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Numerical modeling of nearshore morphological changes under current-wave field

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Title:
Numerical modeling of nearshore morphological changes under current-wave field
Creator:
Kim, Taerim, 1964- ( Dissertant )
Wang, Hsiang ( Thesis advisor )
Dean, Robert G. ( Reviewer )
Hanes, Daniel M. ( Reviewer )
Kurzweg, Ulrich H. ( Reviewer )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1995
Language:
English
Physical Description:
xi, 121 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Beaches ( jstor )
Inlets ( jstor )
Littoral transport ( jstor )
Modeling ( jstor )
Sediment transport ( jstor )
Sediments ( jstor )
Shear stress ( jstor )
Shorelines ( jstor )
Three dimensional modeling ( jstor )
Waves ( jstor )
Coastal and Oceanographic Engineering thesis, Ph. D
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
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 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 numberical 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.
Thesis:
Thesis (Ph. D.)--University of Florida, 1995.
Bibliography:
Includes bibliographical references (leaves 115-120).
General Note:
Typescript.
General Note:
Vita.
Funding:
Technical report (University of Florida. Coastal and Oceanographic Engineering Dept.) ;
General Note:
UFL/COEL-TR/109
Statement of Responsibility:
by Taerim Kim.

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UFL/COEL-TR/109

NUMERICAL MODELING OF NEARSHORE MORPHOLOGICAL CHANGES UNDER A CURRENTWAVE FIELD
by
Taerim Kim

Dissertation

1995




NUMERICAL MODELING OF NEARSHORE
MORPHOLOGICAL CHANGES UNDER A CURRENT-WAVE FIELD
By
TAERIM KIM

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA

1995




ACKNOWLEDGMENTS

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 dissertation 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 Braunshweig, 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.




TABLE OF CONTENTS
ACKNOWLEDGMENTS...................................iii
LIST OF FIGURES....................................... vi
ABSTRACT.............................................x
CHAPTERS
1 INTRODUCTION......................................1I
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 DESCRIPTION OF NEARSHORE HYDRODYNAMIC MODEL....... 11
2.1 Wave Model....................................... 11
2.2 Wave Breaking and Energy Dissipation..................... 14
2.3 Circulation Model................................... 16
2.4 Undertow Current.................................. 17
3 DESCRIPTION OF SEDIMENT TRANSPORT MODEL............ 21
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 CALIBRATION OF SEDIMENT TRANSPORT RATE..............46
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 CONCLUSION AND RECOMMENDATIONS FOR FURTHER STUDY 110
7.1 Conclusions ................................ 110
7.2 Future Study ............................... 112
BIBLIOGRAPHY ................................. 115
BIOGRAPHICAL SKETCH ........................... 121




LIST OF FIGURES

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 Transport 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-SeaTank 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 Experiment 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 Experiment 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
Waves ........ ................................. 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
Waves ........ ................................. 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 Movable 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
Waves ....... ................................. 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 Waves .................................. 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 Experiment and Numerical Model for 8 cm, 1 sec, and Oblique Incident
Waves ....... ................................. 108
6.11 Comparison of Bathymetric Changes after 160 minutes between
Experiment and Numerical Model for 8 cm, 1 sec, and Oblique
Incident Waves .................................. 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
NUMERICAL MODELING OF NEARSHORE
MORPHOLOGICAL CHANGES UNDER A CURRENT-WAVE FIELD By
TAERIM KIM
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.




CHAPTER 1
INTRODUCTION
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 permanent 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, limitations 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




2
transport. At present, practically all the operational models are based on depthintegrated 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 descriptions 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 important 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 studies 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 introduced 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 mechanism 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-




3
meant 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 depthintegrated 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 economics 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 waveinduced currents have been developed. The application of this quasi-3D description of nearshore hydrodynamics has just started in computing nearshore sediment transport 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 transport 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




4
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 computational 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 processes like storm-induced, cyclical daily, and seasonal changes and in long-term
processes.
2. Respond to changes in water level due to tides, storm surges, or long-term
fluctuations.
3. Represent general boundary conditions and coastal structure configurations.
4. Approach an equilibrium bottom configuration under constant forcing and boundary conditions.
The model development and some initial test results are presented in this dissertation. 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.




5
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 physical 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 modification 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 dimension 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




6
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 (3dimensional 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 calculating long-term change in shoreline position. The m ajor 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 deficiency 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 sediment flux balance. This approach usually links a hydrodynamic submodel with a sediment transport submodel. Models of this kind with varying degrees of sophistication 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 energetics 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 inside 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 combining 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.




10
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 study.




CHAPTER 2
DESCRIPTION OF NEARSHORE HYDRODYNAMIC MODEL
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
D D2 +- Vh(CCgVh ) + (02 k'CC) = -WD (2.1)
Dt2Dt gDt
where t is the time, Vh is the horizontal gradient operator, = +
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, o 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
W = +k.U
o2= gk tanh kh




12
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,
at
Substituting the above equation into Equation (2.1), the following equation is obtained,
-2iwU. VhO + U Vh(U. Vhq) + (Vh. U)(0T. VhO) Vh (CqqVhO) +
{ 2 2 k2CC iW(Vh. O)}q = iW (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
S-ig A(x, y) e i(f kcosadx+f kainOdy)
and the proper form of the dispersion relationship is w = 9 + 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




13
and cosO is assumed to be unity. Then, the velocity potential q is approximated as
- ig A(x Y) (fkd)
or
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),
(9 cos0+U)AC+ (Cgcos + U ) A + VA V + -a V
( -kC(l cosO)A C (4)] + WA =0
222
Y
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 gridrow (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 (1988).




14
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 Mc~owan (1894), who asserted that a wave will break when its height reaches a certain fraction of the water depth,
Hb = Khz (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




15
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.Cg1
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 E. is calculated using Horikawa and Kuo's (1966) empirical equation
E.= 1 Pg(Pd)2
where (Pd) represents the stable wave height a breaking wave tends to reach on a constant depth bottom. Values for parameters k and P 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 P = 0.4) suggested by Daily et al. (1984) are used. Daily 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.




16
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) aU a 9U au a 1 1 1 (OS,. 3,\xy ia'r
+ U +_V- ---8X + + lT=I
at ax y +g Ox + pD pD pD \, Ox Oyj p y
49Vu8VOV O 1 1 1 __1
0+ oU+_ g + + + -o
at x W- +g 0y _p ny- pDy -Y + TD _5x_ --y ) pox
o-# + 0(UP) + 0(VD) =0
atOxO
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 + ii; h is the still water depth; # 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; ;., and 'by are the bottom shear stresses; T,', and ry are the surface shear stresses; and S,., Sn,, 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.




17
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 laboratory 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 breaking 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 originally postulated by Nielsen and Sorensen (1970) and later analytically formulated by Daily 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 au o~w 0
Integrating over depth and applying Leibniz rule of integration, the integrated Continuity equation is rewritten as
O ud [T W1r+ UT+h1 = 0
T9X f h Lx X?
Further simplification will result through the use of boundary conditions in two dimensions. The kinematic boundary conditions at surface is
&~ ax




18
The bottom boundary conditions for a fixed bottom is Oh
[U + w]_h = 0
Substituting these conditions into the vertically integrated continuity equation yields
- + T udz =0
9t 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, respectively,
U = UC+UA) 77 = 71c+77w,
where U, and 77, are the time-averaged value of velocity and free surface displacement. U, and 77w 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:
H
77W = -Hcos(kx at)
2
= Hacoshk(h + z)(k at)
2 sinhkh
Substituting these into the integrated continuity equation, &7 + T -h(u, + uw)dz = 0,
then expanding in a Taylor series at 77= 77, which is a mean water surface level, and taking the time-average, + ( + u)dz + -uwl, = 0




19
Removing the wave fluctuations, this equation can be simplified as
- ]- +udz + --; 7 = 0
Here, ( can be expressed as the mass flux of x and y components as followings,
M.= ('-tou-),o pg- k
8a
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 all a n z+am =0
at u+z + ax
Assuming a steady motion, the integrated continuity equation becomes
a
Y-(Q. + M.) =0
where
Q = hr2UCdz
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,
The mean undertow velocity is simply estimated as fi = Q/(im + 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 depth.




a) Wave Height and Set Up
E_- -...............
H = 0.5m
S-5- H = 1.0m
........ H= 1.5m
...... H=2.0m
-10 '
0 50 100 150 200 250
Distance(m)
b) Undertow Current
S0
-~ -
o ................ .... ...... ....
E -0.5 -. .......
\' -.. .,.-"H = 0.5m \ .
.c -1 H=1.0m \.
S..... H = 1.5m
cc
...... H = 2.0m
-1.5 '
0 50 100 150 200 250
Distance(m)
c) Undertow Current
0
-0.5 -..
-H = 0.5m
0 -1 --- H = 1.0m
........ H = 1.5m
> ...... H = 2.0m
-1.0 50 100 150 200 250
Distance(m)
Figure 2.1: Distributions of a)Wave Height b)Discharge of Undertow Current, and c)Mean Undertow Current in Different Input Wave Conditions.




CHAPTER 3
DESCRIPTION OF SEDIMENT TRANSPORT MODEL
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 phenomenon 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 varying 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 transport 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,
Qai = T10JTJO~ztC~~~dd
where Q8j 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 formula. 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.




23
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 single empirical coefficient. Due to the time-averaged and depth-integrated nature of the energetics model, the principal assumption is that the instantaneous sediment transport rate responds to changes in the near bed velocity immediately. This assumption 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 Daily 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 approach 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.




24
3.1 Shear Stress under Wave and Current One of the long-established maxims of the coastal engineers is that 'waves disturb, 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 upstream sediment transport above the roughness elements at the bottom when a weak current was superimposed on waves. Authors of existing sediment transport formulations generally agree that there is a pressing need for more information about currentwave 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 currents, 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 mechanisms. 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 reduction 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).




25
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 =pCf t[Iti with t =t'+u;
where Cf is a friction coefficient which depends on the bottom roughness, and the velocity Ut represents the vectorial sum of the depth-averaged current U" and the instantaneous wave orbital velocity uto. The constant C1 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 considering 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 uw( Liu and Dalrymple, 1978). The total velocity vector 't is expressed as = (U + fi cos O)i+ (V + fi sin 0)5
where, U and V are components of u-' for x and y direction. i 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 + fi2 + 2Ufi cos 0 + 2Vfisin0 The wave orbital velocity fi is expressed as fi = firn cos at
where fi, is the maximum wave orbital velocity at the bottom which is found to be 7rH
Urn T sinh kh
The absolute value of bottom shear stress can be expressed as

[-1 = pC1I I2




and
Tm = max(191)
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 turbulence 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 distribution, modifies the bottom shear stress, and generates high local stresses in the water colun. Recent experiments by Deigaard et al. (1992) showed that the bed shearstresses in the surf zone on average were not very different from offshore region but




27
they exhibited much greater wave-to-wave variations and occasional very large values 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 transport. 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 dissipating 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 energy 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 O9ECg
7"bt = H.- TO




28
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/3Ox.
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 6 (drag/gravitational forces) was found to be mainly a function of the flow Reynolds number R (inertial/viscous forces),
t Tt = (,r/p)O'D
(p -)gD f[ y
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,




29
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




).1 particle parameter, D,

Q2 0.3 0.5

II I i i i i t t

2 3 5 10

-3
particle diameter, d,,*10 (m) a~t T, =16C

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

005 0.

20 30

I

I I




31
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 breaking 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(r. mc)UIc/pg + Ab,(rb, rr)LT,/pg (3.1)
('7 U. /.
q, = f Uh Wdz = f(rt,7,b)UD = ATt,bQ.




Onshore
0
C
z

Type ITyeTp II
Mono-crested Mono-crested
-------Initial profile
Transformed profile
VJ Erosion
"" i"jj Accretion due to onshore transport
- <__ Accretion due to offshore transport
J Direction of net transport
- Breaking point
Bi-crested Ri-crested
Figure 3.2: Type of Net Transport Rate Distribution (from Kajima et al., 1982).




where,
UT,; Integrated depth mean wave induced-currents U,,; Maximum orbital velocity at the bottom U; Mean velocity of the undertow Q,,; Discharge by the undertow ,r,; Shear stress generated by wave and mean current rtb; Shear stress generated by wave and mean current r,; Critical shear stress under wave and mean current Abe; 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, = rH
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
8 CD
The discharge associated with the undertow current is given by as Q= U,D where D is the total depth. The coefficient Abe, Ab,, 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




34
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
0

20 30
Distance(m)

Stress
II I

20 30
Distance(m)

Sediment Transport

10 20 30 40
Distance(m)

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

b)
E
.,
U)

r~L

0

Bottom
Shear Stress
Turbulent
S Shear Stress

10"'

0
0.
C
o
-2.
0

--. Onshore
": f. Transport
Offshore
Transport
*. i."Net
./ Transport

0

_t

-100
-2001

30f'




36
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 proposed by Horikawa (1988) assumes the following functional form, SOh
q= q + IqIq = q.' + e lq.'l A
O y
in which x and y are horizontal cartesian coordinates, q. and q. 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 equation 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 6 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




37
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 surfione 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 experimental 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#; for the same wave height a steeper beach yields a shorter plunging length. An empirical




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

0 10 20 30 40
Distance(m)
x 103 Slope Effect on Sediment Transport

00
0
E
-2
0-4
0
.~4

20 30
Distance(m)

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 9.25tan3
Hb
Basco and Yamashita (1986) developed an expression relating the width of the transition 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 contained rather comprehensive wave information. By regression analysis, the following equation was proposed,
it = 0.12(tanP)o4[ I2.
T. H.
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 ().
it = (1 0.47-0.27-5) for > 0.064
tan/I
it = 0 for < 0.064
where
tan#
(Hb/LLb)(1/2)
and tan#, 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 = 0.556tanflLb4-1465




40
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 prebreaking 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. Generally, 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. Figure 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 breaking 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 dissipated 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

0.15 Slope

Turbulent Shear Stress

120

60
Distance(m)

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

0.3




42
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. Daily and Dean (1984) pointed out that his expression developed for the sediment concentration profile apparently lacks the "cushioning" effect which the




43
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,
Gus = tanh(7 Hi) 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, instantaneous sediment transport rate in both x(cross-shore) and y (longshore) directions, and the equation of mass conservation of sand. The conservation equation of sediment transport is presented in its two-dimensional form, Ah = (0q. Oqy)
t Ox O




Cushioning Effect

0.4 0.6
Wave Height/Depth

Evolution of Sediment Transport Rate

2'
0 5 10 15
Time(hr)

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

S0.5 S0
. -0.5
0
C 1
o
R-1.5 -

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




45
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, respectively. 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) = 1 t1 (h2 hl)dx
q)-t2 t1
where
t, t2 = times of profile surveys
Xo = shoreward location of no profile change, where q(xo) = 0 hl, h2 = profile depths at survey times 1 and 2




CHAPTER 4
CALIBRATION OF SEDIMENT TRANSPORT RATE
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 in). 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.)
* i

4
2
0
-2
-4

-10 0 10 20 30 40 50 60 70 Distance(m)
Profile Change(After 111 Min.)
A. ...

