula-

tions generally agree that there is a pressing need for more information about current-

wave interaction from experimentation. At present, for lack of adequate knowledge,

most of the mathematical models of nearshore processes could not account for most of

the current-wave interaction effects. In nature, the process is certainly complicated.

Nearshore waves induce currents through excess radiation stresses, and resulting cur-

rents, in turn, affect the wave field. Waves and currents interact constantly with

greater or lesser extent through a number of mechanisms such as refraction of the

wave in horizontally nonuniform current field, modification of the wave kinematics by

the (possibly vertically sheared) current and enhancement of the bottom friction, bed

shear-stresses and energy dissipation at the bottom boundary layer and other mecha-

nisms. These interactions could play important roles in nearshore sediment transport

and should be evaluated to the extent possible. One of the known important effects
is the modification of bed shear stress in a combined current wave field. Up till now

the knowledge on this aspect is still comparatively little. Grant and Madsen (1979)

carried out a study to investigate the bottom shear stress in a combined wave and

current flow over rough boundary and proposed a model. O'Connor and Yoo (1988)

also proposed a model based on Bijker's (1966) approach but accounted for the re-

duction in current velocity caused by enhanced eddy motion in the wave boundary

layer. The model appeared to be an improvement over Grant and Madsen's (1979).

The general expression for the time-averaged bottom shear stress for a wave and

current coexistent system is non-linear and is evaluated by the friction law expressed

in the following form:

T = pCfUt\Ut with Ut = U + U

where Cf is a friction coefficient which depends on the bottom roughness, and the ve-

locity Ut represents the vectorial sum of the depth-averaged current Uc and the instan-

taneous wave orbital velocity u,. The constant Cf is calibrated with the laboratory

results. This simple expression for bottom shear stress is based on the assumption

that current and wave particle velocities can be superposed linearly without consid-

ering the enhanced turbulence effects due to their interaction and valid for any wave

angle as long as the magnitude of current is small compared with the orbital velocity

u,( Liu and Dalrymple, 1978). The total velocity vector u' is expressed as

t= (U + i cos 0)i+ (V + fi sin O)

where, U and V are components of u- for x and y direction. ui is a magnitude of the

bottom wave orbital velocity ut, and 0 is the wave angle. Therefore, the magnitude

is given by

IUt \ = U2 + V2 + f2 + 2Ui cos 0 + 2Vi sin0

The wave orbital velocity i is expressed as

u = Ufi cos at

where i, is the maximum wave orbital velocity at the bottom which is found to be

UM T sinh kh

The absolute value of bottom shear stress can be expressed as

I-1 = pCI -t2



7m = max(1ll)

In the development of bed load transport formula, the bottom shear stress is computed

with the combined bottom velocity. The transport is then computed as two separate
components, one from the mean current and the other from the wave transport. This

ad hoc approach may appear to be unreasonable but is a common practice at the

present state of knowledge. This approach is reasonable if one component dominates

the other. For instance, in offshore area, the net sediment transport may be mainly

caused by current owing to the oscillatory nature of the wave field. Then the wave

induced component simply plays a secondary role as a correction term. On the other

hand, inside the surf zone the current field is more difficult to define and it might be

desirable to use the wave-related component to account for the bulk of the sediment

transport. The current component then plays the correction role.

3.2 Shear Stress in the Surf Zone

Modeling surf-zone transport is a difficult task partly because most of the studies

whether experimental, theoretical or numerical dealt with nonbreaking waves. To

formulate an energetic transport model the first order of business is to prescribe rate
of energy dissipation. Inside the surf zone, there are three major energy dissipation

sources at work; they are wave motion-induced shear stress at the bottom, current

velocity-induced shear stress at the bottom and the wave breaking-induced turbu-

lence stress from the surface. When waves are not breaking, the last source is absent

and the shear stresses are all bottom related. The standard quadratic stress formula

is generally applied. The presence of breaking waves changes the pressure distribu-

tion, modifies the bottom shear stress, and generates high local stresses in the water

column. Recent experiments by Deigaard et al. (1992) showed that the bed shear-
stresses in the surf zone on average were not very different from offshore region but

they exhibited much greater wave-to-wave variations and occasional very large val-

ues could occur. For simplicity, bottom stress modification due to breaking-induced

turbulence was not included in in the present model.

There is a wide acceptance of stream power formulas for river sediment trans-

port. It is natural to extend this formulation for sediment transport by waves. This

approach relates sediment transport to flow power, or in the present case the rate of

energy dissipation in the wave field. The use of energy dissipation as a measure of

sediment transport has the obvious advantage of being simple. It can be easily applied

to conditions of non-breaking waves where dissipation is due to bottom friction alone

and of breaking waves where breaking-induced turbulence has a major role in dissi-

pating energy as well. A potential weakness of this approach is that the occurrence

of the maximum energy dissipation (in space and time) does not necessarily coincide

with that of maximum shear stress which is thought to be more directly related to the

magnitude of sediment motion. At present, most of the energetic models are based

on time-averaged and depth-integrated formulation. This formulation will lead to a

simple expression relating sediment transport to a representative energy dissipation

expression, often in terms of its maximum value. This energy dissipation expression is

either directly related to the rate of sediment transport such as the models by Kriebel

(1985) and Larson et al. (1989) or used in the magnitude of sediment suspension. In

the latter case, a transport velocity has to be calculated to complete the formulation.

In the present model, the latter approach is taken. The turbulent shear stress, mainly

responsible for sediment suspension, is drawn by an analogy between the rate of en-

ergy dissipation due to bottom friction under unidirectional flow (Dally and Dean,

1984), and the rate of energy dissipation due to wave breaking and is approximated

by the following equation,

-2h OECg
Hbgt = x

where, E is the wave energy, C, is the group velocity, h is the water depth, and H is

the wave height.

Inside the surf zone, the breaking-induced turbulence effect is added into the

consideration in the present model. To compute the transport velocity, an undertow

model is developed. This undertow flow is mainly driven by the onshore radiation

stress OS.,/zx.

3.3 Sediment-Threshold Theories in Waves and Currents

In the model development it was discovered that the application of a threshold

criterion is essential in correctly predicting the direction of transport (onshore or

offshore). It is one of the major elements to cause net onshore transport in a wave

cycle. The reason is that within a wave cycle the shoreward velocity which mainly

occurs under wave crest is higher than the seaward. The application of a threshold

velocity, thus, could produce a net onshore transport under certain wave conditions.

The concept of sediment threshold motion was first formalized for unidirectional

(river) flows by Shields (1936). Based on laboratory data an empirical curve on the

criterion of sediment threshold motion, known as the Shields diagram, was developed.

The non-dimensional critical value known as Shields'criterion 0 (drag/gravitational

forces) was found to be mainly a function of the flow Reynolds number R (iner-

tial/viscous forces),

t (./p)0s5D
Ot T f[R = ]
(p, p)gD v
where f [ ] indicates 'function of'. The variables are the threshold shear stress at

which motion begins rt, sand density p,, fluid density p, acceleration of gravity g,

median grain size D, and kinematic fluid viscosity v.

Shields' curve has been largely accepted for unidirectional flow. To extend it to
oscillatory flows has been the subject of quite a number of investigations (Bagnold,

1946; Komar and Miller, 1974; Madsen and Grant, 1979) and very different formulas

of preliminary nature have been proposed. The general conclusion has been that still
so little is known about the basic physics on the formation of turbulent oscillatory

boundary layers and how they cause sediment to move. Figure 3.1 shows several

suggested threshold curves for bed load and suspended load as compiled by van Rijn

(1989). For simplicity, the present model uses 0.11 as for threshold for bed load and

0.7 for threshold of suspended load.

3.4 Sediment Transport Formulae

In the present model the area of computation includes both offshore and surf zone.

Since sediment motion inside the surf zone is markedly more active than offshore due

to the presence of strong turbulence, different sediment transport formulas are to be

used for these two regions. A smooth transition between these two regions is also

required. In problem formulation, the surfzone transport is clearly more difficult.

