• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 List of Figures
 List of Tables
 Abstract
 Introduction
 Literature review
 Laboratory studies on three-dimensional...
 Three-dimensional hydrodynamics...
 Three-dimensional hydrodynamics...
 Summary, conclusions and recom...
 Appendix A: Distributions of torque...
 Appendix B: Distributions of torque...
 Appendix C: Filtering of marginal...
 Bibliography
 Biographical sketch






Group Title: Technical report – University of Florida. Coastal and Oceanographic Engineering Program ; 102
Title: Three-dimensional hydrodynamics and morphology associated with rip currents
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Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00075326/00001
 Material Information
Title: Three-dimensional hydrodynamics and morphology associated with rip currents
Physical Description: xix, 200 leaves : ill. ; 29 cm.
Language: English
Creator: Oh, Tae-Myoung, 1959-
Publication Date: 1994
 Subjects
Subject: Coastal and Oceanographic Engineering thesis Ph.D
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1994.
Bibliography: Includes bibliographical references (leaves 195-198).
Statement of Responsibility: by Tae-Myoung Oh.
General Note: Typescript.
General Note: Vita.
Funding: Technical report (University of Florida. Coastal and Oceanographic Engineering Dept.) ;
 Record Information
Bibliographic ID: UF00075326
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: aleph - 002019432
oclc - 32794872
notis - AKK6873

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Title Page
    Acknowledgement
        Acknowledgement 1
        Acknowledgement 2
    Table of Contents
        Table of Contents 1
        Table of Contents 2
    List of Figures
        List of Figures 1
        List of Figures 2
        List of Figures 3
        List of Figures 4
        List of Figures 5
        List of Figures 6
        List of Figures 7
        List of Figures 8
        List of Figures 9
        List of Figures 10
    List of Tables
        List of Tables 1
        List of Tables 2
    Abstract
        Abstract 1
        Abstract 2
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
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    Literature review
        Page 11
        Page 12
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    Laboratory studies on three-dimensional morphology
        Page 41
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    Three-dimensional hydrodynamics on a prismatic beach
        Page 85
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    Three-dimensional hydrodynamics on a barred beach
        Page 132
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    Summary, conclusions and recommendations
        Page 167
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    Appendix A: Distributions of torque compoenents (Ho = 3cm)
        Page 173
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    Appendix B: Distributions of torque compoenents (Ho = 9cm)
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    Appendix C: Filtering of marginal distributions
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    Bibliography
        Page 195
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        Page 197
        Page 198
    Biographical sketch
        Page 199
        Page 200
Full Text



UFL/COEL-TR/102


THREE-DIMENSIONAL HYDRODYNAMICS AND
MORPHOLOGY ASSOCIATED WITH RIP CURRENTS






by



Tae-Myoung Oh


Dissertation


1994
















THREE-DIMENSIONAL HYDRODYNAMICS AND MORPHOLOGY
ASSOCIATED WITH RIP CURRENTS












By

TAE-MYOUNG OH


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


1994


L














ACKNOWLEDGMENTS


My first sincere appreciation and gratitude should belong to God. Throughout

my study here, God has always kept His eyes on me, protected my spirits, and guided

and encouraged to do what I should do. Without His Hands, this study would not

have been possible.

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

Professor Robert G. Dean. He has provided me a goal which I am trying and of

course will try to follow. His encouragement, enthusiasm, unflagging inspiration,

timely advice have taught me not only how to finish the work but also how to access

and love nature. I wish to extend my thanks to my committee members, Dr. Hsiang

Wang, Dr. Daniel M. Hanes, Dr. Ashish J. Mehta, Dr. Robert J. Thieke and Dr.

Ulrich H. Kurzweg, for their precious teaching and assistance. I am also grateful

to all staff, especially Becky Hudson for providing me her generous hospitality and

Helen Twedell for helping me in exploring the Coastal Archives. Special thanks are

due to Subarna Malaker for computer help, Jim Joyner for his help with laboratory

work, and Sidney Schofield for his overall help at the laboratory. I also owe a lot

my fellow students for their hospitality and friendship, especially Taerim Kim and

Taewhan Lee.