4 2 2
0.
-42
-4

-10 0 10 20 30 40 50 60 70 Distance(m)
Profile Change(After 273 Min.)
A.

S2
40-2
-4
-1

0 10 20 30 40
Distance(m)

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
- Big Wave RFume Data
...... Present Model Result
1 1 1 1 I1I11

-Initial profile
- Big Wave Rurne Data ...... Present Model Result
l i t t I llII

-_ ... ." ..- Initial profile -'
..-.- Big Wave Flume Data ...... Present Model Result
,I I I I IIft

0




48
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 Abt, in a range from 0.05 to 0.07 and A, from 1.X10-5(m2/IN) to 1.5X1051(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.




49
Cross-Shore Transport Rate(Experiment)
2
n

a-

_2
o -4
0
CL 0 ,)
ca.-

0 10 20 30 40
Distance(m)

50 60 70

Cross-Shore Transport Rate(Present Model)
2

-2
-4 ... After 62 Min.
..' -- After 111 Min.
-6 -- After 273 Min.
_ t I I II

0 10 20 30 40
Distance(m)

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....
- / 1.*.
* = ~ I ***I
* ~ *.. /

After 62 Min. After 111 Min.

- After 273 Min.

Cl

E
CL
,.
(I

I

I I

10

mJ




50
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 in); 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 mn 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 mim. 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 s
- Big Wave Rume Data ...... Present Model Result
, I I I I

20
Distance(m)

Profile Change(After 3 Hrs)
Pre t Md .. .l ..R..
---- Initial profile 1
- -- Big Wave Rume Data ...... Present Model Result
I I I I I

20
Distance(m)

Profile Change(After 5 Hrs)
..... .-. .... ..
- Initial profile
- Big Wave Flume Data -,
...... Present Model Result
I I I I I
-20 0 20 40 60 E
Distance(m)

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

-20

-20




52
Cross-Shore Transport Rate(Experiment)
I I I I I

i~o ,. d

' "' '. /

...... After Hr
S After 3 Hr
After 5 Hr

I I I I I
-20 0 20 40 60 1
Distance(m)
Cross-Shore Transport Rate(Present Model)

-20 0 20 40 60
Distance(m)

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

Experiment and

-4
-6
-8-


a.
CL
W
C

a"
OC
0 0.
C
I-

-4-

-81-

...... After 1Hr
---- After 3 Hr After 5 Hr
\/
...... Ater \ H
.. After 3 Hr
After 5 Hr




a) Profile Change(After 10 Min.)
-0.2
0
- Initial profile
-0.4 Big Wave Flume Data
S..... Present Model Result
-0 1 2 3 4 5 6
Distance(m)
b) Profile Change(After 20 Min.)
0.2 ..
--..
0 Initial profile
-0.4 Big Wave Flume Data
...... Present Model Result
-0.0A
0 1 2 3 4 5 6
Distance(m)
c) Profile Change(After 40 Min.)
0.2 1.1...
. . . .
0.2
0 -0.4 Initial profile
-0.4 Big Wave Rume Data
...... Present Model Result
-0.0 1 2 3 4 5 6
Distance(m)
Figure 4.5: Comparison between Calculated and Measured Beach Profiles for t= 10, 20, 40 minutes. Data from Air-Sea-Tank Experiment.




54
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 Abe. In this chapter, the characteristics of longshore transport rate are investigated by comparing with CERC formula and the coefficient A. 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 P with the total immersed-weight




55
x loCross-Shore Transport Rate(Experiment)

I I I I
2 3 4 5
Distance(m)

x loCross-Shore Transport Rate(Experiment)

3
Distance(m)

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
0.
co, (U
cc

-0.5 F

-1.5

-2.5 F

\:. =. /. -I "
A Ai,* .

...... After 10 Min. .* After 20 Min.
- After 40 Min.

b)
E E t
o c.
1-

-0.5 F

-1.51

-2.5 F

"\\. ." / I
.. After 10 Min.,
....Afterl10Min.
- After 20 Min.
- After 40 Min.
' '

-3.5
0

Vl .




transport rate it as
i1 = KP
CERC's littoral drift formula (Shore Protection Manual, 1984) which is widely used has the same functional form given as,
Q= K(ECg cos 0 sin O)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 determined 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 shorelines 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




57
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 steepsloped 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
. i
1
;
\ "l0e
\:\

Wave Height = 1.5(m)
Wave Direction
- 0 Deg 10 Deg ........ 20 Deg
...... 30 Deg

100 150
Distance(m)

200

b)
,2000
S1500
0 0.
0 1000
.o 500
0)
0j

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.

20 F

E
4)
0 In a)
e
U,
0
,I

I I I, I.
I..
I..
/
/..* / I-

250

I-




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

Movable Bed Model




60
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




61
r V
Figure 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.




Depth Change(Wave Angle = 0)
After 00 minutes After 05 minutes

0.2
0.0
4'-0.2-0.4
After 10 minutes
After 10 minutes

0.2"
* 0.0. (-0.20
-0.41
6

After 40 minutes
After 40 minutes

0.2
,E 0.0
-0.2
-0.4
6

0.2 0.0
-0.2
-0.4
6 ~ 80
After 20 minutes
0.2 0.0
-0.2
-0.4
6 80
After 80 minutes
0.2 0.0
-0.2
-0.4
6 0

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




63
Depth Change(Wave Angle = 0)

After 00 minutes
,___-20_.
-10
p
... .. .. *
) 2 4 6
After 10 minutes
1-aU
-20
10
-....... :..t:i ..... ...; "- "

0 2 4 6
After 40 minutes

2 4 6 Longshore(m)

E
244 a
.
0
0
.
U

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
0
0 2 4 6
After 20 minutes
-30
4 -20
2 10-.==
.. ....... --
0
0 2 4 6
After 80 minutes
4-.
-10
2
0
0 2 4 6
Longshore(m)

E
0
;2
o

r:
4
0
2
0 C-)

-Ju
-20
1 -0 0




64
a) Profile Change(After 20 Min.)
0.2 1....
- --o -
E 0 .. --------- .................
-0.2 Initial profile
- -. 3-D Wave Basin Data ...... Present Model Result
1 2 3 4 5 6
Distance(m)
b) Profile Change(After 40 Min.)
0.2...
N .. qo.
0.2 Initial profile
-- 3-D Wave Basin Data ...... Present Model Result
0 1 2 3 4 5 6
Distance(m)
c) Profile Change(After 80 Min.)
0.2 ..
E 0 .. ...---- .. .
-0.2 Initial profile
3-D Wave Basin Data ...... Present Model Result
1 2 3 4 5 6
Distance(m)
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 Waves.




65
foreshore erosion and breakpoint bar development. The profiles from the 3-D experiment, 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 development 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 supply 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 11P 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

0.2 0.0
-0.2
-0.4
6 0
After 10 minutes
0.2
0.0
-0.2
-0.4
6 0
3 0 8 4
After 40 minutes
0.2.
-0.0
0.2
-0.4
6 080

0.2
0.0
-0.2
-0.4
6

After 05 minutes

After 20 minutes

0.2
0.0
-0.2
-0.4
6 8 0
After 80 minutes
0.2 0.0
-0.2
-0.4
6 0 08 0

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




67
Depth Change(Wave Angle = 15)

After 00 minutes

2 4 6
After 10 minutes

0 2 4 6
After 40 minutes

2 4 6 Longshore(m)

Figure 4.14: Contours of Bathymetric Beach Movable Bed Experiment.

After 05 minutes
-20
-10
-*40-*
2 4 6
30 2 4 6

After 20 minutes
-30
4
2I
00
0 2 4 6
After 80 minutes
- -30
4
2
0 2 4 6
Longshore(m)
Change for Oblique Incident Waves in Plain

, -aJu
-20
-10 ..

E
04 N
0
2
0
am
Q

4
o
0
0
0
0
0
Oo

~-30
- -20----
-20
- .. ;-0




68
a) Profile Change(After 20 Min.)
0.2...
E 0 ------ -, .
0- Initial profile
....- 3-D Wave Basin Data ...... Present Model Result
2 3 4 5 6
Distance(m)
b) Profile Change(After 40 Min.)
0.2 1...
E 0 --
-0.2 Initial profile
3-D Wave Basin Data ...... Present Model Result
-0 .4 1 1 I I
0 1 2 3 4 5 6
Distance(m)
c) Profile Change(After 80 Min.)
0.2 ....
- - -
E 0.-- -- -- --- -- --- -- --- -02- Initial profile
3-D Wave Basin Data ...... Present Model Result
-0.4 '
0 1 2 3 4 5 6
Distance(m)
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 Waves.




69
calibrations with physical experiment data. For comparison with laboratory experiments, calculated sediment transport rates are separated into their longshore and cross-shore components. The numerical longshore sediment transport is then calibrated 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.




CHAPTER 5
MODEL PERFORMANCE
The model performance is demonstrated here with three types of man-made structures 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.
70




71
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
A aq, + aqy if potential q = actual q
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 shoreline 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)

350

150 200 Distance(m)

Cross-Shore Transport Rate

350

150 200 Distance(m)

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.




73
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 up drift 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.




74
Profile Change(Surge=lm, H=2m)

0 50 100 150 200 250 300
Distance(m)

Cross-Shore Transport Rate

0 0.
a,

100 150 200
Distance(m)

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.

350

-' __ .' -1-'
1 i. 1
I
S- Initial(potential)
II Initial(actual)
S. --- After 8 Hrs.
7/

I Fixed Bar
_P I I I I I I

350




Profile Change(Movable Bar, Surge=1 m, H=2m)
. I I I I 1

0-

50 100

150 200 Distance(m)

250 300 350

Profile Change(Fixed Bar, Surge=1 m, H=2m)

350

150 200 Distance(m)

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
- Initial
S After 4 Hrs.
- After 16 Hrs.




Profile Change(Movable Bar, Surge=2m, H=2.5m)

350

Distance(m)

Profile Change(Fixed Bar, Surge=2m, H=2.5m)

0 50 100 150 200 250 300 350
Distance(m)

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




77
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 oneline 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 conditions. The boundary conditions for the groin in the sediment transport model are given as,
qy(I, J,.oi, + 1) = 0, if qy(I, J,.oi, + 1) > 0
q (I, Jgb., 1) = 0, if qM(I, Jgroin 1) < 0
where % is the transport rate in y direction and Jg,oi 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 transport vector and the resulting topographic changes in the presence of a single groin.




Current

........... I ..............
....................................
0 0 ...................... ... ...................
. II ...........
- -- --
) I I-t. I

200

400

600
Longshore(m)

800

1000

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.

E
...
C C,

E't'

Current

10

L ll / V

rJ t t'




'79
The vectors in Figure 5.6 represent total sediment discharge for a 40-day period. Figure 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 persistently 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 becomes 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 longshore 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




80
Depth Change(After 40days)
-15

. . . . . . . . ..
10
0 200 400 600 800 1000
Longshore(m)
Depth Change(After 40days)
. . .
-: : ........:.... .. ....' : ... :. .. ... .
II I
200 [ -15
150-10
-# r -. r w #J 7 # t# w -............ -- .... !4"
............ 2 -5 .......... .......................
o. .... ....... +... ..... ....... ..o o .... ....o. ..... ...............
0 200 400 600 800 10'00
Longshore(m)
Depth Cha nge(After 40days)
200- -1
1501-10.

.. ...... ... .... ....
2.5
.......... ....... ..
o. .. o .. .. ,., ., ., .. .. ...o
......... 2.5...................

200

400 600
Longshore(m)

.. .. .. .- .... ... ...... .

800

1000

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.

E

O S100
0
50




81
Depth Change(After 70days)
200- -15
150- '-10
100
50- .--------- --_. ..
2.5
... .. + ..5 ....................... .....................................
01 1
0 '
0 200 400 600 800 1000
Longshore(m)
Depth Change(After 140days)
200- -15
150 [-10

200

400

600 800
Longshore(m)

1000

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.

a

a
0 (1(
0 L.

00 a50 --.- .- .- .- .- .------.. ..
S...................... .......... ...............
n'1 1 19 =' I-

0




82
coast causing up drift accretion and downdrift erosion. Immediately adjacent to the downdrift side of the groin, the profile steep ens 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 dowudrift 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 results.
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




Current
.. I I .
-15.............................
I....................................
. ... . . . . . .
.. .......I......... ......... .... .... .....
.... .. I........ I ...................... .......
................ '.....~............... .......................
.. ........ .... .. T . .
. .. .. .. ......... ... .
--------------- .,------------

200

400 600
Longshore(m)

800

1000

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.

200
E '0 150
0 U
U 100
0 C.
50
0 C

)




Depth Change(After 70days)

i..
0
0
0_

200 1-15
150 .-10
100- -5
. ..... .. .... .. ...... .. ..... .

200

400 600
Longshore(m)

800

1000

Depth Change(After 140days)

600
Longshore(m)

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

Time(days)

Sand Bypassing for Three Groins

-:1.2
V
, 0.8 0.6
0
0.4 0.2

150 150

Time(days)

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.




86
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 sometimes 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 follows,
qx(.break + 1, J) = 0, if qx(Ibreak + 1, J) > 0 qx(Ibreak 1, J) = 0, if q, (Ibreak 1,J) < 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 breakwater 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 resulting 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 mechanism (Figure 5.12(b)). When both transport mechanisms are considered, offshore sediment transport dominates causing breakpoint bar formation and severe shore-




Current
i I !ii
. ...... .....
1 .. .. .
o 0 ................ ........4...
.. .................
20 0 ........ ............. ...............
. ................... ...................... ..
. . . .. . . .
E. ...............I*
................................................... ...........
0 .. --. . .
0.. I I I I
0 100 200 300 400 500
Longshore(m)
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.




88
a) Depth Change(After 1 day)
-9
I ....I
200' 7
..................................... ......
............................ ... .........
. . . . . . . .
. ............. .............................
S10 100 20 30 00 50
. . .. .. ......... .... ...... .
I I. IIII
0 100 200 300 400 500
Longshore(m)
b) Depth Change(After Iday)
-9
200 7
5
0 iS... ...
0
.......... ..... ........ .
. .... . . .
1 0 0. .. .. .. ... .. .. .. .
M.......... .-. ,= .........
. ..0 e . ..
. ................... .
. . .. . .
50+-... .... ... .... -.-_-+0
0 100 200 .300 400 500
Longshore(m)
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.




Full Text
LIST OF FIGURES
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
vi


3
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


Depth(m) Depth(m)
76
Profile Change(Movable Bar, Surge=2m, H=2.5m)
Profile Change(Fixed Bar, Surge=2m, H=2.5m)
Figure 5.4: Profile Changes for a)Movable Bar, and b)Fixed Bar Cases in 2 m Storm
Surge and 2.5 m Wave Height.


Current
Figure 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.


63
Depth Change(Wave Angle = 0)
After 05 minutes
aT 4
o
JC
2
m c-
o
After 00 minutes
73
.-20
,-10
E
aT
O
C
(0
I
m
V)
o
o
After 40 minutes
r
o
<0
w 2
w *
o
0 2 4 6
Longshore(m)
After 20 minutes
730
-20
--10
2 4 6
After 80 minutes
^30
' -p3SZH
-T"
h*2- '
4
-1 n <
_ 1
2
^io
0
Longshore(m)
Figure 4.11: Contours of Bathymetric Change for a Normal Incident Waves in Plain
Beach Movable Bed Experiment.