Inside the surfzone, intense sediment suspension is caused by large vortexes due
to wave breaking and the suspended sediment is then transported in the offshore

direction by an undertow current. The importance of the undertow transport has

been shown by a number of investigators (Stive and Wind, 1986; Svendsen, 1984;

Deigaard et al., 1991). A quantitative description of the transport rate depends on

an accurate description of this suspended sediment under breaking and broken waves.

In spite of the importance of this offshore directed suspended transport by undertow,

most of the models do not directly address this effect. For example, the models by

Kriebel (1985), Larson et al. (1989), and Watanabe et al. (1986) all use empirical

criteria for distinguishing onshore and offshore sediment transport. All these criteria

indicate offshore transport in the entire nearshore zone under stormy wave condition

and cause shoreline retreat. This condition appears to prevail in small-scale wave

flume experiments. However, it is not always consistent with the results of large scale

- particle parameter, DN

Q2 0.3 0.5

1-- t f I i t i

2 3 5 10

particle diameter, dO*10 (m) at T =15C

Figure 3.1: Initiation of Motion and Suspension for Unidirectional Flow (from van
Rijn, L.C., 1989).

05 0.1

20 30
I !



experiments. Kajima et al. (1982) demonstrated in large-scale experiments that

extremely intensive onshore transport can occur outside the surf zone and suggested

possible three different sediment transport patterns in nature (Figure 3.2). This

onshore transport can easily occur in offshore zone and is attributed to the sheet flow

movement, which is difficult to appear in small-scale experiments. Also, outside the

surf zone the net movement can be caused by streaming, which even in a closed flume

will result in a forward-directed sediment transport in the sheet flow regime. Elfrink

et al. (1992) discussed this forward-directed transport applying several different wave

theories. Ribberink and Al-Salem (1991) showed experimentally that the nonlinearity

of waves also results in a onshore-directed sediment transport. Hence, improvement

on the criterion for the net transport direction is desirable for the model development.

The study by Shibayama et al. (1989) separated the transport in nearshore zone into

onshore component and offshore component. The net transport rate is treated as the

simple superposition of these two components. A similar approach is adopted here.

In the present study, the sediment transport formula contains two parts, bed load

and suspended load. The bed load transport is based on an energetic approach driven

by mean current and bottom wave orbital velocity. Owing to the asymmetric wave

bottom orbital velocity in a wave cycle, this bed load transport has a net onshore

component. The suspended load transport which dominates in surfzone is built upon

an undertow model. Here, the suspended sediment concentration is related to break-

ing wave energy dissipation and the transport velocity is the mean undertow current.

This component is always directed offshore.

The total transport Q is the sum of bed and suspended load as followings,

Q = Qb+q,

qb = Abc(rw cr)Uc/pg + Abw(bw rcr)Uw/pg (3.1)
('7 = -.. /
q, = Uh dz = f (tu,b)UD = ATt,rbQu

a Y

0 .








0 0


o -c
-: a _,
2 < o .m
w .) c(^ Q

L i


U,; Integrated depth mean wave induced-currents

U,; Maximum orbital velocity at the bottom

U,; Mean velocity of the undertow

Q,; Discharge by the undertow

rT,; Shear stress generated by wave and mean current

turtb; Shear stress generated by wave and mean current

r,; Critical shear stress under wave and mean current

Abc; The coefficient for bed load transport due to current

Ab,; The coefficient for bed load transport due to wave orbital velocity

A,; The coefficient for suspended load transport

D; The water depth

The maximum orbital velocity at the bottom is given by linear wave theory,

T sinh kD

can be also approximated to gH/2C for shallow water waves. The mean velocity of

the undertow was approximated as

1 gH2
S 8 CD

The discharge associated with the undertow current is given by as = UD where

D is the total depth. The coefficient Abc, Abw, and A, in the transport equations

incorporate all unknown factors. In the present model, these empirical coefficients

are to be determined through comparisons of computed beach changes with physical

model experiments.

This simple time-averaged approach omits three aspects of sediment transport

under an oscillatory flow. It ignores the presence of phase lag between sediment

motion and fluid velocity. This aspect is not expected to affect the time-averaged

transport results significantly. This model does not consider the on-offshore motion

of sand based on the trajectories of a suspended sand particle during its fall to the

bottom as described in the heuristic model by Dean (1973). Thus, the suspended

load transport is always directed offshore. Thirdly, since higher peak bottom orbital

velocity in the direction of wave propagation occurs when wave crest passes, the

net bed load transport is with the direction of the wave, or onshore in this case.

Sediment transport by orbital velocity against the wave (offshore in this case) is not

explicitly considered. As a consequence, beach could becomes accretional up to the

breaking point. Under relatively calm weather conditions, when surf zone becomes

very narrow the beach could have an overall appearance of accretional except close

to the shoreline. Figure 3.3 shows an example on the distribution of stress and the

resultant sediment transport rate based on the present formula. The sum of onshore

and offshore transport results onshore transport outside the surf zone and offshore

transport in the surfzone. In spite of the deficiencies mentioned above, the strength

of the present model lies in its simplicity and the fact that transport mechanisms

acting on different time scales are combined in a consistent way.

3.5 Slope Effect

Sediment transport is maintained by the tangential thrust which is required to

overcome the sand grain resistance at the bed. The resistance is mainly due to

bottom friction. It is also influenced by the bottom slope as downslope reduces

resistance and upslope increases resistance. This slope-related transport mechanism

was pointed out as of major importance to the inherent stability of the system and

to the equilibrium bed topography. In fact, the down-slope gravitational transport

is the most important mechanism to keep short-wave perturbed bed from growing

indefinitely and to enable the coastal profile to reach a dynamic equilibrium state.

Profile and Wave Height


Wave Height
--- Profile

mt= ----- I ----- I -----I ----------

20 30


20 30

Sediment Transport

10 20 30 40

Figure 3.3: Distributions of a)Wave Height b)Stress c)Sediment Transport Rate.






Shear Stress
Shear Stress



" -1
E 0


--'.. Onshore
"x /. Transport
S / Offshore
*.\ *." Net
./: Transport






There are two kinds of transport mechanisms relevant to bottom slope (De Vriend et

al., 1994), which are:

-Slope-dependent "active" transport, where the sediment-carrying water motion is

slope dependent, but does not necessarily vanish as the slope goes to zero, and

-Slope-dependent "passive" transport, which vanish as the slope goes to zero. It is

difficult to accurately account for these mechanisms in morphodynamic models with

the present state of knowledge. Rough estimations are used here.

A basic formulation to express the slope gravitational transport component pro-

posed by Horikawa (1988) assumes the following functional form,

q. = q. + exq.I-g,

OY ah

in which x and y are horizontal cartesian coordinates, q, and qy are the transport

components, q. and q; are their equivalents for horizontal bed, h is the water depth

and e are empirical coefficients. Some authors proposed different versions of equa-

tion with different coefficients for the down-stream and the cross-stream components

(Struiksma et al., 1985; Watanabe et al., 1986). At present, there is less confidence
to use this type of formulation for up-slope transport when wave is against the slope

such as a concave upward beach. In this case, sediments are still transported up-slope

by wave motion which is very uncommon in river flow. The gravitational transport

will result in decreased sediment transport. Several suggestions have been proposed

to improve this formula. It seems more reasonable to assume that the parameter e is

a variable rather than a constant, dependent on the ratio of the bedload to the total
load and the slope.

In the present model, the same simple approach as proposed by Horikawa is

employed. A sensitivity test was performed to determine the reasonable ranges of

values of the coefficients and the slopes. Figure 3.4 shows the change of sediment

transport rate at the different conditions of bottom slope and coefficients. As the

slope becomes steeper, the offshore transport in the surfzone increases dramatically

and also the onshore component outside the breaking point changes the direction

gradually to the offshore. This slope effect can be used as one of the mechanisms to

control onshore transport, offshore transport or composition of onshore and offshore

transport as illustrated in (Figure 3.2).