Special thanks go to my church members, especially the members of the edito-

rial board for the Church News Letter (Dongil Kim, Dr. Jaekyung Baek, Joon Lee,

Yongjin Lim and Yoonwha Chung), and also the member of the Continuing Witness-

ing Training Team (Dongil Kim, Jongmin Lee, Insoo Cho and Ms. Inhee Chung).

Their encouragement and prayer will always be remembered.










Finally, I could not finish my acknowledgements without appreciating endless

support and prayer from my family, parents and parents in-law. My wife, Hyunsoon,

and my two daughters, Youngeun and Seieun, are always with me during good times

as well as the bad. My parents and parents in-law are specially thanked for their

support and continuous encouragement and prayer during the stay.


L















TABLE OF CONTENTS




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

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

LIST OF TABLES ................. ................ xvi

ABSTRACT ................... ............... xviii

CHAPTERS

1 INTRODUCTION ..................... .......... 1
1.1 Three-Dimensional Features in Nature ................ 2
1.2 Three-Dimensional Features in a Narrow Wave Tank ...... .. 6
1.3 Objectives ................. ............... 8
1.4 Scope of Study .............................. 10

2 LITERATURE REVIEW ........................... 11
2.1 Introduction ................. .............. 11
2.2 Profile Evolution and Equilibrium Profile ................ 11
2.3 Three-Dimensionality in a Narrow Wave Tank ............. 17
2.4 Rip Currents in Nature ................... ...... 21
2.5 Rip Current Models ............................ 26
2.6 Rip Current Generation Models ..................... 27
2.6.1 Introduction .......................... 27
2.6.2 Prismatic Topography Models .................. 30
2.6.3 Non-Prismatic Topography Models . . .... 35

3 LABORATORY STUDIES ON THREE-DIMENSIONAL MORPHOLOGY 41
3.1 Introduction .............. .. .............. 41
3.2 Laboratory Facilities and Experimental Conditions .......... 42
3.3 Description of Movable Bed Experiments . . . .... 45
3.4 Results and Discussions ................ ......... 47
3.4.1 Reference Test (Experiment MT01) . . . 47
3.4.2 Experimental Repeatability . . . .... 51
3.4.3 Perturbation Tests ........................ 54
3.5 Summary and Conclusions ........................ 78
3.5.1 Summary ................... .......... 78
3.5.2 Conclusions ............................ 82

4 THREE-DIMENSIONAL HYDRODYNAMICS ON A PRISMATIC BEACH 85
4.1 Introduction ................... ............ 85
4.2 Wave-Induced Three-Dimensional Hydrodynamics . . ... 86
4.2.1 Governing Equations ....................... 86










4.2.2 Force Balance Inside the Surf Zone . . . .
4.2.3 Wave-Induced Horizontal Torque Induced on the Surf Zone .
4.3 Description of Fixed Bed Experiments . . . . .
4.3.1 Laboratory Facilities and Experimental Conditions . .
4.3.2 Experimental Wave Conditions . . . . .
4.3.3 Experimental Devices . . . ..... ...
4.4 Vorticity Measurement Tests .......................
4.5 Circulation Tests with Jet Discharge . . . . .
4.5.1 Introduction ............................
4.5.2 Data Measurements ........................
4.5.3 Data Analyses and Discussions . . . . .
4.6 Edge W ave Tests ............................
4.7 Summary and Conclusions . . . . . .
4.7.1 Summ ary .............................
4.7.2 Conclusions ............................

5 THREE-DIMENSIONAL HYDRODYNAMICS ON A BARRED BEACH


5.1 Introduction .................
5.2 Circulation Tests on a Barred Beach .
5.2.1 Description of Circulation Tests .
5.2.2 Wave Heights Measurements .
5.2.3 Data Analyses and Discussions .
5.2.4 Summary ..............
5.3 Longshore Currents on Barred Coastlines .
5.3.1 Governing Equations and Boundary
5.3.2 Perturbation Methods . .
5.3.3 Perturbation Solutions . .
5.3.4 Numerical Example . . .
5.4 Conclusions .................