87
Longshore(m)
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.


Depth(m) Depth(m) Depth(m)
51
Profile Change(After 1 Hrs)
Profile Change(After 3 Hrs)
Profile Change(After 5 Hrs)
Figure 4.3: Comparison between Calculated and Measured Beach Profiles for t= 1,
3, 5 hours. Data from Saville(1957).


UFL/COEL-TR/109
NUMERICAL MODELING OF NEARSHORE
MORPHOLOGICAL CHANGES UNDER A CURRENT-
WAVE FIELD
by
Taerim Kim
Dissertation
1995

NUMERICAL MODELING OF NEARSHORE
MORPHOLOGICAL CHANGES UNDER A CURRENT-WAVE FIELD
By
TAERIM KIM
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1995

ACKNOWLEDGMENTS
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 fur 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.
u

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.
ill

TABLE OF CONTENTS
ACKNOWLEDGMENTS iii
LIST OF FIGURES vi
ABSTRACT x
CHAPTERS
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 DESCRIPTION OF NEARSHORE HYDRODYNAMIC MODEL 11
2.1 Wave Model 11
2.2 Wave Breaking and Energy Dissipation 14
2.3 Circulation Model 16
2.4 Undertow Current 17
3 DESCRIPTION OF SEDIMENT TRANSPORT MODEL 21
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 CALIBRATION OF SEDIMENT TRANSPORT RATE 46
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
IV

7 CONCLUSION AND RECOMMENDATIONS FOR FURTHER STUDY 110
7.1 Conclusions 110
7.2 Future Study 112
BIBLIOGRAPHY 115
BIOGRAPHICAL SKETCH 121
v

LIST OF FIGURES
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
vi

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) Ini tal 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
vii

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
Waves 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
Waves 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
Vlll

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
Waves 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 Waves 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
Waves 108
6.11 Comparison of Bathymetric Changes after 160 minutes between
Experiment and Numerical Model for 8 cm, 1 sec, and Oblique
Incident Waves 109
IX

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
NUMERICAL MODELING OF NEARSHORE
MORPHOLOGICAL CHANGES UNDER A CURRENT-WAVE FIELD
By
TAERIM KIM
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
x

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.
XI

CHAPTER 1
INTRODUCTION
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
1

2
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 models ability for describing the cross shore sedi-

3
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

4
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
processes.
2. Respond to changes in water level due to tides, storm surges, or long-term
fluctuations.
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.

5
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

6
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 models 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.

7
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 energetics 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-

8
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.

9
Figure 1.1: Structure of nearshore morphodynamic model.

10
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
study.

CHAPTER 2
DESCRIPTION OF NEARSHORE HYDRODYNAMIC MODEL
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
+ (V vh(cc,vh4.) + ( Dt
(2.1)
Dt2 v Dt
where t is the time, V* is the horizontal gradient operator,
V7 d d *
Vh = ai, + V
A A
i and j are the unit vector in the x (cross-shore) direction and y (longshore) 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 ^ 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
v = a + k U
a2 = gk tanh kh
11

12
where u> is absolute angular frequency and g is gravity coefficient. The hyperbolic
Equation (2.1) can he reduced to an elliptic form based on the assumption that the
only time dependency of velocity potential is in the phase,
di
dt
iuxf>
Substituting the above equation into Equation (2.1), the following equation is ob
tained,
-2iu, -Vh4> + - Vh( Vfc) + (V, )( Vfc) V, (CCgVht) +
{a2 0,2 k2CCg o,(VA )}4> = icrW (2.2)
where only the phase contribution to the horizontal derivative of ^ 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 ^ is
= ig y) c'( f kcosOdx+f ksinOdy)
a
and the proper form of the dispersion relationship is
uj = a -f 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 6, sinO term can be neglected

13
and cosO is assumed to be unity. Then, the velocity potential is approximated as
a
The e'(fka'nBdy) part 0f the phase function is now absorbed into the amplitude function,
A. By substituting this ^ 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 ikAx ^f), the following parabolic wave equation is
obtained (Winer, 1988),
(q e + u)a, +\ a + Va, + zQa
"54(i s* Va ~ 5 [cc (I).],'+ Ta m
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
(1988).

14
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 = Khb (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 finked 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

15
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 = |[EC, E,C,\
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,
Ea, that the breaker is striving to attain. The local stable wave energy density Es is
calculated using Horikawa and Kuos (1966) empirical equation
e. = |/>s(rd)J
where (Td) 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 Kuos 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.

16
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 axe necessary.
The governing equations are given by (Ebersole and Dalrymple, 1979)
dU TTdU TrdU dfj 1
~dt+ufa +Vfy+9ai + ~D%*
1 1 (
pDTax+ pD V
dSxx dSx
+
'xy
dx dy
+
1 dr¡
P dy
K+U?L+V?L+S+ i i +_L(5i + &) + i2
dt dx dy 9 dy pD v pD ay pD \ dx dy ) p dx
ai+-kvD^h(VD)=*
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 + fj]
h is the still water depth; fj is the elevation of the mean water level due to wave set
up/set down; t¡ is the lateral shear stress due to turbulent mixing; %x and %y are the
bottom shear stresses; tsx and Tay are the surface shear stresses; and Sxx,Sxy, and Syy
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 mill
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
du dw
dx dz
= 0
Integrating over depth and applying Leibniz rule of integration, the integrated conti
nuity equation is rewritten as
d_
dx
udz [u^-
dx
dh .
- w\v + [Ufc + W\-h
= 0
Further simplification will result through the use of boundary conditions in two di
mensions. The kinematic boundary conditions at surface is

r
18
The bottom boundary conditions for a fixed bottom is
[u&+wU = 0
Substituting these conditions into the vertically integrated continuity equation yields
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,
respectively,
U = Vc + Uw
V = Vc + Vw,
where Uc and r¡c are the time-averaged value of velocity and free surface displacement.
Uw and r¡w 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:
cos(kx at)
2 sinhkh
Substituting these into the integrated continuity equation,
then expanding in a Taylor series at rj = rjc which is a mean water surface level, and
taking the time-average,

19
Removing the wave fluctuations, this equation can be simplified as
d d
drjc
dt
o nc a ,
+diLudz+di{,iu'')'=0
Here, (r)wuw)nc can be expressed as the mass flux of x and y components as followings,
pgH2kx
Vc
8 <7
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
dr],
- + -
dt dx
rc dMx
I ucdz H- = 0
J-h
dx
Assuming a steady motion, the integrated continuity equation becomes
d
dx ^x ~ ^
where
/Vc
ucdz
h
Therefore, the depth-integrated discharge of x component by undertow current, Qx,
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,
Qx = -Mx
The mean undertow velocity is simply estimated as = Qx/(ijc + 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
depth.

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

CHAPTER 3
DESCRIPTION OF SEDIMENT TRANSPORT MODEL
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
21

22
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,
Qsi = 7pJ0 J_h ui(z> t)C(z, t)dzdt
where Qai 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.

23
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 energetics 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.

24
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. OConnor and Yoo (1988)
also proposed a model based on Bijkers (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 Madsens (1979).

25
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:
f = pCf\ut\ut with ut = uc + uw
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*w. 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
uw{ Liu and Dalrymple, 1978). The total velocity vector ut is expressed as
ut = (U + cos 6)i -f {V + sin 6)j
where, U and V are components of uc for x and y direction, is a magnitude of the
bottom wave orbital velocity iTw, and 6 is the wave angle. Therefore, the magnitude
is given by
|rij| = y/U2 + V2 + u2 + 2Ucos 9 -f 2Vusin#
The wave orbital velocity is expressed as
= um cos at
where um is the maximum wave orbital velocity at the bottom which is found to be
A 7TH
m T sinh kh
The absolute value of bottom shear stress can be expressed as
|f| = pCf\ut |2

26
and
Tm = max( |f|)
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

27
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 dECg
bt Hy/gE dx

28
where, E is the wave energy, Cg 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 dSxx/dx.
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 Shieldscriterion 0 (drag/gravitational
forces) was found to be mainly a function of the flow Reynolds number R (iner
tial/viscous forces),
0t =
(ps p)gD v
where f [ ] indicates function of. The variables are the threshold shear stress at
which motion begins rt, sand density pa, 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,

29
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

critica) mobility number, 8
> particle diameter, cjqKIO (m) at Ta =15C
Figure 3.1: Initiation of Motion and Suspension for Unidirectional Flow (from van
Rijn, L.C., 1989).

31
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 + qs
qb ~~ ^bci^'cw Tcr)Uc¡PQ -(- A.bw(rbw Tcr')UVJ/p(J (3.1)
cUudz = f(rtUTb)UuD = AsTturbQu
9*

Net transport rate
Onshore
^7
A
Initial profile
Transformed profile
Erosion
Accretion due to onshore transport
Accretion due to offshore transport
Direction of net transport
Breaking point
Bi-crested
co
to
Figure 3.2: Type of Net Transport Rate Distribution (from Kajima et al., 1982).

33
where,
Uc; Integrated depth mean wave induced-currents
-4
Uw] Maximum orbital velocity at the bottom
Uu; Mean velocity of the undertow
Qu, Discharge by the undertow
tcw] Shear stress generated by wave and mean current
riurj; Shear stress generated by wave and mean current
Te,.] Critical shear stress under wave and mean current
Abe] The coefficient for bed load transport due to current
Abw] The coefficient for bed load transport due to wave orbital velocity
Aa] The coefficient for suspended load transport
D\ The water depth
The maximum orbital velocity at the bottom is given by linear wave theory,
u =
w T sinh kD
can be also approximated to gH/2C for shallow water waves. The mean velocity of
the undertow was approximated as
\_gJP_
8 CD
The discharge associated with the undertow current is given by as Qu = UUD where
D is the total depth. The coefficient Abc, Abw, and As 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

34
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.

35
b)
100
0
z
gf-100

£ -200
-300
Stress
r-'"
i
rf
-
\
/
Bottom
Shear Stress *
Turbulent
\
i
Shear Stress -
i ,i
10
20 30
Distance(m)
40
50
I1
S 0

co
CC
tr-1
o
Q.
CO
<5 -2
£ 0
Sediment Transport
1 1 1 1
Onshore
/
Transport
Offshore
-
\ r
Transport
\ '*
Net
*.;//
I l
Transport
I -
10
20 30
Distance(m)
40
50
Figure 3.3: Distributions of a)Wave Height b)Stress c)Sediment Transport Rate.

36
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,
i i i d h
qx = qx + £x\qx
qv = qy + ev\qy\fy
in which x and y are horizontal cartesian coordinates, qx and qy are the transport
components, q], and qy are their equivalents for horizontal bed, h is the water depth
and £ 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

37
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
4Hf,. He also showed that the transition length is dependent on beach slope tan/3; for
the same wave height a steeper beach yields a shorter plunging length. An empirical

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

39
equation is proposed to give,
= 4.0 9.25 fan/?
Hb
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,
= O.^ian/?)-0-44^]"2-36
I0 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 (lt) and local surf similarity parameter (£).
lt = -^-(1 0.47r'275) for £ > 0.064
tanp
It = 0 for £ < 0.064
where
^ tan/3
* = (Hb/Lb)( 1/2)
and tan/3, Hb, Lb, and hb axe respectively the bed slope, wave height, wave length
and water depth at breaking. OShea et al. (1991) analyzed the experimental data
and suggested the following formula without a depth parameter.
-1.465
lt = 0.556tan/3Lb£

\
40
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.

41
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.

42
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. Kriebels (1985) storm profile model was the
first of its kind The SBEACH model which in essence, is a modified version of
Kriebels 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,
Cus=tanh(7^)700
where, CU3 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 s(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,

44
Figure 3.6: a)Distribution of Cushioning Effect. b)Evolution of Sediment Transport
Rate.

45
where h is the water depth, t is the time, and qx and qy are the components of
volumetric net sediment transport rates in the -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,
1 fx
q(x) = 7T / (^2 hl)dx
2 1 'o
where
ti,t2 = times of profile surveys
x0 = shoreward location of no profile change, where q(x0) = 0
hi, h2 = profile depths at survey times 1 and 2

CHAPTER 4
CALIBRATION OF SEDIMENT TRANSPORT RATE
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 Savilles 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 (if = 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
46

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

48
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 Abw in a range from 0.05 to 0.07 and Aa from 1.0xl0-5(m2/Ar)
to 1.5xlO_5(m2/iV).
With these determined Abw and A, values, the model was used to simulate the CE
case CE400. Figure 4.3 shows the comparison of measured and calculated profiles.

49
a)
Cross-Shore Transport Rate(Experiment)
1-2
CO
cc
B-4
Q.
(0
C
H-6
-8.
TT
\V
}
/
.< ../
^ /
V '
After 62 Min.
After 111 Min.
After 273 Min.
-'10 0 10 20 30 40 50 60 70
Distance(m)
b)
Cross-Shore Transport Rate(Present Model)
S..2
0) e-
ro
CC
5-4
CL
OT
c
(0 _
H-6
-a
/
-r:
\
\<
^ ^
/ >
/ /
I /
/
V
V./ ,
A /
After 62 Min.
After 111 Min.
After 273 Min.
-10 0 10 20 30 40 50 60 70
Distance(m)
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).

50
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

Depth(m) Depth(m) Depth(m)
51
Profile Change(After 1 Hrs)
Profile Change(After 3 Hrs)
Profile Change(After 5 Hrs)
Figure 4.3: Comparison between Calculated and Measured Beach Profiles for t= 1,
3, 5 hours. Data from Saville(1957).

Transport Rate(m /m/hr) Transport Rate(m /m/hr)
52
a)
Cross-Shore Transport Rate(Experiment)
10
10
1 r i i
\ u.
V
A / /
* \ y '
'K'
After 1 Hr
* ,*
After 3 Hr
\ /
After 5 Hr
i i
-20 0
20 40 60 80
Distance(m)
Cross-Shore Transport Rate(Present Model)
I 1 I 1 i
r 7 7
/ >
v / 1
Y N/ '
N \ /
" \ /
\/
After 1 Hr
After 3 Hr
After 5 Hr
i t
i t i
-20
20 40
Distance(m)
60
80
Figure 4.4: Comparison of Cross-Shore Transport Rates between Experiment and
Present Model for t= 1, 3, 5 hours. Data from Saville(1957).

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

54
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
Abc. 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 P¡ with the total immersed-weight

T ransport Rate(m /m/min) Transport Rate(m /m/min)
55
a) x 10ross-Shore Transport Rate(Experiment)
10ross-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.

56
transport rate i¡ as
H = KPt
CERCs littoral drift formula (Shore Protection Manual, 1984) which is widely used
has the same functional form given as,
K(ECg cos 0 sin 0)t,
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 CERCs 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,
CERCs 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 CERCs 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

57
transport rate is obtained by integrating the volume under the curves. These total
transport rates are compared with the CERCs 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 20. For larger wave angles, the model yields values slightly higher
than the CERCs formula. The coefficient Af,c 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

58
Distance(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.

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

60
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 fines. Along each fine 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

61
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(m) Depth(m) Depth(m)
62
Depth Change(Wave Angle = 0)
After 00 minutes
After 05 minutes
0 8
After 10 minutes
Figure 4.10: Orthographic Plots of Bathymetric Change for Normal Incident Waves
in Plain Beach Movable Bed Experiment.