3.6 The Transition Zone

A subject of increased research over recent years is the so-called transition zone

effect on the wave setup, undertow current, and sediment transport. Based on exper-

imental wave tank observations after breaking, the incipient wave crest continues to

travel for a distance before it curls over and plunges onto the water surface below. The

zone between the incipient breaking and the plunging point is defined as transition

zone. Across this zone wave transforms from a non-breaking state to a peak turbulent

state where the rate of the energy dissipation is near its peak. This transition zone

effectively represents a region over which wave potential energy and momentum are

progressively transformed into dissipative turbulent kinetic energy and surface rollers.

The locations of breakpoint bars are usually found to be near the end of the transition

zone where the breaking waves are completely disintegrated.

Several approaches have been proposed to evaluate the distance and influence of

the transition zone based on wave tank experiments. Galvin (1969) noted through

small-scale experiments and prototype-scale data that this distance was equal to about

4Hb. He also showed that the transition length is dependent on beach slope tan#f; for

the same wave height a steeper beach yields a shorter plunging length. An empirical

x -10 Slope Effect on Sediment Transport
1 1 1 1 9

0 10 20 30 40

S10.3 Slope Effect on Sediment Transport






20 30

Figure 3.4: Distributions of Sediment Transport Rate with a)Different Slope Affecting
Coefficients b)Different Bottom Slope.

equation is proposed to give,

= 4.0 9.25tan/

Basco and Yamashita (1986) developed an expression relating the width of the transi-

tion zone to the surf parameter. Larson et al. (1989) determined the distance between

the breaking point and the maximum trough depth by analyzing the CRIEPI (Central

Research Institute of Electric Power Industry in Chiba, Japan) data set, which con-

tained rather comprehensive wave information. By regression analysis, the following

equation was proposed,

i = 0.12(tanP)-o.44[ H-236
Lo Ho

Okayasu et al. (1990) applied the concept of a energy dissipation distance, that

varies across the surf zone, to describe a process whereby wave energy is transmitted

to turbulence through organized large vortices. Nairn et al. (1990) expressed the

transition length as a function of both surf similarity parameter at the breaking point

and the breaking depth, and proposed the following empirical relationships between

the transition zone length (It) and local surf similarity parameter (W).

t = h (1 0.47--0'275) for ( > 0.064
It = 0 for < 0.064



and tani, Hb, Lb, and hb are respectively the bed slope, wave height, wave length

and water depth at breaking. O'Shea et al. (1991) analyzed the experimental data

and suggested the following formula without a depth parameter.

It = 0.556tanp/LbS-1.46

The slope used in these equations is subjectively selected and it is defined as the slope

just shoreward of the breaking point. Narin et al.(1993) applied a linearly decaying

parameter to the breaking-induced turbulence inside the transition zone and showed

that the inclusion of the transition zone in profile modeling has an important effect on

the predicted profiles, particularly for the bar features. The SBEACH model (Larson

et al., 1990) introduced four different zones of sediment transport including a pre-

breaking transition zone and a post breaking transition zone, a broken wave zone and

a swash zone. Different transport formulas are used for each zone.

Figure 3.5(a) shows the comparisons of various transition length formulas. Gen-

erally, the transition length decreases as the bottom slope becomes steeper. In the

present model formula I was selected, which is close to CRIEPI data sets. Fig-

ure 3.5(b) shows an example of including the transition length into the sediment

transport model. The inclusion of transition length moves the maximum turbulence

induced stress to the plunging point. This stress decreases exponentially to the break-

ing incipient point.

3.7 Cushioning Effect

Most of the laboratory results as well as field evidence seemed to support the

concept of beach equilibrium. Several approaches have been pursued in the past in

an attempt to characterize the equilibrium state. Keulegan and Krumbein (1949)

studied the characteristics of mild bottom slope where wave energy is mainly dissi-

pated by bottom friction in non-breaking condition. Bruun (1954) and Dean (1984)

both proposed exponential type empirical relationships between water depth and the

seaward distance with a single empirical coefficient 'A' known as the scale parameter.

Moore (1982) found that the scale parameter mainly depends on sediment size after

analyzing numerous beach profiles.

Various Transition Length Formulas


Turbulent Shear Stress



Figure 3.5: a)Comparisons of Various Transition Length Formulas. b)Example for
Application of Transition Length Formula to the Turbulent Shear Stress.


Profile equilibrium can be reached under three kinds of enviorment conditions.

The most obvious case is when there is no force acting on the beach, or the water is

calm. The second case is when the tangential thrust by fluid is not strong enough

to overcome the sand resistance. This state can be found either outside the surfzone

or mild sea condition which has no wave breaking. The third case is when the local

landward sediment transport is balanced by the local seaward sediment transport.

In this case, although there could be active sediment movement, the profile remains

stable. This last case is the case of interest. Including this feature into the model

is a difficult subject. One popular approach is to predesignate an equilibrium profile

shape. The sediment transport formulas should then be consistent to lead the profile

evolution to this equilibrium profile. Kriebel's (1985) storm profile model was the

first of its kind The SBEACH model which in essence, is a modified version of

Kriebel's model followed the same approach. This type of models can be classified as

closed loop model. On the other hand, most sediment transport models which use

detailed approaches do not have a targeted equilibrium profile therefore often fail to

reach an equilibrium state. This type of models is known as open loop model. For

the open loop model to reach equilibrium, mechanisms must be devised to locally

balance the on/offshore transport. The present model is an open loop model. In

the formulation the offshore sediment transport is due to suspended load whereas

the onshore transport is by bed load. In the formulas presented earlier, inside the

surf zone the offshore transport is much too strong to be balanced by the onshore

transport component. The reason is that in the formulation, once wave breaks wave

breaking-induced turbulence immediately produces a strong bottom stress and the

resulting offshore transport is much larger than the onshore transport computed by

the bed load transport equation. Clearly, the offshore transport equation needs to

be modified. Dally and Dean (1984) pointed out that his expression developed for

the sediment concentration profile apparently lacks the "cushioning" effect which the

water column provides in reducing the amount of sediment entrainment as breaking

wave form and trough evolve. This cushioning effect is especially important in the

stabilization of the bar and trough formation. Almost no work has been done for this

cushioning effect. The present model attempted to incorporate this cushioning effect

into the model based on the ratio of the depth and wave height at the plunging point

as follows,

C, = tanh(7-)700

where, C,, is the cushioning effect, H is the wave height, D is the water depth.

Figure 3.6(a) plots this cushioning coefficient and its effect on sediment transport.

As can be seen, when relative water depth increases, the cushioning equation limits

the turbulence penetration to the bottom. When wave height is larger than water

depth, there is no cushioning effect. However, as the water depth at the trough

zone becomes larger, cushioning effect becomes stronger. Finally when water depth

reaches 2.5 times the wave height breaking induced turbulence will not reach the

bottom. This equation is, of course, purely empirical at this stage with no supporting

data. Figure 3.6(b) shows the effect on sediment transport rate. With the inclusion of

this effect, the open loop model presented in this study could reach profile equilibrium

without a predetermined profile shape.

3.8 Profile Change

Changes in the beach profile are calculated at each time step from the local, instan-

taneous sediment transport rate in both x(cross-shore) and y(longshore)directions,

and the equation of mass conservation of sand. The conservation equation of sedi-

ment transport is presented in its two-dimensional form,

Oh qx O9qy)
=( + q
Tt dx Oy

Cushioning Effect

0.4 0.6
Wave Height/Depth

Evolution of Sediment Transport Rate

0 5 10 15

Figure 3.6: a)Distribution of Cushioning Effect. b)Evolution of Sediment Transport


"g 0

r -0.5


................................... ......... .. ....... .........