.......


Conditions


......0.


6 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS .......
6.1 Sum m ary ................................ .
6.2 Conclusions ................................
6.3 Recommendations for Further Study . . . . .

APPENDICES

A DISTRIBUTIONS OF TORQUE COMPONENTS (H, = 3cm) ......

B DISTRIBUTIONS OF TORQUE COMPONENTS (Ho = 9cm) ......

C FILTERING OF MARGINAL DISTRIBUTIONS . . . .

BIBLIOGRAPHY .................................

BIOGRAPHICAL SKETCH ...........................


88
90
93
93
93
96
99
103
103
104
110
125
127
127
130

132


. 132


133
133
135
140
151
153
153
158
158
161
162

167
167
168
172














LIST OF FIGURES




1.1 Schematic Diagram of Nearshore Circulation System with Rip
Currents (from Shepard and Inman, 1950b) . . . 2

1.2 Bar Morphologies Created Digitally by Averaging Ten-Minute Time
Exposure Images. White bands indicate the shore break and re-
gions of concentrated wave breaking on distinct bar morphologies
at the Army Corps of Engineers Field Research Facility at Duck,
North Carolina. (from Holman and Lippmann, 1987) . 4

1.3 An Example of Three-Dimensional Morphology in Two-Dimensional
Narrow Wave Tank Tests (from Beach Erosion Board, 1947). Note
the temporal reduction of three-dimensionality after 10 hours wave
operation . . . . . . . .. 7

2.1 Bar Formation with Increasing Wave Height (drawn based on
Dean, 1985). Here, T is the wave period, and tF is the fall time of
the sediment, defined as the ratio of the suspended height to the
fall velocity of the sediment. . . . ..... 15

2.2 Cross-Tank Variations of the Profiles after 1 hour Wave Run (mod-
ified from Hughes and Fowler, 1990). Note 3-D morphology inside
the surf zone and near the bar area. .. . . . ... 20

2.3 Constitutive Elements of a Rip Current System: the feeder currents,
flows of water parallel to the shore; the neck, the main seaward-
flowing current extending beyond the breaker zone; and the rip head,
in which the rip current lose its identity as the water spreads out.
(from Shepard, Emery and La Fond, 1941) . . ...... 21

2.4 Measured Wave Height and Rip Current Intensity (from Shepard
et al., 1941). These data were obtained daily. Note the direct
relationship between these two variables. Note the definition of
zero intensity of rip current when wave height was 0.6 m (2 ft);
which would suggest that wave height must be larger than 0.6 m
for rip currents to form. ....................... 23

3.1 Schematic Diagram of the Initial Profile and Other Experimental
D details . . . . . . . .. 43

3.2 Three Profiles B1, B2 and B3 across the Tank . . ... 44









3.3 Mean Profile Evolution during Early Stages of Experiment MT01.
Elapsed Times = 0 (Initial Profile), 23, 69, 161 and 242 min. Note
that the profile approached an equilibrium and a level of profile
stability had occurred at 242 min. . . . .. 48

3.4 Comparison of the Mean Profile at 242 min during Experiment
MT01 with the Equilibrium Profile Proposed by Dean (1977).
Note the similarity between two profiles inside the surf zone. 49

3.5 Mean Profile Evolution after the Profile Approached an Equilib-
rium during Experiment MT01. Elapsed Times = 0 (Initial Pro-
file), 242, 297, 352, 407 and 476 min. Note the substantial erosion
of the area seaward of the bar and the deposition of the area imme-
diately landward of the bar trough. Note also landward movement
of the bar. . . . .. . . ...... 50