63
Depth Change(Wave Angle = 0)
After 05 minutes
aT 4
o
JC
2
m c-
o
After 00 minutes
73
.-20
,-10
E
aT
O
C
(0
I
m
V)
o
o
After 40 minutes
r
o
<0
w 2
w *
o
0 2 4 6
Longshore(m)
After 20 minutes
730
-20
--10
2 4 6
After 80 minutes
^30
' -p3SZH
-T"
h*2- '
4
-1 n <
_ 1
2
^io
0
Longshore(m)
Figure 4.11: Contours of Bathymetric Change for a Normal Incident Waves in Plain
Beach Movable Bed Experiment.

Depth(m) Depth(m) Depth(m)
64
Profile Change(After 20 Min.)
Profile Change(After 40 Min.)
Profile Change(After 80 Min.)
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
Waves.

65
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 A\¡c value in the numerical model and to check the K value
in CERCs formula. By applying wave height, and angle used in the experiment to
the CERCs 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 Inmans 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 I¡P¡ type of formulas
the K coefficient was adjusted downward to the range of 0.05 0.4 based on model

Depth(m) Depth(m) Depth(m)
66
Depth Change(Wave Angle = 15)
After 00 minutes
After 05 minutes
Figure 4.13: Orthographic Plots of Bathymetric Change for Oblique Incident Waves
in Plain Beach Movable Bed Experiment.

Cross-shore(m) Cross-shore(m) Cross-shore(m)
67
Depth Change(Wave Angle = 15)
After 00 minutes
-30
-20
,-10
=7= ^
2 4 6
After 10 minutes
0
^30
-20
7: . 7.; iy. .'IQ-. ~ :
2 4 6
After 40 minutes
,-20
.-10
2 4 6
Longshore(m)
After 05 minutes
-30
-20
10
2 4 6
After 20 minutes
=30
4-
40-
XT
0 2 4 6
After 80 minutes
Longshore(m)
Figure 4.14: Contours of Bathymetric Change for Oblique Incident Waves in Plain
Beach Movable Bed Experiment.

68
Distance(m)
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
Waves.

69
calibrations witb 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 Af¡c = 0.1. This value is also smaller than the previous value which
gave good agreement with CERCs formula.

CHAPTER 5
MODEL PERFORMANCE
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.
70

71
The sediment conservation equation should he 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,
dh dq^ dq^
dt dx dy
if potential q > actual q
if potential q = actual q
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-
fine 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.

Transport Rate(m /m/hr) Depth(m)
72
Profile Change(Surge=2m, H=2m)
Cross-Shore Transport Rate
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.

73
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.

Transport Rate(m/m/hr) Depth(m)
74
Profile Change(Surge=1m, H=2m)
Cross-Shore Transport Rate
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.

Depth(m) Depth(m)
75
Profile Change(Movable Bar, Surge=1m, H=2m)
Profile Change(Fixed Bar, Surge=1 m, H=2m)
Figure 5.3: Profile Changes for a)Movable Bar, and b)Fixed Bar Cases in 1 m storm
Surge and 2 m Wave Height.

Depth(m) Depth(m)
76
Profile Change(Movable Bar, Surge=2m, H=2.5m)
Profile Change(Fixed Bar, Surge=2m, H=2.5m)
Figure 5.4: Profile Changes for a)Movable Bar, and b)Fixed Bar Cases in 2 m Storm
Surge and 2.5 m Wave Height.

77
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 Deans 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.
Li 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,
QyfiJgroin 4" 1) 0, if 9j/(7, Jgroin 4" 1) ^ 0
9y(7, Jgroin 1) = 0, if 7y(^, J groin 1) < 0
where qy is the transport rate in y direction and JgT0in 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.

78
Current
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.

79
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

Cross-shore(m) Cross-shore(m)
80
a)
Depth Change(After 40days)
Longshore(m)
Depth Change(After 40days)
T 1 1 1
0 200 400 600 800 1000
Longshore(m)
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.

Cross-shore(m) Cross-shore(m)
81
a)
200
150 i
100
50 :
r=5-
Depth Change(After 70days)
,2.5
,-15
10
200 400 600 800 1000
Longshore(m)
Depth Change(After 140days)
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.

82
coast causing up drift 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
results.
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

Current
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.

84
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.

Transport Rate(m /m/day) T ransport Rate(m /m/day)
85
Sand Bypassing for One Groin
Sand Bypassing for Three Groins
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.

86
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
follows,
Qx(,Ibreak "4* 1> J) 0, if Qxi^break "4" lj <7) ^ 0
^xi^break 1*^) = 0, if Qx(break lj*^) 0
where qx is the transport rate in x direction and break is the 7th 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-

87
Longshore(m)
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.

Cross-shore(m) Cross-shore(m)
88
Depth Change(After 1day)
Longshofe(m)
200-
150:
100 r
50 -
Depth Change(After 1day)
Longshore(m)
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.

89
line erosion as well. When only current transport mechanism is considered bottom
changes are more or less confined behind the breakwater and shoaling grows only sea
ward from the shoreline. Figure 5.13 shows the topographic changes after 2 days and
7 days under the same wave condition but with only current transport mechanism.
It is clear that salient feature grows rather rapidly. Shoreline, on the other hand,
changes only slightly. The absence of swash transport mechanism might be one of
the reasons that shoreline change is so slight. Figure 5.14 shows the wave profile and
circulation pattern under an oblique wave of 15 degree angle with 1 m wave height
and 6 sec wave period. The circulation cells are now skewed toward downdrift. The
resulting bottom changes are also skewed as shown in Figure 5.15. Now even without
wave transport mechanisms the shoreline erosion becomes visible. Again, the salient
feature grows rapidly.
A case of long breakwater under normal wave attack is also illustrated. Figure 5.16
shows the wave profile and current pattern when 1 m, 6 sec incident waves approach
a beach with a longshore parallel breakwater. For the long breakwater case, two
symmetric circulation cells are separated by a calm zone. Figure 5.17 shows the
development of two salients near the two ends of the breakwater. This type of features
are also observed in the field.

90
Figure 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.

Current
Figure 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.

Cross-shore(m) Cross-shore(m)
92
Longshore(m)
Depth Change(After 7days)
Figure 5.15: Depth Changes after a)2 days, and b)7 days on the Plain Beach with
Breakwater for 1 m, 6 sec, and 15 degree Incident Wave.

93
Current
Longshore(m)
Figure 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.

Cross-shore(m) Cross-shore(m)
94
a)
Depth Change(After 1day)
.-9 1 .-9
200
-7 ,-7
150
r5 r5 -
100

50
..+0 .;
A
1 1 1 1 1
(
) 100 200 300 400 500
Longshore(m)
Depth Change(After 2days)
,-9 1 ' J ,-9
200
r7 r7
150
-5 ,-5 -
100
L ^ -
N z
50
- .0 . ... 4. .;
n
1 1 1 1 1
\I i i I 1 1
0 100 200 300 400 500
Longshore(m)
Figure 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.

CHAPTER 6
INLET EXPERIMENT
The sedimentary processes in the vicinity of a tidal inlet present a complex dy
namic interaction problem between fluid and sediment motion. There exist water
level changes at the shoreline by tide and periodical tidal currents in and out of the
inlet. This tidal current interacts with wave and wave induced longshore current.
Under the combined effects of waves, longshore current, tidal current and coastal
structures, the behavior of the sediment movement and morphological evolution in
the inlet region is a very complicated process and the current knowledge is extremely
limited. In early years, the engineering interest in inlets is mainly on inlet stability,
maintenance of navigation channels, and manmade structures, e.g., jetty structures.
Recently, inlet management has become a national issue, and more quantitative in
formation as well as predictive capability for beach-inlet systems is needed, e.g., the
systems sediment budget, the affected shoreline change at the macroscopic level, and
the nearshore morphological change at a finer spacial scale. At present, knowledge
and tool are extremely limited. Reliable mathematical formulation to predict the
hydrodynamics, sediment transport and the resulting topographic changes near the
inlet are still lacks. Laboratory modeling using movable bed-material is still a viable
tool despite its limitations such as expensive cost, time consuming, and scale effects
(Wang et al., 1992). Numerical model on inlet morphology is at its infancy. An at
tempt is made here to apply the present model to an inlet beach system. The results
must be considered as tentative.
95

96
On a separate study, an inlet-beach physical model was constructed in the wave
basin facility in the Coastal and Oceanographic Engineering Laboratory at the Uni
versity of Florida. The purpose of that study was to examine the generation and
growth of an ebb tidal shoal and to measure the influence of the ebb tidal shoal and
the effect of partial ebb shoal removal to the downdrift beach.
The inlet beach model consists of an idealized inlet on a plain beach with profile
identical to that in the plain beach model. Figure 6.1 shows the schematics of the
inlet beach model. The model was constructed between two guide walls 16 m apart.
The idealized inlet runs perpendicular to the shoreline and has a straight, rectangular
channel with uniform width and depth equal to 1.5 m and 20 cm, respectively. The
inlet has two parallel jetties extending offshore with the updrift jetty twice as long
as the downdrift jetty. These jetties are made of concrete blocks and impervious
to sediment transport. The experiments were carried out under the condition of
7.5 degree oblique waves. Similar to the oblique wave case in the plain beach model
experiment, additional source sand was placed immediately inside the updrift sidewall
boundary. The downdrift return flow channel also served as sediment catch basin.
The test conditions are as follows:
Wave condition: 8 cm wave height, 1 sec wave period, 7.5
Current condition: 0.14 m/sec ebb current, 0.1 m/sec flood current
Tidal range(between flood and ebb): 3 cm
The flood and ebb tidal conditions were simulated alternatively in the model at every
40 minute intervals by holding the high and low water levels, respectively, and revers
ing tidal currents in the inlet. Periodical bottom surveys were carried out, mostly
between tidal current change overs. Figure 6.2 shows photos taken during the inlet
beach experiment. Figure 6.3 and Figure 6.4 give, respectively, the orthographic and
the contour plots of the bathemetric changes. Shoreline erosion occurred on both

97
Inlet Movable Bed Model
Figure 6.1: Schematic Map of the Inlet Beach Movable Bed Model for Oblique Waves.

98
Figure 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.

99
sides of the inlet. It was evident that downdrift erosion was considerably more severe
than up drift.
Numerical simulations were performed for the given physical model conditions.
Figure 6.5 shows the simulated wave pattern based on initial bottom contours for
ebb condition. Figure 6.6 plots nearshore current patterns under ebb and flood con
ditions. Figure 6.7 shows sediment transport vectors on the initial bottom contours
under ebb and flood conditions. In both cases, sediment transports axe strongly di
rected toward offshore. Figure 6.8 and 6.9 show, respectively, the depth changes in
the numerical simulation in orthographic and contour plots. In both physical and
numerical models cross-shore transport is found to be much stronger than longshore
transport on either side of the inlet under the tested condition. Therefore, results in
both cases showed strong shoreline erosion and the formation of longshore breakpoint
bar. A commonly observed phenomenon of accretion on the updrift side of the up-
drift jetty was not found, largely owing to the strong test wave condition. However,
updrift/downdrift shoreline offset due to the littoral drift disruption by the jetties
were evident in physical and numerical results. Ebb shoal formation, if any, was not
evident in the numerical model. In the physical model, there appeared to have a
tendency of formation of an elongated ebb tidal shoal. Detailed analysis is still in
progress under a separate project.
The predicted gross longshore transport rates at different times are also compared
to those measured in the physical model. This comparison serves the purpose check
the longshore transport formula as well as for sediment budget analysis. Figure 6.10(a)
shows the total sediment transport vectors after 160 minutes. Because of the vector
sum of cross-shore transport and longshore transport, each vector was oblique to the
downdrift and it was more slanted near the breaking point where strong longshore
transport occurs. Figure 6.10(b) presents the comparisons of longshore transport

100
Depth Change(Experiment)
After 000 minutes
After 020 minutes
Figure 6.3: Orthographic Plots of Bathymetric Change for Oblique Incident Waves
in Inlet Beach Movable Bed Experiment.

Cross-shore(m) Cross-shore(m) Cross-shore(m)
101
Depth Change(Experiment)
After 000 minutes
.-3
.-30
1
,-20
,-20
1 n
^ ' ~ 'jTB'-- : ~
, . T* * "
0
5
10 15
After 040 minutes
Longshore(m)
After 020 minutes
After 160 minutes
Longshore(m)
Figure 6.4: Contours of Bathymetric Change for Oblique Incident Waves in Inlet
Beach Movable Bed Experiment.

102
X
Figure 6.5: Calculated Wave Crests on the Initial Profile in Inlet Beach Movable Bed
Experiment for 8 cm, 1 sec, and Oblique Incident Wave.

103
Figure 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 Waves.

Cross-shore(m) Cross-shore(m)
104
Sediment Transport(Ebb)
Sediment Transport(Flood)
Figure 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 Waves.

105
Depth Change(Present Model)
After 000 minutes After 020 minutes
After 040 minutes After 080 minutes
After 120 minutes After 160 minutes
Figure 6.8: Orthographic Plots of Calculated Bathymetric Change for Oblique Inci
dent Waves in Inlet Beach Movable Bed Experiment.

Cross-shore(m) Cross-shore(m) Cross-shore(m)
106
Depth Change(Present Model)
After 000 minutes
,-'30
.-30
I
,-20
r^
.-10"
+7T
r~ ^
0
5
10 15
After 040 minutes
Longshore(m)
After 020 minutes
o
CO
1
(
o
CO

n
,-20
-2.0
,-1"
C ,-10
:!:+W
m...
0 5 10 15
After 160 minutes
,-30
.-30
1
-^0
,-2 C
r10 a
,-1
1
,0
^tor.
':-T0^
0
5
10 15
Longshore(m)
Figure 6.9: Contours of Calculated Bathymetric Change for Oblique Incident Waves
in Inlet Beach Movable Bed Model.

107
rates at different run times. The results showed that in terms of gross longshore
transport, the numerical model gives close estimate for ebb cycle but significantly
underpredicts for flood cycle. In the numerical model, the transport rates during
ebb and during flood are not much as different, which is thought as a consequence
that the fundamental transport mechanism is largely the same in the model with no
differentiation between flood and ebb. In the physical model, the transport during
flood is much stronger than during ebb which suggests different mechanisms are at
work such as different water level changes, different current blocking effects. The
lack of swash transport mechanism in the numerical model could also be a cause of
the discrepancy. Field experiment by Bodge (1986) and laboratory experiments by
Kamphuis (1991(b)) all showed that large concentration of sediment in suspension in
the swash zone that are responsible for the observed peak in longshore transport and
erosion of the beach face. This swash transport coupled with high water level during
flood tide is likely to result in higher longshore transport rate during flood cycle.
Finally, Figure 6.11 shows the changes of the topographies by plotting the differ
ence between the initial contours and the contours after 160 minutes. The numerical
model appears to be able to reproduce reasonably well some of the general features
found in the physical model, as the locations of erosion and accretion, the position and
size of breakpoint bars and the shoreline offset. Detailed topographic comparisons
are still difficult and may not be too meaningful owing partly the three dimensional
effects produced in the physical model.