Envelope of the Maximum
Onshore Transport Rate
Envelope of the Maximum
Offshore Transport Rate

where h is the water depth, t is the time, and q, and q, are the components of

volumetric net sediment transport rates in the x-direction and y-direction, respec-

tively. The volumetric rate is in unit of volume/length/time. The new bathymetry

will eventually affect wave transformations, breaker location, current patterns and

modify sediment transport distributions. For 2-D beach profile case, we can calculate

sediment transport rate from successive profile surveys. By integrating the equation

of mass conservation from profile changes, a time averaged net distribution of the

cross-shore transport rate is obtained for the elapsed time between two surveys. The

transport rate q(x) across the profile is thus calculated from the mass conservation

equation written in difference form with respect to time as,

q(x) = t1 L (h2 h)dx
t2 t1 o


t, t2 = times of profile surveys
Xo = shoreward location of no profile change, where q(xo) = 0

hi, h2 = profile depths at survey times 1 and 2


The nearshore sediment transport characteristics under storm wave conditions as

predicted by the model are illustrated here. In order to validate the 3-D morphological

response model, cross-shore transport rate and longshore transport rate are calibrated

separately by using available experiment data or empirical formulas.

4.1 Cross-Shore Transport Rate

For the calibration of cross-shore transport rate, three sets of 2-D tank experiment

data were used. These included the case of a sand beach backed by a sloping dike

tested in the German Big Wave Flume (GWK), case CE 400 from Saville's large

wave tank tests (CE), and small scale wave tank experiment data collected at the

laboratory in the Department of Coastal and Oceanographic Engineering, University

of Florida (UF). Comparisons were made between computed values and experimental

results both in profile changes and transport rates.

The GWK data (Dette and Uliczka, 1986), were used for calibration. The Big

Wave Flume is 324 m long, 7 m deep and 5 m wide. The initial profile is composed

of two bottom slope which are +2 m above SWL and 10 m wide dune with 1 to 4

seaward slope down to 1 m below SWL and following 1 to 20 slope down to channel

floor. The experiment used sand with a median diameter of 0.33 mm. The test

profile was subjected to regular wave attack (H = 1.5 m, T = 6 sec, h = 5.0 m).

Figure 4.1 shows the comparison between the predicted profiles and the experimental

results at run times of 62, 111, and 273 minutes, respectively. The computed wave

Profile Change(After 62 Min.)






.10 0 10 20 30 40 50 60 70

Profile Change(After 111 Min.)
A -... -



-10 0 10 20 30 40 50 60 70

Profile Change(After 273 Min.)
A ---




0 10 20 30 40

50 60 70

Figure 4.1: Comparison between Computed and Measured Beach Profiles for t= 62,
111, 273 minutes. Data from Dette and Uliczka (1986).

-- Initial profile
SBig Wave Ruffme Data
.... Present Model Result

-.. .-- -.--.-.-. -.-.-. -.

---- Initial profile
- Big Wave Flume Data
...... Present Model Result


--- Initial profile |
- Big Wave Flume Data
...... Present Model Result





height distribution across shore is also shown. The waves cut back the foreshore to

produce a vertical scarp and a bar formed shoreward of the breaking point which grew

and moved offshore with continued wave action. The numerical model satisfactorily

reproduced the observed foreshore erosion and main breakpoint bar development.

The volume of the main breakpoint bar and the amount of erosion on the foreshore

are rather well predicted by the numerical model. Simulated shoreline retreat and bar

growth were initially rapid and gradually slowed as the bar moved offshore to reach a

location close to that of the observed bar at the end of the run (20 hr). However, the

bar trough is less well reproduced. All smaller features inshore of the main breakpoint

bar were, of course, not reproduced in the simulations.

Figure 4.2 shows the comparison of the cross-shore transport rate between the

profile changes in Figure 4.1. Initially, a high peak appears near the shoreline as
beach material slumps down slope into the foreshore zone in this experiment. These

material was transported offshore to form the bar. The seaward changes of the peak

transport rate explain the the offshore movement of the bar. With the exception at

the initial stage, the predicted transport rate distribution is in good agreement with

the laboratory data. At the initial stage the experimental values were larger than

predicted. There are many factors that could contribute to the difference such as

slumping effect mentioned earlier. It was also found later in small scale experiments

conducted at UF that the profile erosion particularly in the dune region was much

more severe in the initial stage if the beach is dry and loosely compacted as opposed

to wet and well compacted. The best overall fit of both profile and transport rate

was obtained by using Asb in a range from 0.05 to 0.07 and A, from 1.0x10-5(m2/N)
to 1.5x10-5(m2/N).

With these determined Ab, and A, values, the model was used to simulate the CE

case CE400. Figure 4.3 shows the comparison of measured and calculated profiles.


Cross-Shore Transport Rate(Experiment)

nt ......---- ---- -- '- .--.--- *"" --- -



o -4


0 10 20 30 40

50 60 70

Cross-Shore Transport Rate(Present Model)


-4 .... After 62 Min.
..' *-- After 111 Min.

-6 -- After 273 Min.


0 10 20 30 40

50 60 70

Figure 4.2: Comparison of Cross-Shore Transport Rates between Experiment and
Present Model for t= 62, 111, 273 minutes. Data from Dette and Uliczka (1986).

\ .I....


= ~ I ***

After 62 Min.

After 111 Min.

- After 273 Min.







The test conditions were: initial uniform slope = 1/15; grain size = 0.22 mm; wave

height and period of 1.62 m and 5.6 sec in the horizontal section of the tank (depth
= 4.42 m); and constant water level. The numerical and test results are shown for

simulation times of 1, 3, and 5 hours. In this case, the bar development was also well

predicted except at the initial stage. However, the profile change near the shoreline

shows very different results between the experiment and the model. In experiment,

there was strong erosion at the foreshore region above the water level, but this erosion
was limited near the shoreline in the numerical model. The spatial distribution of the

transport rate from the CE tests were very different from that of the GWK tests. Here

in the CE case, peak transport initially occurred near the breaking point and did not

show any onshore transport outside the breaking point (The numerical model results

did show a very small onshore transport component). Also, in the CE experiments,

the transport in swash zone apparently played an important role to cause shore face

erosion. It seemed that at the initial stage most of the wave energy was expended to

produce the bar. Once a small bar was formed, more wave energy was transmitted
over the bar causing swash zone erosion. This mechanism apparently played a minor

role in the GWK where dune erosion was dominated by the slope effect. The numerical

model does not have an appropriate swash zone transport mechanism. Therefore, it

was unable to reproduce the large erosion near the shoreline in the experiment.

Next comparison was for the small scale experiments carried out in the wave
tank, in the Department of Coastal and Oceanographic Engineering, University of

Florida. The tank is 45.7 m long, 1.9 m deep and 1.8 m wide. The initial profile

has a composite slope of 1 to 2.90 near the shoreline followed by 1 to 14.46 slope

down to channel floor and used sand with a median diameter of 0.20 mm. The

test profile was subjected to regular wave attack (H = 0.1 m, T = 1.33 sec, h =

52.0cm). The predicted profiles are shown at times of 10, 20, and 40 minutes together

with the measured profiles(Figure 4.5). The computed wave height distributions

Profile Change(After 1 Hrs)

--- Initial profile
Big Wave Flume Data
...... Present Model Result
, I I I I I


Profile Change(After 3 Hrs)


--- Initial profile -
Big Wave Flume Data
...... Present Model Result


Profile Change(After 5 Hrs)

-- Initial profile '-s
Big Wave Flume Data .
-..... Present Model Result-

-20 0 20 40 60 E

Figure 4.3: Comparison between Calculated and Measured Beach Profiles for t= 1,
3, 5 hours. Data from Saville(1957).




Cross-Shore Transport Rate(Experiment)
i I I I I

r.. Bd
-S. _

.., ,
' '9.* /

****. After 1 Hr

S- After 3 Hr

After 5 Hr

-20 0 20 40 60

Cross-Shore Transport Rate(Present Model)

-20 0 20 40 60

Figure 4.4: Comparison of Cross-Shore Transport Rates between
Present Model for t= 1, 3, 5 hours. Data from Saville(1957).