3.6 Initial Profile and Three Profiles B1, B2 and B3 and Mean Profile
at 476 min during Experiment MT01. Note three-dimensionality
inside the surf zone and near the bar area, which is 3-D morphology
associated with rip currents, and also that the centerline profile
B2 is almost the same as the mean profile. . . .... 51

3.7 Mean Profile Evolution after the Profile Approached an Equilib-
rium during Experiment MT02. Elapsed Times = 0 (Initial Pro-
file), 207, 297, 352, and 407 min. Note the substantial erosion
of the area seaward of the bar and the deposition of the area
immediately landward of the bar trough, which occurred during
Experiment MTO1 (see Figure 3.5), thus providing experimental
repeatability. ............. ............ 52

3.8 Comparison of the Mean Profile at 207 min during Experiment
MT03 with the Mean Profiles at the Same Time during Experi-
ments MT01 and MT02. Note the similarity between those three
m ean profiles ................... ......... 53

3.9 Mean Profile Evolution during Experiment MT03. Elapsed Times
= 0 (Initial Profile), 207, 352, 476 and 545 min. Note rapid change
during 476 to 545 min with landward movement of the bar and
another peak of the berm ...................... 55

3.10 Initial Profile and Three Profiles (Bl, B2 and B3) and the Profile
along Rip Channel inside the Surf Zone at 545 min during Ex-
periment MT03. Note overall 2-D conditions inside the surf zone
except a very narrow deep channel near glass side wall. . 56

3.11 Induced Perturbation to Deepen the Bar Trough at 69 min during
Experiment MT04: (a) Comparison of the Modified Mean Profile
with Pre-Modified Mean Profile, (b) Three Profiles before Modifi-
cation, and (c) Three Profiles after Modification . ... 57


I









3.12 Comparison of Pre-Modified Profile at 69 min with Pre-Modified
Profile at 138 min during Experiment MT04: (a) Comparison of
Mean Profiles, (b) Three Profiles before Modification at 69 min,
and (c) Three Profiles before Modification at 138 min. . 58

3.13 Induced Perturbation to Provide Asymmetric Area Seaward of
the Bar at 138 min during Experiment MT04: (a) Comparison
of the Modified Mean Profile with Pre-Modified Mean Profile, (b)
Three Profiles before Modification, and (c) Three Profiles after
Modification. Note the dominantly 2-D profile before modification
and the asymmetric area seaward of the bar after modification. .59

3.14 Profile Evolution from 138 min to 207 min during Experiment
MT04: (a) Comparison of the Modified Mean Profile at 138 min
with Mean Profile at 207 min, (b) Three Profiles after Modifica-
tion at 138 min, and (c) Three Profiles at 207 min. . ... 61

3.15 Profile Evolution from 297 min to 352 min during Experiment
MT04: (a) Comparison of the Mean Profile at 297 min with Mean
Profile at 352 min, (b) Three Profiles at 297 min, and (c) Three
Profiles at 352 min. Note the erosion of the area seaward of the bar
and deposition of the area immediately landward of the bar trough.
Note also the differences in the three-dimensionalities between two
elapsed tim es .............................. 63

3.16 Induced Perturbation to Remove Half Part of the Bar Crest at
352 min Wave Run during Experiment MT04: (a) Comparison
of the Modified Mean Profile with Pre-Modified Mean Profile, (b)
Three Profiles before Modification, and (c) Three Profiles after
Modification.................... .......... 64

3.17 Profile Evolution from 352 min to 407 min during Experiment
MT04: (a) Comparison of the Pre-Modified Mean Profile at 352
min with Mean Profile at 407 min, (b) Three Profiles before Mod-
ification at 352 min, and (c) Three Profiles at 407 min. Note the
complete recovery of the bar crest with a smaller rotational angle
(less than 10 degrees) ......................... 65

3.18 Isolines of Profile Elevations at 545 min during Experiment MT04.
These photographs showed: (1) the weak 3-D berm, (2) deep and
narrow channel near steel side wall, (3) depositional area occupy-
ing large portion of the surf zone, and (4) clockwise rotation of the
bar. Elevation contours were established by placing black yarn at
waterline during lowering of water level. . . ... 67