108
b)
Longshore Transport
JE 0.25
E
0.2
of
0.15
cc
c
g. 0.1
CO
c

£ 0.05
1 "1 1
1 1
o
1
1 1
-
*: Numerical Model
-
O: Physical Model
o
(Ebb)
(Flood)
(Ebb)
(Flood)
X
o
X
X
X
i 1
O
L-
1 1
0
20 40 60
80 100
120
140 160
Time(min)
Figure 6.10: a)Calculated Total Sediment Transport Field after 160 minutes
b)Comparison of Longshore Transport Rates between Inlet Experiment and Numeri
cal Model for 8 cm, 1 sec, and Oblique Incident Waves.

Cross-shore(m) Cross-shore(m)
109
Depth Difference(Experiment)
Depth Difference(Present Mode!)
Longshore(m)
Figure 6.11: Comparison of Bathymetric Changes after 160 minutes between Exper
iment and Numerical Model for 8 cm, 1 sec, and Oblique Incident Waves.

CHAPTER 7
CONCLUSION AND RECOMMENDATIONS FOR FURTHER STUDY
7.1 Conclusions
This dissertation presents the results of a study on developing a three-dimensional
numerical model for predicting nearshore morphological changes under the combined
effects of currents and waves as well as the presence of typical coastal structures. In
particular, this study seeks to i) develop an improved sediment transport model in
the surfzone by including the effect of undertow current, wave breaking turbulence,
and transition zone effect, ii) present a physical mechanism that enables the beach
to approach an equilibrium state under steady environment without resorting to a
pre-determined profile shape, iii) calibrate and verify the cross-shore and longshore
transport formulae developed for the numerical model by using 2-D tank experiments,
3-D basin experiments, and currently accepted empirical formulae, iv)test the model
performance by applying the model to a variety of typical coastal structures including
artificial bottom bars, groin systems, and breakwaters, and finally v)apply the nu
merical model to an inlet -beach system which has complex interactions among fluid,
sediment, and structures and compare with a 3-D basin inlet beach experiment.
The major conclusions from this study are summarized as follows:
1) The hydrodynamic model computes fully interactive current and wave fields
based on coupled parabolic wave equation and depth-averaged circulation equa
tions. For breaking model, energy dissipation formulations using empirical equa-
110

Ill
tions for stable wave deformations are used. The mean undertow current is
calculated as the sum of the return flows compensating for the onshore mass
flux due to breaking bores, and Eulerian mass transport.
2) The rate of sediment transport is treated as the summation of two mechanisms
one due to the mean current and wave orbital velocity, and the other due to the
wave induced turbulence and undertow current.
3) The cross-shore transport is composed of onshore directed transport by bed
load due to bottom wave orbital velocity and offshore-directed transport by
suspended load due to undertow current. Since the offshore transport is much
larger than onshore transport in the surfzone, the resultant sediment transport
rate distribution is composed of two directional transport; offshore transport in
the surfzone, onshore transport outside the breaking point.
4) By including transition zone effect, breakpoint bar is formed near the plung
ing point, not the point of initial breaking. This is much more realistic when
compared with field and laboratory evidence.
5) A water column cushioning effect is introduced. This physical effect enables
the beach to reach an equilibrium state under steady wave condition without
resorting to a pre-determined profile shape.
6) The model has been successfully compared with the evolution of beach profiles in
the 2-D Germans Big Wave Flume tests, CERCs large tank tests, and Air-Sea-
Tank experiment. The model is capable of describing the growth and movement
of main breakpoint bars and corresponding berm processes with reasonable re
liability. Calculated cross-shore bathymetry changes are in qualitatively good
agreement with the observed beach profile evolution. The breakpoint bar loca
tion is well predicted and the evolution reaches a quasi equilibrium state under

112
constant wave conditions. However, the trough size is not well predicted and the
rate of erosion at the shoreline are underestimated because of the poor swash
model.
7) The comparison of longshore transport rate between present model and CERC
formula shows close agreement for different angles when the coefficient Aic in
the model is adjusted to compatible with CERCs K coefficient of 0.77. An
independent calibration was carried out by a 3-D basin experiment. The K
coefficient in the CERCs formula was adjusted downward to 0.23 which is more
in line with other existing experimental data as well as the field results along
the east coast of Florida.
8) The model performance was illustrated by applying the model to different
coastal structures such as artificial fixed bars, groins, and breakwaters.
9) The model was further tested with inlet beach movable bed experiment. The
general capabilities of applying the model to inlet-beach systems is illustrated.
Further improvement and verification are required for actual quantitative ap
plications.
7.2 Future Study
The deterministic morphological model developed in this dissertation is based on
the integration of various process elements such as waves, currents, and sediment
transport. Clearly all constituent processes in the model are not perfect and have
ample room for improvement. Suggestions of further research often start by attempt
ing to fill the immediate gaps in the model found in calibrations and modifications or
even applications. This approach could run the risk of not reaching to the essentials.
Nevertheless, a few suggestions are given here.

113
1) In order to make the sediment transport model approach an equilibrium state
under steady wave condition, a cushioning effect was introduced which employs
a purely artificial formula. Although this effect is essential in the model, no solid
evidence is provided to support this concept.
2) Slope effect is found to be very important for stabilizing the bottom change
in the numerical model, especially outside the breaking point. This is because
outside the breaking point the bed load transport is always directly towards the
shoreline and gravity is the only counter force to maintain equilibrium.
3) Transition zone effect is one of the currently active research subjects. By this
effect, the location of bar was clearly improved. However, there is lack of dy
namically based formulations.
4) Much work has been done for wave-current interactions outside the breaking
zone. Interactions inside the surfzone are still largely a void.
5) Swash zone processes are not included in the model. From laboratory evidence,
it appears to be that such mechanism must be developed and included.
6) The presented examples are mainly focused on the development of bar profiles
during storm conditions. The model does have the potential to study the re
covery of a beach profile under gentle conditions. Verification tests should be
carried out.
7) Currently, the numerical model was calibrated only by sediment transport.
Ideally, the model should be calibrated for current, wave and sediment trans
port simultaneously. More complete calibrations and verifications against field
data and controlled laboratory experiments under different wave conditions are
needed to improve coefficient determinations and confidence level.

114
In addition to the aforementioned specifics, extension to random wave applica
tion is a must if the model is to apply to long term simulation.

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BIOGRAPHICAL SKETCH
The author, Taerim Kim, was born in Seoul, Korea, on May 11, 1964. He gradu
ated from Jung-Ang high school in 1983 and enrolled at the Seoul National University
in 1983. He received a Bachelor of Science degree in oceanography in February, 1987.
He continued his study at Seoul National University and earned a Master of Science
degree in Oceanography in August, 1989. In order to fulfill his military duty, he
underwent a six-month military training for lieutenant. To pursue his Ph.D. in the
department of Coastal and Oceanographic Engineering at the University of Florida,
he came to the United States of America on August 15, 1990. This was his first start
as independent of his family. Although he couldnt be with his own family during
his stay in Gainesville, he enjoyed experiences that can only be found on ones own.
He traveled in many parts of America, Europe, and Japan. He watched most of the
films produced during the past five years. He lived a very simple and self-sufficient
fife. During his Ph.D. program he gained extensive experience in physical modeling as
well as numerical modeling. In August of 1995, he was granted the degree of Doctor
of Philosophy from the Coastal and Oceanographic Engineering Department. He is
happy to join his family as the fifth Ph.D. He will remember his fife in Gainesville as
a very precious time and will begin another big step for the future.
121



77
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 Deans 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.
Li 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,
QyfiJgroin 4" 1) 0, if 9j/(7, Jgroin 4" 1) ^ 0
9y(7, Jgroin 1) = 0, if 7y(^, J groin 1) < 0
where qy is the transport rate in y direction and JgT0in 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.


99
sides of the inlet. It was evident that downdrift erosion was considerably more severe
than up drift.
Numerical simulations were performed for the given physical model conditions.
Figure 6.5 shows the simulated wave pattern based on initial bottom contours for
ebb condition. Figure 6.6 plots nearshore current patterns under ebb and flood con
ditions. Figure 6.7 shows sediment transport vectors on the initial bottom contours
under ebb and flood conditions. In both cases, sediment transports axe strongly di
rected toward offshore. Figure 6.8 and 6.9 show, respectively, the depth changes in
the numerical simulation in orthographic and contour plots. In both physical and
numerical models cross-shore transport is found to be much stronger than longshore
transport on either side of the inlet under the tested condition. Therefore, results in
both cases showed strong shoreline erosion and the formation of longshore breakpoint
bar. A commonly observed phenomenon of accretion on the updrift side of the up-
drift jetty was not found, largely owing to the strong test wave condition. However,
updrift/downdrift shoreline offset due to the littoral drift disruption by the jetties
were evident in physical and numerical results. Ebb shoal formation, if any, was not
evident in the numerical model. In the physical model, there appeared to have a
tendency of formation of an elongated ebb tidal shoal. Detailed analysis is still in
progress under a separate project.
The predicted gross longshore transport rates at different times are also compared
to those measured in the physical model. This comparison serves the purpose check
the longshore transport formula as well as for sediment budget analysis. Figure 6.10(a)
shows the total sediment transport vectors after 160 minutes. Because of the vector
sum of cross-shore transport and longshore transport, each vector was oblique to the
downdrift and it was more slanted near the breaking point where strong longshore
transport occurs. Figure 6.10(b) presents the comparisons of longshore transport


119
Naim, R. B. and Southgate, H. N.,1993. Deterministic profile modeling of
nearshore processes. Part 2. Sediment transport and beach profile development,
Coastal Eng., 19:pp. 57-96.
Nielson, D.M., and Sorensen, T. 1970., Sand transport phenomena on coasts with
bars, Proc. 12th ICCE, ASCE, pp.855-866.
OConnor, B.A. and Yoo, D., 1988., Mean bed friction of combined wave/current
flow, Coastal Eng., 12:pp. 1-21.
Oh, T.M., 1988. Three-dimensional hydrodynamics and morphology associated
with rip currents ,Ph.D. Dissertation, Coastal and Oceanographic Engineering
Department, University of Florida. UFL/COEL/TR-104.
Ohnaka, S. and Watanabe, A., 1990. Modeling of Wave-Current Interaction and
Beach Change, Proc. 22nd Coastal Eng. Conf., Delft, The Netherlands, pp.
2443-2456.
Okayasu, A., Watanabe, A., and Isobe, M., 1990. Modeling of energy transfer
and undertow in the surf zone, Proc. 22nd Coastal Eng. Conf., Delft, The
Netherlands, pp. 123-135.
OShea, K.F., Nicholson, J. and OConnor, B.A., 1991., Analysis of existing labo
ratory data to find expression for the transition zone length, Report MCE/1,
Dept. Civil Eng., University of Liverpool, UK.
Owen, M.W. and Thorn, M.F.C., 1978. Sand transport in waves and currents,
Hydraul. Res. Stn, Annual Rep. HMSO, London, pp.
Perlin, M., and Dean, R.G., 1985. 3-D model of bathymetric response to struc
tures, Journal of Waterway, port, coastal and ocean engineering. Vol.lll, No.2,
pp.153-170.
Ribberink, J.S. and Al-Salem, A., 1991. Near-bed sediment transport and sus
pended sediment concentrations under waves, Int. Symp. on the Transport of
Suspended Sediments and its Mathematical Modelling, Florence, Italy, Septem
ber 2-5,1991. pp.153-170.
Sato, S. and Tanaka, N., 1966. Field investigation on sand drift at Port Kashima
facing the Pacific Ocean, Proc. 10th Coastal Eng. Conf., pp. 595-614.
Saville, T., 1957. Scale Relationship for Equilibrium Profiles, Int. Assoc, of Hy
draulic Research, 1957
Shibayama, T., Sato, S., Asada, H. and Temmyo, T., 1989., A method to evaluate
sediment transport rate in wave-current coexistent system, Coastal Eng. in
Japan, Vol. 32, No.2, pp.161-171.
Shimizu, T., Nodani, H. and Kondo, K., 1990. Practical application of the three-
demensional beach evolution model, Coastal Eng., 22:pp. 2481-2493.
Shore Protection Manual, 1984(4th edition). Coastal Engineering Research Center,
U.S. Army Corps of Engineers, Vicksburg.


90
Figure 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.


79
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


NUMERICAL MODELING OF NEARSHORE
MORPHOLOGICAL CHANGES UNDER A CURRENT-WAVE FIELD
By
TAERIM KIM
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1995


23
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 energetics 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.


Ill
tions for stable wave deformations are used. The mean undertow current is
calculated as the sum of the return flows compensating for the onshore mass
flux due to breaking bores, and Eulerian mass transport.
2) The rate of sediment transport is treated as the summation of two mechanisms
one due to the mean current and wave orbital velocity, and the other due to the
wave induced turbulence and undertow current.
3) The cross-shore transport is composed of onshore directed transport by bed
load due to bottom wave orbital velocity and offshore-directed transport by
suspended load due to undertow current. Since the offshore transport is much
larger than onshore transport in the surfzone, the resultant sediment transport
rate distribution is composed of two directional transport; offshore transport in
the surfzone, onshore transport outside the breaking point.
4) By including transition zone effect, breakpoint bar is formed near the plung
ing point, not the point of initial breaking. This is much more realistic when
compared with field and laboratory evidence.
5) A water column cushioning effect is introduced. This physical effect enables
the beach to reach an equilibrium state under steady wave condition without
resorting to a pre-determined profile shape.
6) The model has been successfully compared with the evolution of beach profiles in
the 2-D Germans Big Wave Flume tests, CERCs large tank tests, and Air-Sea-
Tank experiment. The model is capable of describing the growth and movement
of main breakpoint bars and corresponding berm processes with reasonable re
liability. Calculated cross-shore bathymetry changes are in qualitatively good
agreement with the observed beach profile evolution. The breakpoint bar loca
tion is well predicted and the evolution reaches a quasi equilibrium state under


113
1) In order to make the sediment transport model approach an equilibrium state
under steady wave condition, a cushioning effect was introduced which employs
a purely artificial formula. Although this effect is essential in the model, no solid
evidence is provided to support this concept.
2) Slope effect is found to be very important for stabilizing the bottom change
in the numerical model, especially outside the breaking point. This is because
outside the breaking point the bed load transport is always directly towards the
shoreline and gravity is the only counter force to maintain equilibrium.
3) Transition zone effect is one of the currently active research subjects. By this
effect, the location of bar was clearly improved. However, there is lack of dy
namically based formulations.
4) Much work has been done for wave-current interactions outside the breaking
zone. Interactions inside the surfzone are still largely a void.
5) Swash zone processes are not included in the model. From laboratory evidence,
it appears to be that such mechanism must be developed and included.
6) The presented examples are mainly focused on the development of bar profiles
during storm conditions. The model does have the potential to study the re
covery of a beach profile under gentle conditions. Verification tests should be
carried out.
7) Currently, the numerical model was calibrated only by sediment transport.
Ideally, the model should be calibrated for current, wave and sediment trans
port simultaneously. More complete calibrations and verifications against field
data and controlled laboratory experiments under different wave conditions are
needed to improve coefficient determinations and confidence level.