Experiment and













...... After Hr
_.After 3 Hr /
\/After 5 Hr
.. After 1 Hr

SAfter 3 Hr

After 5 Hr

a) Profile Change(After 10 Min.)
--2 -- -----.-----*---------------------

S Initial profile
-- Big Wave Flume Data
S..... Present Model Result

.0 1 2 3 4 5 6

b) Profile Change(After 20 Min.)
0.2-------------------- -------*-------

S-- Initial profile
-0.4 Big Wave Flume Data
...... Present Model Result
0 1 2 3 4 5 6

c) Profile Change(After 40 Min.)

0 -. Initial profile
-0.4 Big Wave Rume Data
...... Present Model Result
-0 1 2 3 4 5 6

Figure 4.5: Comparison between Calculated and Measured Beach Profiles for t= 10,
20, 40 minutes. Data from Air-Sea-Tank Experiment.

across shore are also shown. The experimental results were somewhat similar to that

obtained in the GWK. The beach experienced a vertical scarp as waves cut back the

foreshore. The breakpoint bar was located shoreward of the breaking point which

grew and moved further offshore with continued wave action. The profile change

showed a deeper cut at the trough region than the GWK case. The comparisons of

transport rates are shown in Figure 4.6. It can be seen that the transport rate showed

two prominent peaks inside the breaking zone, one near the shoreline and the other

corresponding to the trough erosion. With the exception of the trough erosion, the

numerical model appeared to perform reasonably well.

4.2 Longshore Transport Rate

Longshore sediment transport plays a very important role particularly in long

term beach evolution. The longterm evolution of many coastlines is the result of

slight gradients in the longshore transport rate. In the longshore transport, sand

grains are set in motion mainly by wave action and then transported by longshore

current. The longshore wave-driven currents and transport are influenced by the

form of the coastal profile. Therefore, it is required to use realistic bathymetries

in the modeling of the littoral drift to correctly predict the morphological changes.

Available data suitable for calibration and verification of longshore transport rate are

scarce and mostly limited to 2-D cases. The 2-D data will not yield information on

Asc. In this chapter, the characteristics of longshore transport rate are investigated
by comparing with CERC formula and the coefficient Ac was calibrated based on a

3-D basin experiment.

The popular longshore sediment transport formulas are all based on the simple

assumption that the rate of transport is proportional to the longshore component

of wave power. Komar and Inman (1970) proposed a longshore transport formula

by relating the longshore wave power component Pi with the total immersed-weight


x loCross-Shore Transport Rate(Experiment)

2 3 4 5

SloCross-Shore Transport Rate(Experiment)


Figure 4.6: Comparison of Cross-Shore Transport Rate between Experiment and
Present Model for t= 10, 20, 40 minutes. Data from Air-Sea-Tank Experiment.






-0.5 F


-2.5 F

-A -
i" .--
\. /t-/ I "


...... After 10 Min.
*- After 20 Min.

- -After 40 Min.





-0.5 F


-2.5 F

5,."-I /
-- ^--------.. ,"

,./ *.-. After 10 Min.
.-.- After 20 Min.
-- After 40 Min.



V, .

transport rate ii as

it = KPi

CERC's littoral drift formula (Shore Protection Manual, 1984) which is widely used

has the same functional form given as,

SK(ECg cos 0 sin )b
pg(s 1)(1 -p)

where Q is the volumetric longshore transport rate, E is wave energy, Cg is group

velocity, s is specific gravity, p is porosity and K is an empirical transport coefficient.

Therefore, these formulas are all based on energetic concept with empirically deter-

mined coefficient based on field evidence. Most one-line shoreline evolution models

employ CERC's formula or its equivalent. It is recognized that longshore transport
formulas of this kind were developed for long term averaging situation and for shore-

lines without the presence of structures. It is always questionable that such formulas

are suitable for shoreline evolution modeling as most of these models are intended for

predicting shoreline evolution with the presence of structures.

In the present model, the sediment transport formulas as presented are of very

different nature. However, for lack of laboratory and/or field data for verification,

CERC's formula is used here as a bench mark to test the model. A case of 2-D beach

that has an initial profile of a uniform slope (1/20) was used here to compare the

characteristics of the present model and CERC's formula. Figure 4.7(a) shows the

longshore transport distribution across the surf zone as calculated by the model at

different wave angles under the same wave height of 1.5 m. The transport patterns

are all bell-shaped with a uni-modal peak inside the breaking point. This shape is

consistent with observations on beaches of more or less uniform slopes excluding the

swash zone ( dual peaks were common if swash zone is included). It is also shown that

the longshore transport rate increases drastically as wave angle increases. The total

transport rate is obtained by integrating the volume under the curves. These total

transport rates are compared with the CERC's formula in Figure 4.7(b) which plots

the transport rate vs wave height for different wave angles. The comparisons are good

for wave up to 200. For larger wave angles, the model yields values slightly higher

than the CERC's formula. The coefficient Ab, in the transport equation given by

Equation (3.1) is equal to unity and 0.77 was used for the K value of CERC formula

in this comparisons.

As discussed earlier, most experiments and field measurements were conducted for

cross-shore transport, and there is very little information on longshore transport rate.

Therefore, a plain beach movable bed physical model was constructed in a wave basin

to investigate the sediment transport patterns and the resulting topographic changes.

The experiments were performed in the 16x23 m 3-D wave basin of the Coastal

Engineering Laboratory of the Department of Coastal and Oceanographic Engineering

at University of Florida. The 3-D wave basin has several advantages over wave flume.

Reflection patterns in wave height measurements are reduced, alongshore effects on

wave transformation are included and alongshore currents and sediment transport can

be studied. The designed initial beach profile consists of a flat backshore, a steep-

sloped foreshore, and a mild-sloped offshore, and has simple straight shoreline and

parallel offshore contours. The beach extends seaward to about 6 m from the shoreline

where it merges to the fixed basin floor. From shoreline to the offshore wave generator,

the distance is equal to 24 m. The water depth at the toe of the beach is equal to 40

cm. Figure 4.8 shows the model setup in the laboratory. Two set of experiments were

carried out with two different incident wave directions, one normal to the shoreline

and the other at 15 degree oblique to the shore normal. In order to generate correct

wave angle and prevent alongshore wave energy spreading, two sidewalls parallel to the

incident wave rays were constructed as wave guides. In the oblique wave experiment,

additional sand in the form of a feeder beach was placed at the updrift boundary

Longshore Transport

I '

/ aeHiht=15m


Wave Height = 1.5(m)
Wave Direction
-- 0 Deg
- 10 Deg
........ 20 Deg

.....-- 30 Deg

100 150




o 500
j 1000


Longshore Transport

Wave Direction

O 10 Deg X
- -+20 Deg
...... 30 Deg
./." +
*-.- X 45 Deg ./." ,

,. "* -

0.5 1 1.5 2 2.5
Wave height(m)

Figure 4.7: a)Distributions of Longshore Transport Rate in Different Wave Directions
b)Comparison of Longshore Trasnport Rates between CERC Formula and Present
Model in Different Wave Directions.














Movable Bed Model

Figure 4.8: Schematic Map of the Plain Beach Movable Bed Model for Normal and
Oblique Waves.

to supply the longshore sediment transport. And, at the downdrift boundary, the

model was connected with a return flow channel which also served as a catch basin

for longshore sediment. The topographic changes were monitored by surveying a total

of 5 bottom profile lines. Along each line survey was carried out from the shoreline

to minus 30.5 cm contour at intervals of 7.6 cm. The surveys were carried out at run

times of 5 min, 10 min, 20 min, 40 min, and 80 min, respectively. Figure 4.9 shows

photos taken during the experiment under normal wave test condition. Figure 4.10

presents the orthographic plots of bottom bathymetries at different times. Figure 4.11

plots contours at different run times. It can be seen that even though the experiment

was intended for a pure 2-D case, 3-D features were evident and grew with time.