3.19 Initial Profile with 3-D Berm Area for Experiment MT05 . 69

3.20 Initial Profile and Three Profile B1, B2 and B3 at 476 min during
Experiment MT05. Note dominantly 2-D morphology. . 70









3.21 Mean Profile Evolution during Experiment MT05. Elapsed Times
= 0 (Initial Profile), 476, 545 and 614 min. Note rapid change
during 545 to 614 min with landward movement of the bar and
another peak of the berm. However, the overall shape of the profile
was surprisingly unchanged . . . . ... 71

3.22 Mean Profile Evolution during Experiment MT05. Elapsed Times
= 0 (Initial Profile), 890, 959 and 1028 min. Note the back-and-
forth movement of the bar, otherwise the profiles approached an
equilibrium ......................... .. .. 72

3.23 Mean Profile Evolution during Experiment MT06. Elapsed Times
= 0 (Initial Profile), 242, 352 and 476 min. Note the deep channel
across the tank at about the mean water line at 476 min 74

3.24 Comparison of the Mean Profile at 614 min during Experiment
MT05 with that during Experiment MT06. Note good agreement
of the overall shape. ....................... ... 74

3.25 Mean Profile Evolution during Experiment MT06. Elapsed Times
= 0 (Initial Profile), 614 and 683 min. Note the large berm with
peak moving seaward at 683 min ................... 76

3.26 Mean Profile Evolution during Experiment MT06. Elapsed Times
= 0 (Initial Profile), 683, 752, 890 and 1166 min. Note that the
profile approached an equilibrium with reduced overall slope. 77

4.1 Cartesian Coordinate System. An angle of incidence 0 is defined
as the angle made between x-axis and the wave direction . 86

4.2 Schematic Diagram of Fixed Bed Wave Tank Experiments. Based
on right-handed coordinate system, counter-clockwise rotation is
defined as positive ........................... 94

4.3 Vorticity Meter and its Supporting Rod . . ... 97

4.4 Water Jet with Four Nozzles for the Case of Ho = 9cm . 98

4.5 Schematic Diagram of the Vorticity Measurement Tests with the
Definition of Each Test. Each test is defined as a different combi-
nation of wave and/or jet operation time. Note the breakerline as
affected by jet-induced opposing currents to the incoming waves,
and also counter-clockwise circulation outside the surf zone. 100

4.6 Cumulative Rotation at a Point within the Surf Zone as Influenced
by Jet and Waves during the Vorticity Measurement Tests. Pos-
itive revolution means counter-clockwise rotation of the vorticity
m eter. . . . . . . . . 102

4.7 Wave Height Distributions without the Presence of Jet-Induced
Circulation when Ho = 3cm (Test F211). Wave heights are given
in cm ..... .. .... .. ...... ... .. 105









4.8 Wave Height Distributions in the Presence of Jet-Induced Circu-
lation when Ho = 3cm (Test F212). Wave heights are given in
cm. Note higher wave heights in the vicinity of the jet return flow
due to both the counter current and refraction around the return
current. ................... ........... 106

4.9 Wave Height Distributions without the Presence of Jet-Induced
Circulation when Ho = 9cm (Test F221). Wave heights are given
in cm ........... ..... .............. 107

4.10 Wave Height Distributions in the Presence of Jet-Induced Circu-
lation when Ho = 9cm (Test F222). Wave heights are given in
cm. Note higher wave heights in the vicinity of the jet return flow
due to both the counter current and refraction around the return
current. ................... ........... 108

4.11 Wave Crest Lines in the Presence of Jet-Induced Circulation: (a)
Ho = 3cm (Test F212) and (b) Ho = 9cm (Test F222). Dotted
lines represent the breakerline. This figure is drawn to the scale.
Note when Ho = 9cm that waves displaced due to the opposing
current appeared to overtake the waves riding jet-induced current
near x = lm, where the vorticity measurements were performed. 109