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


24
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. OConnor and Yoo (1988)
also proposed a model based on Bijkers (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 Madsens (1979).


Depth(m) Depth(m) Depth(m)
66
Depth Change(Wave Angle = 15)
After 00 minutes
After 05 minutes
Figure 4.13: Orthographic Plots of Bathymetric Change for Oblique Incident Waves
in Plain Beach Movable Bed Experiment.


Transport Rate(m /m/hr) Depth(m)
72
Profile Change(Surge=2m, H=2m)
Cross-Shore Transport Rate
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.


BIBLIOGRAPHY
Badiei, P., Kamphuis, J.W., and Hamilton, D.G. 1994., Physical experiments on
the effecits of groins on shore morphology, Book of Abstracts, 24th, ICCE,
ASCE, V 2, pp 516-517.
Bagnold, R.A., 1946., Motion of waves in shallow water: interaction between
waves and sand bottoms , Proc. Roy. Soc., Ser. A., 187, pp. 1-55.
Bagnold, R.A., 1963., Mechanics of marine sedimentation , In The Sea: Ideas
and Observations, Interscience, New York, 3:507-553.
Bailard, J.A., 1981. An energetics total load sediment transport model for a plane
sloping beach, J. Geoph. Res., 86(cll), pp.10938-10954.
Bailard, J.A. and Inman, D.L., 1981. An energetics bed load transport model for
a plane sloping beach;local transport, J. Geoph. Res., 86(c), pp.2035-2043.
Basco, D.R. and Yamashita, T., 1986., Toward a simple model of breaking tran
sition region in surfzone , Proc. 20th Coastal Eng. Conf., pp. 955-970.
Battjes, J.A. and Janssen, J.P.F.M., 1978., Energy loss and set-up due to breaking
of random waves , Proc. 16th Coastal Eng. Conf., pp. 569-587.
Bijker, E.W., 1966., The increase of bed shear stress in a current due to wave
motion , Proc. 10th Coastal Eng. Conf., Tokyo, pp.746-765.
Bijker, E.W., Hijum, E. V. and Vellinger, P., 1976., Sand transport by waves ,
Proc. 15th Coastal Eng. Conf., Hawaii, pp.1149-1167.
Bodge, K.R., 1986. Short-term impoundment of longshore sediment trans
port ,Ph.D. Dissertation, Coastal and Oceanographic Engineering Department,
University of Florida. UFL/COEL/TR-065 pp. 345.
Briand, M.-H.G. and Kamphuis, J.W., 1993a. Waves and currents on natural
beaches: a quasi 3-D numerical model, Coastal Eng., 20:101-134.
Briand, M.-H.G. and Kamphuis, J.W., 1993b. Sediment transport in the surf zone:
a quasi 3-D numerical model, Coastal Eng., 20:135-156.
Bruun, P., 1954. Coastal erosion and the development of beach profiles, Tech.
Memo. No. 44, Beach Erosion Board, U.S. Army Corps of Engineers.
115


117
Glavin, C.J., 1969. Breaker travel and choice of design wave height, Journal of
Waterway, Port, Coastal and Ocean Engineering, ASCE, Vol.95, No. 2. pp.175-
200.
Grant, W. D. and Madsen, O.S., 1979., Combine wave and current interaction
with a rough bottom, J. Geophys. Res., Vol. 84, pp. 1797-1808.
Grant, W. D. and Madsen, O.S., 1986., The continental-shelf bottom boundary
layer, Ann. Rev. Fluid Mech., 18;pp. 265-305.
Hansen, J.B. and Svendsen, I.A. 1986. Experimental investigation of the wave
and current motion over a longshore bar, Proc. 20th ICCE, Taipei, Taiwan,
pp.1166-1179.
Hanson, H. and Kraus, N.C. 1989. Genesis: Generalized model for simulating
shoreline change, CERC report 89-19, US Corps of Engineering, Vicksburg,
185 pp.
Hanson, H. and Kraus, N.C. 1990. Shoreline response to a single transmissive
detached breakwater, Proc. 22th, ICCE, ASCE pp. 2034-2046.
Horikawa, K., 1988., Nearshore dynamics and coastal processes , University of
Tokyo Press, pp. 522.
Horikawa, K., and Kuo, C.T. 1966., A study of wave transformation inside the
surf zone, Proc. 10th ICCE, ASCE, Tokyo, pp.217-233.
Hsu, J.R.C. and Silvester, R., 1990., Accretion behind single offshore breakwater,
Journal of waterway, port, coastal and ocean engineering, ASCE, Vol.116, No.
3. pp.362-380.
Inman, D.L. and Bowen, A. J., 1962., Flume experiments on sand transport by
waves and currents , Proc. 8th Coastal Eng. Conf., Mexico, pp.137-150.
Jonsson, I.G., 1966., Wave boundary layers and friction factors, Proc. 10th,
ICCE, ASCE pp.127-148.
Jonsson, I.G., 1990., Wave current interactions , In:B. Le Mehaute and D.M.
Hanes(Editors), The Sea, Vol. 9A, Wiley-Interscience, New York, pp.65-120.
Kajima, R., Shimizu, T., Maruyama, K., and Saito, S., 1982., Experiments
on beach profile change with a large wave flume, Proc. 18th, ICCE, ASCE
pp.1385-1404.
Kamphuis, J.W., 1991a. Alongshore sediment transport distribution, Journal of
waterway, port, coastal and ocean engineering, ASCE, Vol.117, No. 6., pp.624-
640.
Kamphuis, J.W., 1991b. Alongshore sediment transport distributions, Proc.
Coastal Sediments91, Seattle, ASCE, pp.170-183.
Katopodi I. and Ribberink J. S., 1992. Quasi-3D modelling of suspended sedimet
trasport by currents and waves, Coastal Eng., 18;pp. 83-110.


Cross-shore(m) Cross-shore(m) Cross-shore(m)
67
Depth Change(Wave Angle = 15)
After 00 minutes
-30
-20
,-10
=7= ^
2 4 6
After 10 minutes
0
^30
-20
7: . 7.; iy. .'IQ-. ~ :
2 4 6
After 40 minutes
,-20
.-10
2 4 6
Longshore(m)
After 05 minutes
-30
-20
10
2 4 6
After 20 minutes
=30
4-
40-
XT
0 2 4 6
After 80 minutes
Longshore(m)
Figure 4.14: Contours of Bathymetric Change for Oblique Incident Waves in Plain
Beach Movable Bed Experiment.


CHAPTER 7
CONCLUSION AND RECOMMENDATIONS FOR FURTHER STUDY
7.1 Conclusions
This dissertation presents the results of a study on developing a three-dimensional
numerical model for predicting nearshore morphological changes under the combined
effects of currents and waves as well as the presence of typical coastal structures. In
particular, this study seeks to i) develop an improved sediment transport model in
the surfzone by including the effect of undertow current, wave breaking turbulence,
and transition zone effect, ii) present a physical mechanism that enables the beach
to approach an equilibrium state under steady environment without resorting to a
pre-determined profile shape, iii) calibrate and verify the cross-shore and longshore
transport formulae developed for the numerical model by using 2-D tank experiments,
3-D basin experiments, and currently accepted empirical formulae, iv)test the model
performance by applying the model to a variety of typical coastal structures including
artificial bottom bars, groin systems, and breakwaters, and finally v)apply the nu
merical model to an inlet -beach system which has complex interactions among fluid,
sediment, and structures and compare with a 3-D basin inlet beach experiment.
The major conclusions from this study are summarized as follows:
1) The hydrodynamic model computes fully interactive current and wave fields
based on coupled parabolic wave equation and depth-averaged circulation equa
tions. For breaking model, energy dissipation formulations using empirical equa-
110


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
NUMERICAL MODELING OF NEARSHORE
MORPHOLOGICAL CHANGES UNDER A CURRENT-WAVE FIELD
By
TAERIM KIM
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
x


118
Keulegan, G.H., and Krumbein, W.C., 1949. Stable configuration of bottom slope
in a shallow sea and its bearing on geological processes, Transactions of Amer
ica Geophysical Union, 30(6), pp. 855-861.
Kirby, J. T., 1984. A note on linear surface wave-current interaction over slowly
varying topography, J. Geophys. Res., Vol. 89, No. Cl, pp. 745-747
Komar, P.D. and Inman, D.L. 1970., Longshore sand transport on beaches, J.
Geophys. Res., Vol. 75, No. 30, pp. 5914-5927
Komar, P.D. and Miller, M.C. 1974., Sediment threshold under oscillatory waves,
Proc. 14th, ICCE, ASCE, V 2, pp.756-775.
Kraus, N.C., Hanson, H., and Blomgren, S.H. 1994., Modern functional design of
groin systems, Book of Abstracts, 24th, ICCE, ASCE, V 2, pp.204-205.
Kriebel, D. L., 1985. Numerical simulation of time-dependent beach and dune
erosion,Coastal Eng., Vol 9, pp. 221-245.
Larson, M., Kraus, N. C. and Byrnes, M. R., 1989. SBEACH: Numerical Model
for Simulating Storm-Induced Beach Change, Technical Report CERC-89-9,
Coastal Engineering Research Center, US Army Corps of Engineers.
Lee, J.L., 1993. Wave-current interaction and quasi-three-dimensional modeling
in nearshore zone,Ph.D. Dissertation, Coastal and Oceanographic Engineering
Department, University of Florida. UFL/COEL/TR-095.
Lee-Young, J.S. and Sleath, J.F.A., 1988., Initial motion in combined wave-current
flow, Proc. 21th, ICCE, ASCE pp.1140-1151.
Liu, P.L.F. and Dalrymple, R.A., 1978., Bottom frictioanl stresses and longshore
currents due to waves with large angles of incidence, J. Mar. Res., 36:pp. 357-
375.
Longuet-Higgins, M.S. 1970a., Longshore currents generated by obliquely incident
sea waves, I, J. Geophys. Res., 75(33):pp. 6778-6789.
Longuet-Higgins, M.S. 1970b., Longshore currents generated by obliquely incident
sea waves, II, J. Geophys. Res., 75(33):pp. 6790-6801.
McCowan, J. 1894., On the highest wave of permanent type , Philos. Mag. J.
Sci., Vol. 38.
Moore, B.D. 1982., Beach profile evolution in response to changes in water level
and wave height, MCE Thesis, Department of Civil Engineering, University of
Delaware.
Nadaoka K., Yagi H. and Kamata H., 1991. A simple quasi-3-D model of suspended
sediment transport in a nonequilibrium state, Coastal Eng., 15:pp.459-474.
Naim, R. B., Roelvink, J.A. and Southgate, H. N.,1990. Transition zone width and
implications for modeling surfzone hydrodynamics, Proc. 22th, ICCE, ASCE
pp. 68-81.


45
where h is the water depth, t is the time, and qx and qy are the components of
volumetric net sediment transport rates in the -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,
1 fx
q(x) = 7T / (^2 hl)dx
2 1 'o
where
ti,t2 = times of profile surveys
x0 = shoreward location of no profile change, where q(x0) = 0
hi, h2 = profile depths at survey times 1 and 2


42
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. Kriebels (1985) storm profile model was the
first of its kind The SBEACH model which in essence, is a modified version of
Kriebels 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


19
Removing the wave fluctuations, this equation can be simplified as
d d
drjc
dt
o nc a ,
+diLudz+di{,iu'')'=0
Here, (r)wuw)nc can be expressed as the mass flux of x and y components as followings,
pgH2kx
Vc
8 <7
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
dr],
- + -
dt dx
rc dMx
I ucdz H- = 0
J-h
dx
Assuming a steady motion, the integrated continuity equation becomes
d
dx ^x ~ ^
where
/Vc
ucdz
h
Therefore, the depth-integrated discharge of x component by undertow current, Qx,
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,
Qx = -Mx
The mean undertow velocity is simply estimated as = Qx/(ijc + 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
depth.


2
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 models ability for describing the cross shore sedi-


56
transport rate i¡ as
H = KPt
CERCs littoral drift formula (Shore Protection Manual, 1984) which is widely used
has the same functional form given as,
K(ECg cos 0 sin 0)t,
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 CERCs 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,
CERCs 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 CERCs 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


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


73
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.


48
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 Abw in a range from 0.05 to 0.07 and Aa from 1.0xl0-5(m2/Ar)
to 1.5xlO_5(m2/iV).
With these determined Abw and A, values, the model was used to simulate the CE
case CE400. Figure 4.3 shows the comparison of measured and calculated profiles.


r
18
The bottom boundary conditions for a fixed bottom is
[u&+wU = 0
Substituting these conditions into the vertically integrated continuity equation yields
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,
respectively,
U = Vc + Uw
V = Vc + Vw,
where Uc and r¡c are the time-averaged value of velocity and free surface displacement.
Uw and r¡w 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:
cos(kx at)
2 sinhkh
Substituting these into the integrated continuity equation,
then expanding in a Taylor series at rj = rjc which is a mean water surface level, and
taking the time-average,


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FILES


120
Sleath, J.F.A., 1990., Sea bed boundary layers, In:B. Le Mebaute and D.M.
Hanes (Editors), The Sea, Vol. 9A, Wiley-Interscience, New York, pp.693-727.
Stive, M.J.F. and Wind, H.G., 1986., Cross-shore mean flow in the surf zone,
Coastal Eng., 10(4):pp. 325-340.
Struiksma, N. Olesen, K.W., Flokstra, C. and De Vriend, H.J., 1985,Bed defor
mation in curved alluvial channels, J. Hydr. Res., Vol. 23 no.l, pp.57-79.
Suh, K.D. and Hardaway C.S. 1994., Numerical modeling of tombolo formation,
Book of Abstracts, 24th, ICCE, ASCE, V 2, pp. 480-481.
Svendsen, I.A. 1984., Wave heights and set-up in a surf zone, Coastal Eng., 8:pp.
303-329.
Svendsen, I.A., and Lorenz, R.S. 1989., Velocities in combined undertow and
longshore currents, Coastal Eng., 13: pp. 55-79.
van Rijn, L.C., 1989. Handbook sediment transport by currents and waves, Delft
Hydraulics, Rept. H461, Appr. 400pp.
van Rijn, L.C. and Meijer, K., 1989. Three dimensional mathematical modelling
of suspended sediment transport in currents and waves, IAHR Symp., Copen
hagen, Denmark.
Wang, H., Lin, L., Zhong, H., and Miao, G., 1992, Sebastian Inlet Physical Model
Studies, Part II Movable Bed Model, Coastal and Oceanographic Engineer
ing Department, University of Florida. UFL/COEL-91/014.
Wang, H. and Kim T., 1993. Assesing artificial bars by the numerical model,
Annual National Conference on Beach Preservation Technology, St, Petersburg,
Florida, pp. 191-206
Wang, Z.B., De Vriend, H.J. and Louters, T., 1991. A morphodynamic model for
a tidal inlet, Proc. CMOE91, Barcelona, Spain, pp.235-245.
Watanabe, A., Maruyama, K., Shimizu, T., Sakakiyama, T., 1986. Numerical
prediction model of three dimensional beach deformation around a structure,
Coastal Eng. in Japan. 29, pp.179-194.
Watanabe, A., Shimizu, T., and Kondo, K., 1991. Field application of a numerical
model of beach topography change, coastal sediments91, pp.1815-1828.
Willis, D.H., 1979. Sediment load under wave and currents, National Research
Council Canada, DME/NAE Quarterly Bull. No. 1979(3), Ottawa.
Winer, H.S., 1988. Numerical Modeling of Wave-Induced Currents Using a
Parabolic Wave Equation, Ph.D. Dissertation, Coastal and Oceanographic En
gineering Department, University of Florida. UFL/COEL/TR-080.