The difficulty of maintaining 2-D feature in movable bed experiment is a well known

fact. Oh (1994) even found 3-D phenomena in a narrow 2-D wave tank experiment

and attempted to explain the inevitability on the growth of 3-D features. Clearly the

numerical model is not capable of producing 3-D topographic features. Therefore,

comparison of topographic changes between numerical and experimental result might

not be as meaningful. However, individual cross-sectional profile should maintain

the essential features. From examining the test results typical profile evolution along

the beach can be characterized by erosion at the shoreline and the formation of a

breakpoint bar at the offshore limit of the surf zone. Much the same as the 2-D tank

experiments, in the beginning a large amount of sediment was removed from the beach
face and from the surfzone and the profiles experienced very rapid transformation.

The process slowed down progressively showing a slowing of the offshore translation

of the breakpoint bar.

Figure 4.12 shows the comparisons of profile evolutions between the numerical

model and experiments. Here, the comparisons were made for the center profile which

is believed to be less influenced by the 3-D effects. The numerical model is considered

successful to duplicate the main features of the profile shape evolution such as the


r -

.1 a


Figure 4.9: Photograph of a)Plain Beach Movable Bed Model and b)Resultant Mor-
phological Changes for Normal Incident Waves in the 3-D Basin Experiment.

Depth Change(Wave Angle = 0)

After 00 minutes After 05 minutes




After 10 8
After 10 minutes


E 0.0.


3 0 8 4 0
After 40 minutes
After 40 minutes

,E 0.0





6 0

After 20 minutes




6 0

After 80 minutes




6 0

Figure 4.10: Orthographic Plots of Bathymetric Change for Normal Incident Waves
in Plain Beach Movable Bed Experiment.


Depth Change(Wave Angle = 0)

After 00 minutes



...10 .. ... ...

) 2 4 6
After 10 minutes



0 2 4 6
After 40 minutes

2 4 6



Figure 4.11: Contours of Bathymetric Change for a Normal Incident Waves in Plain
Beach Movable Bed Experiment.

After 05 minutes

4 -20.

10 -

2 ---...-.--.-:'L-. '-

0 2 4 6
After 20 minutes

4 -20

2 10

0 2 4 6
After 80 minutes



0 2 4 6










a) Profile Change(After 20 Min.)

S-0.2 Initial profile
-- 3-D Wave Basin Data
...... Present Model Result
-0.4 '' '''
0 1 2 3 4 5 6

b) Profile Change(After 40 Min.)

E 0 ... .. .. .. -. .. .. .. .. .

S-0.2' Initial profile
-- -3-D Wave Basin Data
...... Present Model Result
-0.4 '
0 1 2 3 4 5 6

c) Profile Change(After 80 Min.)
0.2 j ------------- -- -------------- |

E 0-------

-0.2 Initial profile
3-D Wave Basin Data
...... Present Model Result
.0.4 1 1 -
0 1 2 3 4 5 6

Figure 4.12: Comparison between Computed and Measured Beach Profiles for t= 20,
40, 80 minutes. Data from Plain Beach Movable Bed Experiment for Normal Incident

foreshore erosion and breakpoint bar development. The profiles from the 3-D exper-

iment, however, clearly contained more irregular features of 3-D nature, particularly

near the breakpoint bar, than their counter parts in 2-D experiments. Figures 4.13

and 4.14 show, respectively, the orthographic and bathymetric contours plots under

15 degree oblique wave condition. Here, the 3-D features were more pronounced,

specially near the boundaries. Figure 4.15 compares the profile changes at the center

section in the experiment with the numerical results. The breakpoint bar develop-

ment as well as its size and location were predicted well by the numerical model. The

foreshore erosions were grossly underpredicted by the numerical model. However, one

can not conclude from this comparison that the numerical model is deficient. In the

numerical model, the influx of source material at the updrift boundary is governed by

the input wave condition based on straight parallel contours. In the experiment, once

3-D feature developed, the gradient of longshore transport rate started to produce

nonuniform change of contour and shoreline, and it is very difficult to provide correct

source material at the updirft boundary. The excessive erosion at the foreshore zone

appeared in the laboratory results could be attributed to the inadequate source sup-

ply at the updrift boundary. The fact that the model can reproduce well the cross

shore feature under oblique wave condition is reassuring.

After 80 minutes run time, a total of 0.28 m3 sand was collected at the sediment

trap channel located in the downdrift boundary. This longshore transported material

was used to calibrate the Ab, value in the numerical model and to check the K value

in CERC's formula. By applying wave height, and angle used in the experiment to

the CERC's formula, it was found that K = 0.23 from the results. This value of

the proportionality coefficient obtained in this study is smaller than 0.77 in Komar

and Inman's formula and is rather close to the value in Sato and Tanaka (1966)'s

formula. It is noted here that many one line models utilizing 11PI type of formulas

the K coefficient was adjusted downward to the range of 0.05 0.4 based on model

Depth Change(Wave Angle = 15)

After 00 minutes


6 0

After 10 minutes




6 0
0 8

After 40 minutes


E 0.0.

6 0
0 8





After 05 minutes

After 20 minutes
After 20 minutes




6 0

After 80 minutes



6 3 0 8 0

Figure 4.13: Orthographic Plots of Bathymetric Change for Oblique Incident Waves
in Plain Beach Movable Bed Experiment.


Depth Change(Wave Angle = 15)

After 00 minutes

2 4 6
After 10 minutes

0 2 4 6
After 40 minutes

2 4 6

Figure 4.14: Contours of Bathymetric
Beach Movable Bed Experiment.

After 05 minutes



0 2 4 6
0 2 4 6

After 20 minutes

4 -



0 2 4 6

Change for Oblique Incident Waves in Plain




. .. ...t.







- 0 .-1


a) Profile Change(After 20 Min.)

E 0 -------.

S-0.2 Initial profile
3-D Wave Basin Data
-..... Present Model Result
-0. 1 1
S1 2 3 4 5 6

b) Profile Change(After 40 Min.)
0.2 1

-5 O----------------------------------
E 0 -

S-0.2 Initial profile
-- -3-D Wave Basin Data
...... Present Model Result
-0.4 '
0 1 2 3 4 5 6

c) Profile Change(After 80 Min.)
0.2 .
0.2(-------- ------------*-----'-----

E 0--- -----.,

S-0.2 Initial profile
3-D Wave Basin Data
...... Present Model Result
-0.4 '
0 1 2 3 4 5 6

Figure 4.15: Comparison between Computed and Measured Beach Profiles for t= 20,
40, 80 minutes. Data from Plain Beach Movable Bed Experiment for Oblique Incident

calibrations with physical experiment data. For comparison with laboratory exper-

iments, calculated sediment transport rates are separated into their longshore and

cross-shore components. The numerical longshore sediment transport is then cali-

brated with measured total lonshore transport quantitatively. The best fitting value

was found to be Ab, = 0.1. This value is also smaller than the previous value which

gave good agreement with CERC's formula.


The model performance is demonstrated here with three types of man-made struc-

tures including artificial fixed bottom bar, shore perpendicular structures (groins),

and offshore breakwaters. The purpose is not for model calibration or verification

as there is no available data in hand. Rather, model utilizations are illustrated with

realistic coastal structures. This clearly is the ultimate goal of this study .

5.1 Artificial Bar

It is known that under storm waves, beach will respond by eroding material from

the beach face and the formation of longshore bar(s) in the vicinity of breaking point.

As previously discussed about cushioning effect, this breakpoint bar is believed to

have the effect of slowing down beach erosion by dissipating incoming wave energy

and retarding offshore sediment transport. Recently, artificial bars are being proposed

as beach protective measures based on this reasoning. However, these artificial bars,

unlike natural longshore bars will not respond to changes of wave climate and water

level. Therefore, their long term effectiveness and benefit are hard to assess. The

present model was applied to the case of fixed longshore structures such as submerged

artificial longshore bars and the beach responses with artificial longshore bar under

storm wave conditions were examined (Wang and Kim, 1992).