4.12 Distributions of the Total Torque when Ho = 3cm (Test F212).
The values varied from -5.77 to 4.82 in 1/sec2. Solid lines represent
positive isolines while dotted lines represent negative values. Note
the generally positive values within the surf zone, which indicates
positive circulation in opposition to the jet-induced circulation.
Near the breakerline, negative circulation occurs due to continuity. 112

4.13 Distributions of the Total Torque when Ho = 9cm (Test F222).
The values varied from -5.12 to 5.85 in 1/sec2. Solid lines represent
positive isolines while dotted lines represent negative values. Note
the generally positive values within the surf zone, which indicates
positive circulation in opposition to the jet-induced circulation.
Near the shoreline and the breakerline, negative circulations occur
due to continuity............................ 113

4.14 Marginal Distributions of Individual Components along x-axis in
cm/sec2 when Ho = 3cm (Test F212): (a) Components I and
II and (b) Components III, IV and V. Note that all components
converge to zero in the area far offshore (x = 200 cm) and demon-
strate generally positive values within the surf zone (except Com-
ponent IV), which tend to induce counter-clockwise circulation in
opposition to the jet-induced flow. . . . .. 115

4.15 Marginal Distributions of Individual Components along x-axis in
cm/sec2 when Ho = 9cm (Test F222): (a) Components I and
II and (b) Components III, IV and V. Note that all components
converge to zero at near x = 400 cm. . . . .. 116









4.16 Marginal Distributions of Total Torque and the Contributions
of Radiation Stresses Components along x-axis in cm/sec2 when
Ho = 3cm (Test F212). Note that torque by S.. is dominant
over the torque contributed by Sx, and Sy. Note also that the
contribution by Sy tends to approximately cancel out the con-
tribution by Sx, within the surf zone. The total torque changes
from positive values near the shoreline and inside the surf zone (to
x = 60cm) to negative values near and beyond the breakerline,
thus indicating positive circulation over the surf zone, resulting in
opposing effects of waves on the jet-induced circulation. . 118

4.17 Marginal Distributions of Total Torque with the Contributions
of Radiation Stresses Components along x-axis in cm/sec2 when
Ho = 9cm (Test F222). Note that torque by Sx is dominant over
the torque contributed by Sxy and S,,. Note also the distribution
of total torque changing from negative values near the shoreline to
positive ones inside and outside the surf zone, thus indicating pos-
itive circulation within the surf zone, resulting in opposing effects
of waves on the jet-induced circulation. . . ... 120

4.18 Marginal Distributions of Total Torque and the Contributions of
Radiation Stresses Components based on Momentum Equations
along x-axis in N m/m when Ho = 3cm (Test F212). Note the
distribution of total torque changing from positive values near the
shoreline and inside the surf zone (to x = 0.7m) to negative values
near and beyond the breakerline (to x = 1.4m), thus indicating
positive circulation within the surf zone, resulting in opposing ef-
fects of waves on the jet-induced circulation. . . ... 122

4.19 Marginal Distributions of Total Torque and the Contributions of
Radiation Stresses Components based on Momentum Equations
along x-axis in N m/m when Ho = 9cm (Test F222). Note that
the contribution by Sy, is dominant within the surf zone, while the
torque by S., is dominant near and beyond the breakerline. Posi-
tive circulation occurs within the surf zone, resulting in opposing
effects of waves on the jet-induced circulation . . ... 124

5.1 Installation of Three-Dimensional Bar when Ho = 3cm. 3-D bar
extends from one wall (y = -0.3m) to two-thirds of the tank width
(y = 0.lm), while 2-D bar extends to the whole width of the tank. 134

5.2 Wave Height Distributions in the Presence of the Two-Dimensional
Bar when Ho = 3cm (Test F311). Wave heights are given in cm.
A dark area represents the area covered by the 2-D bar. Note the
uniformity of the wave crest lines including the breakerline in the
longshore direction.............. ............ 136