T ransport Rate(m /m/min) Transport Rate(m /m/min)
55
a) x 10ross-Shore Transport Rate(Experiment)
10ross-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.


Cross-shore(m) Cross-shore(m)
80
a)
Depth Change(After 40days)
Longshore(m)
Depth Change(After 40days)
T 1 1 1
0 200 400 600 800 1000
Longshore(m)
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.


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


34
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.


Cross-shore(m) Cross-shore(m)
81
a)
200
150 i
100
50 :
r=5-
Depth Change(After 70days)
,2.5
,-15
10
200 400 600 800 1000
Longshore(m)
Depth Change(After 140days)
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.


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.
XI


UFL/COEL-TR/109
NUMERICAL MODELING OF NEARSHORE
MORPHOLOGICAL CHANGES UNDER A CURRENT-
WAVE FIELD
by
Taerim Kim
Dissertation
1995


Cross-shore(m) Cross-shore(m) Cross-shore(m)
106
Depth Change(Present Model)
After 000 minutes
,-'30
.-30
I
,-20
r^
.-10"
+7T
r~ ^
0
5
10 15
After 040 minutes
Longshore(m)
After 020 minutes
o
CO
1
(
o
CO

n
,-20
-2.0
,-1"
C ,-10
:!:+W
m...
0 5 10 15
After 160 minutes
,-30
.-30
1
-^0
,-2 C
r10 a
,-1
1
,0
^tor.
':-T0^
0
5
10 15
Longshore(m)
Figure 6.9: Contours of Calculated Bathymetric Change for Oblique Incident Waves
in Inlet Beach Movable Bed Model.


84
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.


Cross-shore(m) Cross-shore(m)
109
Depth Difference(Experiment)
Depth Difference(Present Mode!)
Longshore(m)
Figure 6.11: Comparison of Bathymetric Changes after 160 minutes between Exper
iment and Numerical Model for 8 cm, 1 sec, and Oblique Incident Waves.


86
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
follows,
Qx(,Ibreak "4* 1> J) 0, if Qxi^break "4" lj <7) ^ 0
^xi^break 1*^) = 0, if Qx(break lj*^) 0
where qx is the transport rate in x direction and break is the 7th 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-


107
rates at different run times. The results showed that in terms of gross longshore
transport, the numerical model gives close estimate for ebb cycle but significantly
underpredicts for flood cycle. In the numerical model, the transport rates during
ebb and during flood are not much as different, which is thought as a consequence
that the fundamental transport mechanism is largely the same in the model with no
differentiation between flood and ebb. In the physical model, the transport during
flood is much stronger than during ebb which suggests different mechanisms are at
work such as different water level changes, different current blocking effects. The
lack of swash transport mechanism in the numerical model could also be a cause of
the discrepancy. Field experiment by Bodge (1986) and laboratory experiments by
Kamphuis (1991(b)) all showed that large concentration of sediment in suspension in
the swash zone that are responsible for the observed peak in longshore transport and
erosion of the beach face. This swash transport coupled with high water level during
flood tide is likely to result in higher longshore transport rate during flood cycle.
Finally, Figure 6.11 shows the changes of the topographies by plotting the differ
ence between the initial contours and the contours after 160 minutes. The numerical
model appears to be able to reproduce reasonably well some of the general features
found in the physical model, as the locations of erosion and accretion, the position and
size of breakpoint bars and the shoreline offset. Detailed topographic comparisons
are still difficult and may not be too meaningful owing partly the three dimensional
effects produced in the physical model.


49
a)
Cross-Shore Transport Rate(Experiment)
1-2
CO
cc
B-4
Q.
(0
C
H-6
-8.
TT
\V
}
/
.< ../
^ /
V '
After 62 Min.
After 111 Min.
After 273 Min.
-'10 0 10 20 30 40 50 60 70
Distance(m)
b)
Cross-Shore Transport Rate(Present Model)
S..2
0) e-
ro
CC
5-4
CL
OT
c
(0 _
H-6
-a
/
-r:
\
\<
^ ^
/ >
/ /
I /
/
V
V./ ,
A /
After 62 Min.
After 111 Min.
After 273 Min.
-10 0 10 20 30 40 50 60 70
Distance(m)
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).


14
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 = Khb (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 finked 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


100
Depth Change(Experiment)
After 000 minutes
After 020 minutes
Figure 6.3: Orthographic Plots of Bathymetric Change for Oblique Incident Waves
in Inlet Beach Movable Bed Experiment.


36
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,
i i i d h
qx = qx + £x\qx
qv = qy + ev\qy\fy
in which x and y are horizontal cartesian coordinates, qx and qy are the transport
components, q], and qy are their equivalents for horizontal bed, h is the water depth
and £ 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


Depth(m) Depth(m) Depth(m)
62
Depth Change(Wave Angle = 0)
After 00 minutes
After 05 minutes
0 8
After 10 minutes
Figure 4.10: Orthographic Plots of Bathymetric Change for Normal Incident Waves
in Plain Beach Movable Bed Experiment.


65
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 A\¡c value in the numerical model and to check the K value
in CERCs formula. By applying wave height, and angle used in the experiment to
the CERCs 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 Inmans 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 I¡P¡ type of formulas
the K coefficient was adjusted downward to the range of 0.05 0.4 based on model


57
transport rate is obtained by integrating the volume under the curves. These total
transport rates are compared with the CERCs 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 20. For larger wave angles, the model yields values slightly higher
than the CERCs formula. The coefficient Af,c 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


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AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES


Cross-shore(m) Cross-shore(m) Cross-shore(m)
101
Depth Change(Experiment)
After 000 minutes
.-3
.-30
1
,-20
,-20
1 n
^ ' ~ 'jTB'-- : ~
, . T* * "
0
5
10 15
After 040 minutes
Longshore(m)
After 020 minutes
After 160 minutes
Longshore(m)
Figure 6.4: Contours of Bathymetric Change for Oblique Incident Waves in Inlet
Beach Movable Bed Experiment.


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.
ill


26
and
Tm = max( |f|)
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


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,
Cus=tanh(7^)700
where, CU3 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 s(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,


TABLE OF CONTENTS
ACKNOWLEDGMENTS iii
LIST OF FIGURES vi
ABSTRACT x
CHAPTERS
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 DESCRIPTION OF NEARSHORE HYDRODYNAMIC MODEL 11
2.1 Wave Model 11
2.2 Wave Breaking and Energy Dissipation 14
2.3 Circulation Model 16
2.4 Undertow Current 17
3 DESCRIPTION OF SEDIMENT TRANSPORT MODEL 21
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 CALIBRATION OF SEDIMENT TRANSPORT RATE 46
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
IV


2.4 Undertow Current
Inside the surf zone, the 2-D model is inadequate as the model will yield mill
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
du dw
dx dz
= 0
Integrating over depth and applying Leibniz rule of integration, the integrated conti
nuity equation is rewritten as
d_
dx
udz [u^-
dx
dh .
- w\v + [Ufc + W\-h
= 0
Further simplification will result through the use of boundary conditions in two di
mensions. The kinematic boundary conditions at surface is


33
where,
Uc; Integrated depth mean wave induced-currents
-4
Uw] Maximum orbital velocity at the bottom
Uu; Mean velocity of the undertow
Qu, Discharge by the undertow
tcw] Shear stress generated by wave and mean current
riurj; Shear stress generated by wave and mean current
Te,.] Critical shear stress under wave and mean current
Abe] The coefficient for bed load transport due to current
Abw] The coefficient for bed load transport due to wave orbital velocity
Aa] The coefficient for suspended load transport
D\ The water depth
The maximum orbital velocity at the bottom is given by linear wave theory,
u =
w T sinh kD
can be also approximated to gH/2C for shallow water waves. The mean velocity of
the undertow was approximated as
\_gJP_
8 CD
The discharge associated with the undertow current is given by as Qu = UUD where
D is the total depth. The coefficient Abc, Abw, and As 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


7
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 energetics 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-


31
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 + qs
qb ~~ ^bci^'cw Tcr)Uc¡PQ -(- A.bw(rbw Tcr')UVJ/p(J (3.1)
cUudz = f(rtUTb)UuD = AsTturbQu
9*


7 CONCLUSION AND RECOMMENDATIONS FOR FURTHER STUDY 110
7.1 Conclusions 110
7.2 Future Study 112
BIBLIOGRAPHY 115
BIOGRAPHICAL SKETCH 121
v


61
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.


25
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:
f = pCf\ut\ut with ut = uc + uw
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*w. 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
uw{ Liu and Dalrymple, 1978). The total velocity vector ut is expressed as
ut = (U + cos 6)i -f {V + sin 6)j
where, U and V are components of uc for x and y direction, is a magnitude of the
bottom wave orbital velocity iTw, and 6 is the wave angle. Therefore, the magnitude
is given by
|rij| = y/U2 + V2 + u2 + 2Ucos 9 -f 2Vusin#
The wave orbital velocity is expressed as
= um cos at
where um is the maximum wave orbital velocity at the bottom which is found to be
A 7TH
m T sinh kh
The absolute value of bottom shear stress can be expressed as
|f| = pCf\ut |2


Cross-shore(m) Cross-shore(m)
88
Depth Change(After 1day)
Longshofe(m)
200-
150:
100 r
50 -
Depth Change(After 1day)
Longshore(m)
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.


82
coast causing up drift 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
results.
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


Cross-shore(m) Cross-shore(m)
104
Sediment Transport(Ebb)
Sediment Transport(Flood)
Figure 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 Waves.


Current
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.


critica) mobility number, 8
> particle diameter, cjqKIO (m) at Ta =15C
Figure 3.1: Initiation of Motion and Suspension for Unidirectional Flow (from van
Rijn, L.C., 1989).


93
Current
Longshore(m)
Figure 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.


28
where, E is the wave energy, Cg 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 dSxx/dx.
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 Shieldscriterion 0 (drag/gravitational
forces) was found to be mainly a function of the flow Reynolds number R (iner
tial/viscous forces),
0t =
(ps p)gD v
where f [ ] indicates function of. The variables are the threshold shear stress at
which motion begins rt, sand density pa, 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,


Cross-shore(m) Cross-shore(m)
94
a)
Depth Change(After 1day)
.-9 1 .-9
200
-7 ,-7
150
r5 r5 -
100

50
..+0 .;
A
1 1 1 1 1
(
) 100 200 300 400 500
Longshore(m)
Depth Change(After 2days)
,-9 1 ' J ,-9
200
r7 r7
150
-5 ,-5 -
100
L ^ -
N z
50
- .0 . ... 4. .;
n
1 1 1 1 1
\I i i I 1 1
0 100 200 300 400 500
Longshore(m)
Figure 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.


16
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 axe necessary.
The governing equations are given by (Ebersole and Dalrymple, 1979)
dU TTdU TrdU dfj 1
~dt+ufa +Vfy+9ai + ~D%*
1 1 (
pDTax+ pD V
dSxx dSx
+
'xy
dx dy
+
1 dr¡
P dy
K+U?L+V?L+S+ i i +_L(5i + &) + i2
dt dx dy 9 dy pD v pD ay pD \ dx dy ) p dx
ai+-kvD^h(VD)=*
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 + fj]
h is the still water depth; fj is the elevation of the mean water level due to wave set
up/set down; t¡ is the lateral shear stress due to turbulent mixing; %x and %y are the
bottom shear stresses; tsx and Tay are the surface shear stresses; and Sxx,Sxy, and Syy
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.


Transport Rate(m/m/hr) Depth(m)
74
Profile Change(Surge=1m, H=2m)
Cross-Shore Transport Rate
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.


44
Figure 3.6: a)Distribution of Cushioning Effect. b)Evolution of Sediment Transport
Rate.


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
Waves 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 Waves 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
Waves 108
6.11 Comparison of Bathymetric Changes after 160 minutes between
Experiment and Numerical Model for 8 cm, 1 sec, and Oblique
Incident Waves 109
IX


CHAPTER 6
INLET EXPERIMENT
The sedimentary processes in the vicinity of a tidal inlet present a complex dy
namic interaction problem between fluid and sediment motion. There exist water
level changes at the shoreline by tide and periodical tidal currents in and out of the
inlet. This tidal current interacts with wave and wave induced longshore current.
Under the combined effects of waves, longshore current, tidal current and coastal
structures, the behavior of the sediment movement and morphological evolution in
the inlet region is a very complicated process and the current knowledge is extremely
limited. In early years, the engineering interest in inlets is mainly on inlet stability,
maintenance of navigation channels, and manmade structures, e.g., jetty structures.
Recently, inlet management has become a national issue, and more quantitative in
formation as well as predictive capability for beach-inlet systems is needed, e.g., the
systems sediment budget, the affected shoreline change at the macroscopic level, and
the nearshore morphological change at a finer spacial scale. At present, knowledge
and tool are extremely limited. Reliable mathematical formulation to predict the
hydrodynamics, sediment transport and the resulting topographic changes near the
inlet are still lacks. Laboratory modeling using movable bed-material is still a viable
tool despite its limitations such as expensive cost, time consuming, and scale effects
(Wang et al., 1992). Numerical model on inlet morphology is at its infancy. An at
tempt is made here to apply the present model to an inlet beach system. The results
must be considered as tentative.
95


29
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


114
In addition to the aforementioned specifics, extension to random wave applica
tion is a must if the model is to apply to long term simulation.


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


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


\
40
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.


12
where u> is absolute angular frequency and g is gravity coefficient. The hyperbolic
Equation (2.1) can he reduced to an elliptic form based on the assumption that the
only time dependency of velocity potential is in the phase,
di
dt
iuxf>
Substituting the above equation into Equation (2.1), the following equation is ob
tained,
-2iu, -Vh4> + - Vh( Vfc) + (V, )( Vfc) V, (CCgVht) +
{a2 0,2 k2CCg o,(VA )}4> = icrW (2.2)
where only the phase contribution to the horizontal derivative of ^ 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 ^ is
= ig y) c'( f kcosOdx+f ksinOdy)
a
and the proper form of the dispersion relationship is
uj = a -f 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 6, sinO term can be neglected


9
Figure 1.1: Structure of nearshore morphodynamic model.


Transport Rate(m /m/day) T ransport Rate(m /m/day)
85
Sand Bypassing for One Groin
Sand Bypassing for Three Groins
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.