It was assumed that the artificial bar is low and streamlined so that no wave

reflection and energy dissipation other than the usual breaking and friction effects

need to be considered. Under such simplification, the present model is applicable.


The sediment conservation equation should be modified as bottom scouring will not go

beyond the fixed bar. Therefore, for fixed bottom portion, the sediment conservation
equation is modified as

Ah = 0, if potential q > actual q
9h 8qz qy%
-- = q- + if potential q = actual q
at ax ay

where potential q is the transport rate based on the movable bed, and actual q is for
fixed bed.

The case used here is based on a 2-dimensional prototype profile typical to a Baltic

coast. A storm condition of 2 m surge and waves of H=2 m, T=6 sec, with normal

incident wave angle is used as input to generate the configuration of a 2-D natural

longshore bar after 20 hours run time. This configuration shown in Figure 5.1(a)

represents a quasi-stable profile under the given condition and is used to define the

fixed bar condition by fixing the bottom contour between the tick marks as shown.

The hatched portion can be viewed as the volume of the artificial bar with respect

to the original profile. Obviously this configuration represents the optimal for shore-

line protection for the selected storm environment. The question is how would this

configuration respond to changing water levels and wave conditions if the bar is fixed

in one case and movable in the other. Two different input conditions are used here

for comparisons. The first one is to decrease the storm surge to 1 m but kept the

same wave height at 2 m. The second one is to keep the same surge level at 2 m and

increasing the wave height to 2.5 m.

In the first case, the water level is reduced to 1 m storm surge but the wave height

is kept the same. Now the bar is very near to the water level initially. The wave which

has the same height as the high water case will now break further offshore and a bar

will tend to form near the new breaking point.

Profile Change(Surge=2m, H=2m)


150 200

Cross-Shore Transport Rate


150 200

Figure 5.1: a)Inital and Quasi-Stable Profiles in 2 m Storm Surge and 2 m Wave
Height. b)Cross-Shore Transport Rate Distributions after 1 hour and 16 hours.

Figure 5.2(a), (b) show the profile changes after 8 hours, and sediment transport

rate distribution change for actual and potential transport, respectively. Here the

hatched portion of the bottom in the form of a longshore bar is fixed. Initially, the

cross-shore transport is zero over the bar as the material will only accumulate leeward

of the bar. At the later time( shown here after 8 hours) material begins to by-pass

the bar and moves offshore. Figure 5.3 shows the comparisons of profile change for a

fixed bar and natural bar under a new condition. For the natural bar case, the initial

bar will simply move seaward to its new stable location. For the fixed bar case the

new breakpoint bar has to gather material from somewhere else which, in this case,

from the foreshore area of the fixed bar, since enough sand is not transported over the

bar as time goes, scouring will occur at the toe of the fixed bar. In the second case

(Figure 5.4), when the wave height is increased while maintaining the same water

level, the natural bar as well as the breaking point will move seaward requiring larger

volume to reach a stable bar shape. If, on the other hand, the bar is fixed a second

natural bar will be formed seaward of the fixed bar but welded to the fixed bar.

5.2 Groins

Groins are shore perpendicular structures which are built to intercept littoral

transport from updrift. They are used to trap sand locally or as end structures to

stabilize sand placed in conjunction with beach nourishment projects. For trapping

sand, a series of groins is often used. The presence of groins is generally known to cause

accretion on the updrift end and erosion on the downdrift end. However,the presence

of groin(s) also often significantly alters the nearshore hydrodynamics. Circulation

cells could appear at various location depending upon the interactions of waves and

structures. As a consequence, unexpected erosional and accretional patterns might

occur. Therefore, the ability to be able to predict morphological changes associated

with groin structure is undoubtedly useful in coastal engineering.


Profile Change(Surge=lm, H=2m)

0 50 100 150 200 250 300

Cross-Shore Transport Rate



100 150 200

250 300

Figure 5.2: a)Profile Change, and b)Cross-Shore Transport Rate Change for Fixed
Bar Case in 1 m Storm Surge and 2 m Wave Height.



.- Initial(potential)
I Initial(actual)
S- After 8 Hrs.

I Fixed Bar
_l I I I I I I


Profile Change(Movable Bar, Surge=1m, H=2m)
I I, II I 1


50 100

150 200

250 300 350

Profile Change(Fixed Bar, Surge=1m, H=2m)


150 200

Figure 5.3: Profile Changes for a)Movable Bar, and b)Fixed Bar Cases in 1 m storm
Surge and 2 m Wave Height.

. .......... .. ....... ..... .......... ......
Still Water Line

.-.- After 4 Hrs.
After 16 Hrs.


Profile Change(Movable Bar, Surge=2m, H=2.5m)



Profile Change(Fixed Bar, Surge=2m, H=2.5m)

0 50 100 150 200 250 300 350

Figure 5.4: Profile Changes for a)Movable Bar, and b)Fixed Bar Cases in
Surge and 2.5 m Wave Height.

2 m Storm

Perlin and Dean (1985) developed an N-line model using a simple wave refraction

and diffraction scheme to determine the modifications of incoming wave angle and

wave height. This hydrodynamic model then drives the longshore sediment transport

equation to modify the topography. The model, in essence, is an extension of one-

line models. Kraus (1994) investigated parameters governing beach response to groins

and incorporated them into the so-called GENESIS model that can be used to predict

shoreline changes in the presence of groins. The model is also driven by a wave model

that considers refraction and diffraction but no current. Therefore, the sediment

transport formula like Perlin and Dean's model is purely wave related. Badiei et al.

(1994) carried out series of movable bed tests for groins and discussed the effect of

groins on erosion and accretion patterns, the trapping capacity of a set of groins, and

the effect of groin length on bar-groin interaction.

In the present model, the presence of a groin is reflected in the boundary con-

ditions. The boundary conditions for the groin in the sediment transport model are

given as,

qy(I, Jgroi + 1) = 0, if qy(I, Jgroin + 1) > 0

qy(I, Jg.roi -1) = 0, if qy(I,Jgroin -) <0

where q, is the transport rate in y direction and Jgoin is the Jth grid column which

has the groin.

Figure 5.5 shows an example of the calculated wave profile and nearshore current

condition for a single groin with incident wave of 0.5 m, 6 sec approaching the beach

at 15 degree angle. The longshore current is directed seaward by the groin at the

updrift side. At the downdrift side longshore current reestablishes itself by drawing

water from offshore in the vicinity of the groin. Figure 5.6 shows the sediment trans-

port vector and the resulting topographic changes in the presence of a single groin.


.. ..... ...... .. ... .. .... ....... .. ...... ....
. . . . . . . . . . . . .
~~O0 : :: : :: .. :.... . .::

00 "a ......................... ........
.. . I-'11 1 1 ... ..'.... ''I .. i .- ... ... .. .. .....
---.-------------------- -- ---------

)I It.t.1 I-






Figure 5.5: a)Wave Crests, and b)Current Field on the Plain Beach with a Single
Groin for 0.5 m, 8 sec, and 10 degree Incident Waves.








Lll/ *



The vectors in Figure 5.6 represent total sediment discharge for a 40-day period. Fig-

ure 5.6(a) is the case where both wave transport mechanism and current transport

mechanism are activated in the transport equation whereas Figure 5.6(b) presents

the case with only current transport part. When both mechanisms are present per-

sistently for a long time the dominant resulting transport is directed offshore causing

shoreline erosion and the formation of breakpoint bars. On the downdrift side of the

groin, there is a shadow zone immediately adjacent to the groin where the offshore

transport is small. However, just outside the sheltered area offshore transport be-

comes stronger than the normal plain beach configuration. Consequently, the profiles

near the groin are different from the normal equilibrium shape. When only current

sediment transport mechanism is considered, shoreline advances on the updrift side of

the groin and retreats on the downdrift side due to the moderate gradient of the long-

shore wave energy flux owing to the presence of the groin and the deflected current

near the groin.