5.3 Wave Height Distributions in the Presence of Three-Dimensional
Bar when Ho = 3cm (Test F312). Wave heights are given in cm.
A dark area represents the area covered by the 3-D bar. Note that
wave fields are not greatly influenced by the presence of return flow
due to the 3-D bar, resulting in a more or less uniform breakerline. 137









5.4 Wave Height Distributions in the Presence of Two-Dimensional
Bar when Ho = 9cm (Test F321). Wave heights are given in
cm. A dark area represents the area covered by the 2-D bar.
Note the nonuniformity of the wave crest lines inside the surf zone
(especially near x = 120cm)....................... 138

5.5 Wave Height Distributions in the Presence of Three-Dimensional
Bar when Ho = 9cm (Test F322). Wave heights are given in cm.
A dark area represents the area covered by the 3-D bar. Note that
wave fields are substantially influenced by the return flow induced
due to the presence of the 3-D bar. Note also almost uniform
breakerline due to deeper water depth at the area of return flow
than the area over the bar ...................... .139

5.6 Marginal Distributions of Individual Components along x-axis in
cm/sec2 when Ho = 3cm: (a) Components I, II and VI in the
presence of the 2-D Bar (Test F311) and (b) Components I, II and
VI in the presence of the 3-D Bar (Test F312) . . .... 143

5.7 Marginal Distributions of Individual Components along x-axis in
cm/sec2 when Ho = 9cm: (a) Components I, II and VI in the
presence of the 2-D Bar (Test F321) and (b) Components I, II and
VI in the presence of the 3-D Bar (Test F322) . . ... 144

5.8 Marginal Distributions of Total Torque and the Contributions
of Radiation Stresses Components along x-axis in cm/sec2 when
Ho = 3cm in the Presence of the 3-D Bar (Test F312). Note that
torque by S., is dominant over the torque contributed by Sy.
Note also the positive values within the surf zone and in the area
seaward of the bar ........................... 145

5.9 Marginal Distributions of Total Torque and the Contributions
of Radiation Stresses Components along x-axis in cm/sec2 when
Ho = 9cm in the Presence of the 3-D Bar (Test F322). Note that
torque by S.x is dominant over the torque contributed by Sy.
Note also the positive values within the surf zone and in the area
seaward of the bar. Hence, positive circulation occurs within the
surf zone, which tends to suppress the bar-induced circulation. 146

5.10 Marginal Distributions of Total Torque and the Contributions of
Radiation Stresses Components based on Momentum Equations
along x-axis in N m/m when Ho = 3cm in the Presence of
the 3-D Bar (Test F312). Note the distribution of total torque
changing from positive values near the shoreline and inside the
surf zone (to x = 0.75m) to negative values over the bar region
and again to positive, thus indicating positive circulation within
the surf zone, resulting in opposing effects of waves on the 3-D
bar-induced circulation. ....................... 149









5.11 Marginal Distributions of Total Torque and the Contributions of
Radiation Stresses Components based on Momentum Equations
along x-axis in N m/m when Ho = 9cm with the 3-D Bar
(Test F322). Note that the contribution by Sy is dominant term
over the whole area of interest except over the bar area, where
the contribution by Sx, is dominant. Positive circulation occurs
within the surf zone, resulting in opposing effects of waves on the
3-D bar-induced circulation. . . . ..... 150

5.12 Definition Sketch for Mean Longshore Currents on Barred Coastlinesl53

5.13 Momentum Theory Applied to Net Flow over a Bar ...... ..156

5.14 Non-Dimensional Longshore Velocity. Here, L represents the half
length of the bar, and y does the longshore distance from the
center of the bar. Note the linear pattern of the velocity near
y = 0, while it demonstrates nonlinear pattern near y = L. . 163

5.15 Maximum Longshore Velocity. Note that the maximum velocity
approaches a limit value as the half length of the bar increases. 164

5.16 Non-Dimensional Set-Up. Here, L represents the half length of
the bar, and y does the longshore distance from the center of the
bar. ..................... ............. 165