78
Current
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.


Net transport rate
Onshore
^7
A
Initial profile
Transformed profile
Erosion
Accretion due to onshore transport
Accretion due to offshore transport
Direction of net transport
Breaking point
Bi-crested
co
to
Figure 3.2: Type of Net Transport Rate Distribution (from Kajima et al., 1982).


71
The sediment conservation equation should he 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,
dh dq^ dq^
dt dx dy
if potential q > actual q
if potential q = actual q
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-
fine 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.


41
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.


98
Figure 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.


58
Distance(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.


54
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
Abc. 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 P¡ with the total immersed-weight


22
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,
Qsi = 7pJ0 J_h ui(z> t)C(z, t)dzdt
where Qai 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.


105
Depth Change(Present Model)
After 000 minutes After 020 minutes
After 040 minutes After 080 minutes
After 120 minutes After 160 minutes
Figure 6.8: Orthographic Plots of Calculated Bathymetric Change for Oblique Inci
dent Waves in Inlet Beach Movable Bed Experiment.


112
constant wave conditions. However, the trough size is not well predicted and the
rate of erosion at the shoreline are underestimated because of the poor swash
model.
7) The comparison of longshore transport rate between present model and CERC
formula shows close agreement for different angles when the coefficient Aic in
the model is adjusted to compatible with CERCs K coefficient of 0.77. An
independent calibration was carried out by a 3-D basin experiment. The K
coefficient in the CERCs formula was adjusted downward to 0.23 which is more
in line with other existing experimental data as well as the field results along
the east coast of Florida.
8) The model performance was illustrated by applying the model to different
coastal structures such as artificial fixed bars, groins, and breakwaters.
9) The model was further tested with inlet beach movable bed experiment. The
general capabilities of applying the model to inlet-beach systems is illustrated.
Further improvement and verification are required for actual quantitative ap
plications.
7.2 Future Study
The deterministic morphological model developed in this dissertation is based on
the integration of various process elements such as waves, currents, and sediment
transport. Clearly all constituent processes in the model are not perfect and have
ample room for improvement. Suggestions of further research often start by attempt
ing to fill the immediate gaps in the model found in calibrations and modifications or
even applications. This approach could run the risk of not reaching to the essentials.
Nevertheless, a few suggestions are given here.


Transport Rate(m /m/hr) Transport Rate(m /m/hr)
52
a)
Cross-Shore Transport Rate(Experiment)
10
10
1 r i i
\ u.
V
A / /
* \ y '
'K'
After 1 Hr
* ,*
After 3 Hr
\ /
After 5 Hr
i i
-20 0
20 40 60 80
Distance(m)
Cross-Shore Transport Rate(Present Model)
I 1 I 1 i
r 7 7
/ >
v / 1
Y N/ '
N \ /
" \ /
\/
After 1 Hr
After 3 Hr
After 5 Hr
i t
i t i
-20
20 40
Distance(m)
60
80
Figure 4.4: Comparison of Cross-Shore Transport Rates between Experiment and
Present Model for t= 1, 3, 5 hours. Data from Saville(1957).


Depth(m) Depth(m)
75
Profile Change(Movable Bar, Surge=1m, H=2m)
Profile Change(Fixed Bar, Surge=1 m, H=2m)
Figure 5.3: Profile Changes for a)Movable Bar, and b)Fixed Bar Cases in 1 m storm
Surge and 2 m Wave Height.


15
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 = |[EC, E,C,\
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,
Ea, that the breaker is striving to attain. The local stable wave energy density Es is
calculated using Horikawa and Kuos (1966) empirical equation
e. = |/>s(rd)J
where (Td) 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 Kuos 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.


96
On a separate study, an inlet-beach physical model was constructed in the wave
basin facility in the Coastal and Oceanographic Engineering Laboratory at the Uni
versity of Florida. The purpose of that study was to examine the generation and
growth of an ebb tidal shoal and to measure the influence of the ebb tidal shoal and
the effect of partial ebb shoal removal to the downdrift beach.
The inlet beach model consists of an idealized inlet on a plain beach with profile
identical to that in the plain beach model. Figure 6.1 shows the schematics of the
inlet beach model. The model was constructed between two guide walls 16 m apart.
The idealized inlet runs perpendicular to the shoreline and has a straight, rectangular
channel with uniform width and depth equal to 1.5 m and 20 cm, respectively. The
inlet has two parallel jetties extending offshore with the updrift jetty twice as long
as the downdrift jetty. These jetties are made of concrete blocks and impervious
to sediment transport. The experiments were carried out under the condition of
7.5 degree oblique waves. Similar to the oblique wave case in the plain beach model
experiment, additional source sand was placed immediately inside the updrift sidewall
boundary. The downdrift return flow channel also served as sediment catch basin.
The test conditions are as follows:
Wave condition: 8 cm wave height, 1 sec wave period, 7.5
Current condition: 0.14 m/sec ebb current, 0.1 m/sec flood current
Tidal range(between flood and ebb): 3 cm
The flood and ebb tidal conditions were simulated alternatively in the model at every
40 minute intervals by holding the high and low water levels, respectively, and revers
ing tidal currents in the inlet. Periodical bottom surveys were carried out, mostly
between tidal current change overs. Figure 6.2 shows photos taken during the inlet
beach experiment. Figure 6.3 and Figure 6.4 give, respectively, the orthographic and
the contour plots of the bathemetric changes. Shoreline erosion occurred on both


35
b)
100
0
z
gf-100

£ -200
-300
Stress
r-'"
i
rf
-
\
/
Bottom
Shear Stress *
Turbulent
\
i
Shear Stress -
i ,i
10
20 30
Distance(m)
40
50
I1
S 0

co
CC
tr-1
o
Q.
CO
<5 -2
£ 0
Sediment Transport
1 1 1 1
Onshore
/
Transport
Offshore
-
\ r
Transport
\ '*
Net
*.;//
I l
Transport
I -
10
20 30
Distance(m)
40
50
Figure 3.3: Distributions of a)Wave Height b)Stress c)Sediment Transport Rate.


CHAPTER 2
DESCRIPTION OF NEARSHORE HYDRODYNAMIC MODEL
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
+ (V vh(cc,vh4.) + ( Dt
(2.1)
Dt2 v Dt
where t is the time, V* is the horizontal gradient operator,
V7 d d *
Vh = ai, + V
A A
i and j are the unit vector in the x (cross-shore) direction and y (longshore) 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 ^ 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
v = a + k U
a2 = gk tanh kh
11


CHAPTER 4
CALIBRATION OF SEDIMENT TRANSPORT RATE
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 Savilles 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 (if = 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
46


97
Inlet Movable Bed Model
Figure 6.1: Schematic Map of the Inlet Beach Movable Bed Model for Oblique Waves.


4
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
processes.
2. Respond to changes in water level due to tides, storm surges, or long-term
fluctuations.
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.


8
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.


27
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 dECg
bt Hy/gE dx


68
Distance(m)
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
Waves.


10
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
study.


102
X
Figure 6.5: Calculated Wave Crests on the Initial Profile in Inlet Beach Movable Bed
Experiment for 8 cm, 1 sec, and Oblique Incident Wave.


CHAPTER 5
MODEL PERFORMANCE
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.
70


Depth(m) Depth(m) Depth(m)
64
Profile Change(After 20 Min.)
Profile Change(After 40 Min.)
Profile Change(After 80 Min.)
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
Waves.


13
and cosO is assumed to be unity. Then, the velocity potential is approximated as
a
The e'(fka'nBdy) part 0f the phase function is now absorbed into the amplitude function,
A. By substituting this ^ 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 ikAx ^f), the following parabolic wave equation is
obtained (Winer, 1988),
(q e + u)a, +\ a + Va, + zQa
"54(i s* Va ~ 5 [cc (I).],'+ Ta m
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
(1988).


37
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
4Hf,. He also showed that the transition length is dependent on beach slope tan/3; for
the same wave height a steeper beach yields a shorter plunging length. An empirical


6
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 models 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.


60
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 fines. Along each fine 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


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) Ini tal 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
vii


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
Waves 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
Waves 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
Vlll


CHAPTER 1
INTRODUCTION
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
1


89
line erosion as well. When only current transport mechanism is considered bottom
changes are more or less confined behind the breakwater and shoaling grows only sea
ward from the shoreline. Figure 5.13 shows the topographic changes after 2 days and
7 days under the same wave condition but with only current transport mechanism.
It is clear that salient feature grows rather rapidly. Shoreline, on the other hand,
changes only slightly. The absence of swash transport mechanism might be one of
the reasons that shoreline change is so slight. Figure 5.14 shows the wave profile and
circulation pattern under an oblique wave of 15 degree angle with 1 m wave height
and 6 sec wave period. The circulation cells are now skewed toward downdrift. The
resulting bottom changes are also skewed as shown in Figure 5.15. Now even without
wave transport mechanisms the shoreline erosion becomes visible. Again, the salient
feature grows rapidly.
A case of long breakwater under normal wave attack is also illustrated. Figure 5.16
shows the wave profile and current pattern when 1 m, 6 sec incident waves approach
a beach with a longshore parallel breakwater. For the long breakwater case, two
symmetric circulation cells are separated by a calm zone. Figure 5.17 shows the
development of two salients near the two ends of the breakwater. This type of features
are also observed in the field.


CHAPTER 3
DESCRIPTION OF SEDIMENT TRANSPORT MODEL
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
21


39
equation is proposed to give,
= 4.0 9.25 fan/?
Hb
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,
= O.^ian/?)-0-44^]"2-36
I0 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 (lt) and local surf similarity parameter (£).
lt = -^-(1 0.47r'275) for £ > 0.064
tanp
It = 0 for £ < 0.064
where
^ tan/3
* = (Hb/Lb)( 1/2)
and tan/3, Hb, Lb, and hb axe respectively the bed slope, wave height, wave length
and water depth at breaking. OShea et al. (1991) analyzed the experimental data
and suggested the following formula without a depth parameter.
-1.465
lt = 0.556tan/3Lb£


BIOGRAPHICAL SKETCH
The author, Taerim Kim, was born in Seoul, Korea, on May 11, 1964. He gradu
ated from Jung-Ang high school in 1983 and enrolled at the Seoul National University
in 1983. He received a Bachelor of Science degree in oceanography in February, 1987.
He continued his study at Seoul National University and earned a Master of Science
degree in Oceanography in August, 1989. In order to fulfill his military duty, he
underwent a six-month military training for lieutenant. To pursue his Ph.D. in the
department of Coastal and Oceanographic Engineering at the University of Florida,
he came to the United States of America on August 15, 1990. This was his first start
as independent of his family. Although he couldnt be with his own family during
his stay in Gainesville, he enjoyed experiences that can only be found on ones own.
He traveled in many parts of America, Europe, and Japan. He watched most of the
films produced during the past five years. He lived a very simple and self-sufficient
fife. During his Ph.D. program he gained extensive experience in physical modeling as
well as numerical modeling. In August of 1995, he was granted the degree of Doctor
of Philosophy from the Coastal and Oceanographic Engineering Department. He is
happy to join his family as the fifth Ph.D. He will remember his fife in Gainesville as
a very precious time and will begin another big step for the future.
121


108
b)
Longshore Transport
JE 0.25
E
0.2
of
0.15
cc
c
g. 0.1
CO
c

£ 0.05
1 "1 1
1 1
o
1
1 1
-
*: Numerical Model
-
O: Physical Model
o
(Ebb)
(Flood)
(Ebb)
(Flood)
X
o
X
X
X
i 1
O
L-
1 1
0
20 40 60
80 100
120
140 160
Time(min)
Figure 6.10: a)Calculated Total Sediment Transport Field after 160 minutes
b)Comparison of Longshore Transport Rates between Inlet Experiment and Numeri
cal Model for 8 cm, 1 sec, and Oblique Incident Waves.


5
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


116
Dally, W. R. and Dean, R. G., 1984. Suspended sediment transport and beach
profile evolution, Journal of Waterway, Port, Coastal and Ocean Engineering,
Vol.109, No. 4. pp.401-405.
Dally, W. R., Dean, R. G. and Dalrymple, R. A., 1984. A model for breaker decay
on beaches, Proc. 19th Coastal Eng. Conf., Houston, pp.82-98.
Davies, A.G., Soulsby, R.L. and King, H.L., 1988. A numerical model of the
combined wave and current bottom boundary layer, J. Geoph. Res., 93(d),
pp.491-508.
Dean, R. G., 1973., Heuristic models of sand transport in the surf zone, Proc.
conference on Engineering Dynamics in the Surf Zone, Sydney, pp. 208-214.
Dean, R.G., 1977. Equilibrium beach profiles:US Atlantic and Gulf coasts, Proc.
Ocean Engineering Tech. Report No. 12, Dept, of Civil Eng., Univ. of Delaware,
Newark.
Deigaard, R., Bro Millelesen, M., and Fredsoe, J., 1991. Measurements of the bed
shear stress in a surf zone, Inst. Hydrodynamic and Hydraulic Eng., Progress
report 73: 21-30.
Dette, H.H. and Uliczka, K., 1986. Seegangserzeugte Wechselwirkung Zwischen
Vorland und Vorstrand und Kustenschutzbauwerk, Technisher Bericht SFB
205/TPA6, University Hannover, Germany.
De Vriend H.J., 1986. 2DH computation of transient sea bed evolution, Proc.
20th ICCE, Taipei, Taiwan, pp.1689-1712.
De Vriend, H. J. and Kitou, N., 1990. Incorporation of wave effects in a 3D hydro
static mean current model, Proc. 22nd ICCE, Delft, The Netherlands, pp.1005-
1018.
De Vriend, H.J. and Stive, M.J.F., 1987. Quasi-3D modeling of nearshore cur
rents, Coastal Eng., ll;pp.565-601.
De Vriend, H.J.,Zyserman, J., Pechn, Ph., Roelvink, J.A., Southgate, H.N. and
Nicholson, J., 1994. Medium-term coastal area modelling, Coastal Engineer
ing special issue on coastal morphodynamic modelling, pp. 1-30
Eagleson, P.S., Glenne, B., and Dracup, J.A., 1963., Equilibrium characteristics
of sand beaches, Journal of Hydraulics Division, ASCE., 89(HY1), pp. 35-57.
Ebersole, B.A. and Dalrymple, R.A., 1979. A numerical model for nearshore circu
lation including convective accelerations and lateral mixing, Ocean Engineering
Report No. 21, Dept, of Civil Eng., Univ. of Delaware, Newark, Delaware.
Elfrink, B., BrHedegaard, I., Deigaard, R. and Fredsce, J., 1992. The net sediment
transport in non-breaking waves, Proc. MAST G6 coastal Morphodynamics,
Final workshop, Pisa, Italy.


Cross-shore(m) Cross-shore(m)
92
Longshore(m)
Depth Change(After 7days)
Figure 5.15: Depth Changes after a)2 days, and b)7 days on the Plain Beach with
Breakwater for 1 m, 6 sec, and 15 degree Incident Wave.


69
calibrations witb 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 Af¡c = 0.1. This value is also smaller than the previous value which
gave good agreement with CERCs formula.


103
Figure 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 Waves.


50
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


ACKNOWLEDGMENTS
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 fur 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.
u