Since coasts are subject to varying wave climate, to perform long-term simulations

one must, in theory, incorporate time variations of wave trains in the model. This

is not an easy task. The problem can be simplified considerably if as observed

by many investigators, in the long run some of the wave-induced short-term effects

such as cross-shore transport may have compensated themselves. Hence, most of

the existing numerical models intended for evaluating the long-term effects of shore

structures consider only the longshore transport mechanism. In the present model

this mechanism is embedded in the current transport equation. Therefore, to serve the

same stated purpose, one may consider turning the wave transport mechanism off in

the present model. An example is given here with only current transport mechanism.

The morphological changes after 70 days and 140 days are shown in Figure 5.7 (a) and

(b), respectively. The typical morphological changes near the groins as often observed
are seen more clearly. The groin blocks the prevailing natural littoral drift along the


Depth Change(After 40days)


<;UU l----------------- ----- -----

0 200 400 600 800 1000

Depth Change(After 40days)

200 [--15
150 -10
......" '.'. ... ... .. ...
1 0 0 "1 .. ... . . . .'' . . . . . ..
. . . . ... ... I . . . .

............ 2 -5 ...............................

0 200 400 600 800 1000

Depth Change(After 40days)

200 1


- ...... .... . ... ..
......... ...... ..

................. ................. .



400 600

. ... ..... -.... ..........



Figure 5.6: Sediment Transport Field and Resultant Depth Changes a)with and
b)without Wave-borne Transport on the Plain Beach with a Single Groin for 0.5
m, 8 sec, and 10 degree Incident Waves after 40 days.





'' "



Depth Change(After 70days)

200- -15

150- '-10


50- -.-.-.-.-.-.-.-.--- -----.-.
... ..... +. 5 ......... ..... .......... .....................................
1 1
0 200 400 600 800 1000

Depth Change(After 140days)

200- -15

150[ -10



600 800


Figure 5.7: Depth Changes after a)70 days, and b)140 days on the Plain Beach with
a Single Groin for 0.5 m, 8 sec, and 10 degree Incident Waves.




5 0 -- --- -- --- -- ---- --- -- -
--------- -----' 3' -----
....;+ .......................7 .............
n111, =.-


coast causing updrift accretion and downdrift erosion. Immediately adjacent to the

downdrift side of the groin, the profile steepens creating a channeling effect conducive

to promoting rip current.

Single groin is seldom found in coastal application and groups of groin are more

common. The case of a three-groin group is illustrated here. Figure 5.8 shows the

wave and current patterns for the three-groin. In each compartment, a current cell is

generated that draws flow toward the shore at the updrift end of the compartment and

redirects it seaward at the downdrift end. The corresponding morphological changes

after 70 days and 140 days, respectively, are shown in Figure 5.9 (a) and (b). It is

shown that shoreline and bottom contours advances at the updrift of first groin and

retreats at the down drift of the last groin. In each compartment, erosion occurs at

the updrift end and accretion takes place at the downdrift end. Figure 5.10 presents

the sediment transport by-passing patterns around the groins. For the single groin

case (Figure 5.10 (a)), the bypassing rate steadily increases up until 70 days then

starts to decrease. For the three-groin case (Figure 5.11 (b)), sediment bypassing

around the first two groins increases steadily but sediment bypassing around the last

groin starts to decrease after 100 days similar to the one groin case. The decreasing

of bypassing after a certain time is rather unexpected and counter intuitive. A closer

examination on the current pattern shows that the circulation cell becomes stronger

as the shoreline eroded at the downdrift side and some sediment transport by the

circulation counteract to the bypassing transport. At present, there is a lack of reliable

data especially on the morphological effects of groins to compare with numerical


5.3 Breakwater

An offshore breakwater is generally a shore parallel structure designed to protect

the beach behind the structure against severe erosion. Behind the breakwater wave


-15............ .....
-- ....-..............................
.. ..... .......... ............. ........ -

....... ...... .. .... g. ......... .... ....................
I.... .....**......... .. .t................ ..
. ......... ................. ..' ....... ........ ... ......

.. .... ...... .... .... .....................
.-- ..--------------II ------ -----


400 600



Figure 5.8: a)Wave Crests, and b)Current Field on the Plain Beach with Three Groins
for 0.5 m, 8 sec, and 10 degree Incident Waves.


'0 150
l 100




Depth Change(After 70days)
Si i I



200 -15

150 .-10

100- -5

150.. ---------- ..

....... ...... ....' ..... .. .. ......'." ...............
r\ ____ i ____ i i ---- I---- ---


400 600



Depth Change(After 140days)


Figure 5.9: Depth Changes after a)70 days, and b)140 days on the Plain Beach with
Three Groins for 0.5 m, 8 sec, and 10 degree Incident Waves.

Sand Bypassing for One Groin


Sand Bypassing for Three Groins

- 1.2

r 0.8






Figure 5.10: Sediment Bypassing Transport Rate for a)Single Groin, and b)Three
Groins on the Plain Beach for 0.5 m, 8 sec, and 10 degree Incident Waves.

height is reduced and circulation cells are generated which draw sediment into the

sheltered area. A salient feature soon appears which grows into a tombolo and some-
times becomes attached to the breakwater. Many numerical models, some based on

rather artificial mechanisms are able to produce the described topographic changes.

Hsu and Silvester (1990) proposed empirical formulas for predicting shoreline change.

Hanson and Kraus (1990) employed a numerical model (GENESIS) to investigate
the various depositional types in the lee of a single detached breakwater. Suh and

Hardway (1994) developed a one-line numerical model for predicting shoreline change

in the vicinity of multiple breakwaters and compared with the field data.

The boundary condition for the breakwater in the sediment transport model is as

qx(Ibreak + 1, J) = 0, if qx(Ibreak + 1, J) > 0

qx(Ibreak 1,J) = 0, if q,(Ireak 1, ) < 0

where q. is the transport rate in x direction and Ibreak is the Ith grid row which has
the breakwater.

A number of cases are illustrated here. First, a short shore parallel breakwa-

ter under normal and oblique wave attacks. Figure 5.11 shows the wave profile and
nearshore circulation pattern under the normal incident wave condition with 1 m

height and 8 sec period. Two symmetrical circulation cells are generated behind the

breakwater. Figure 5.12 shows the vectors of total sediment transport and the result-

ing changes after one day under the attack of the given wave condition. Again, one

shows the results when both wave transport and current transport mechanisms are

considered (Figure 5.12(a)) and the other includes only the current transport mech-

anism (Figure 5.12(b)). When both transport mechanisms are considered, offshore

sediment transport dominates causing breakpoint bar formation and severe shore-


200. ....... .. .....

oE .-........-.. -----4
..15 0

E. .... ....... .. .....
10 ........ ... ... ....... . .
S............ .... .. ............. .......

......... .. ..... .. ............ ........ ..................

Figure 5.11: a)Wave Crests, and b)Current Field on the Plain Beach with Breakwater
for 1 m, 6 sec, and Normal Incident Waves.
for 1 m, 6 sec, and Normal Incident Waves.


a) Depth Change(After 1day)
-9 -9
I I. .

2 00 : ... .. .... .......... ...... ...........
S .... .. . .. . .. . .

w 150 .o- 5 o... o,,t oo,,,oo..;.. ... o **,oo**@ o ............

Si 11 111I.............. .........t11....................11


0 i i i ....... tIi
.. .. ................. ...... ..... .. ..
... .... . ..

0 100 200 300 400 500

b) Depth Change(After 1day)
-9 -9

200- -7 -7
... i ...7. 1 .

s ie 150 an -5 -5 -
0 I _'... .....____
I? ____ .*..*.......... .. .. ".. .. .... .......
1 0 . . . .. . .. . . . .

0 100 200 300 400 500

Figure 5.12: Sediment Transport Field and Resultant Depth Changes a)with and
b)without Wave-borne Transport on the Plain Beach with a Breakwater for 1 m, 6
sec, and Normal Incident Waves after 1 day.

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