A.1 Distributions of the Component I when Ho = 3cm (Test F212).
The values varied from -0.07 to 0.97 in 1/sec2. Solid lines represent
positive isolines while dotted lines represent negative values. Note
that Component I is generally positive and confined mainly near
the shoreline, where water depth is shallow. . . ... 174

A.2 Distributions of the Component II when Ho = 3cm (Test F212).
The values varied from -1.39 to 1.76 in 1/sec2. Solid lines represent
positive isolines while dotted lines represent negative values. Note
that Component II is generally positive within the surf zone and
negative near the breakerline. . . . . . 175

A.3 Distributions of the Component III when Ho = 3cm (Test F212).
The values varied from -1.30 to 0.56 in 1/sec2. Solid lines represent
positive isolines while dotted lines represent negative values. Note
that Component III is generally small except the area near the
breakerline. ................... .......... 176

A.4 Distributions of the Component IV when Ho = 3cm (Test F212).
The values varied from -5.80 to 2.44 in 1/sec2. Solid lines represent
positive isolines while dotted lines represent negative values. Note
large negative values in the vicinity of return currents. . 177









A.5 Distributions of the Component V when Ho = 3cm (Test F212).
The values varied from -0.87 to 1.96 in 1/sec2. Solid lines represent
positive isolines while dotted lines represent negative values. Note
that Component V shows mainly positive values near the area of
higher waves due to opposing currents. . . ... 178

A.6 Distributions of (Tv)1 when Ho = 3cm (Test F212). The values
varied from -4.18 to 5.30 in 1/sec2. Solid lines represent positive
isolines while dotted lines represent negative values. Note that
(Tv)1 is generally positive within the surf zone and negative near
the breakerline, which is essentially the same as the Component II. 179

A.7 Distributions of (Tv)2 when Ho = 3cm (Test F212). The values
varied from -1.16 to 1.77 in 1/sec2. Solid lines represent positive
isolines while dotted lines represent negative values. Note that
(Tv)2 is generally negative within the surf zone and positive near
the breakerline ............................. 180

A.8 Distributions of (Tv)3 when Ho = 3cm (Test F212). The values
varied from -5.23 to 2.73 in 1/sec2. Solid lines represent positive
isolines while dotted lines represent negative values. Note the very
complicated variations of (Tv)3. . . . . .. 181

B.1 Distributions of the Component I when Ho = 9cm (Test F222).
The values varied from -0.58 to 0.13 in 1/sec2. Solid lines represent
positive isolines while dotted lines represent negative values. Note
that Component I is generally negative and confined mainly near
the shoreline, where water depth is shallow. . . ... 183

B.2 Distributions of the Component II when Ho = 9cm (Test F222).
The values varied from -0.89 to 1.58 in 1/sec2. Solid lines represent
positive isolines while dotted lines represent negative values. Note
that Component II is generally positive within the surf zone and
negative near the breakerline. . . . ...... ...... 184

B.3 Distributions of the Component III when Ho = 9cm (Test F222).
The values varied from -2.66 to 1.46 in 1/sec2. Solid lines represent
positive isolines while dotted lines represent negative values. Note
that Component III is generally small except large negative values
near the breakerline. ............ .......... .. ..185

B.4 Distributions of the Component IV when Ho = 9cm (Test F222).
The values varied from -5.84 to 5.27 in 1/sec2. Solid lines represent
positive isolines while dotted lines represent negative values. Note
the very complicated variations of the Component IV. . 186

B.5 Distributions of the Component V when Ho = 9cm (Test F222).
The values varied from -2.35 to 2.35 in 1/sec2. Solid lines represent
positive isolines while dotted lines represent negative values. Note
that Component V shows mainly positive values near the area of
higher waves due to opposing currents . . . .. 187









B.6 Distributions of (Tv)1 when Ho = 9cm (Test F222). The values
varied from -2.68 to 4.73 in 1/sec2. Solid lines represent positive
isolines while dotted lines represent negative values. Note that
(Tv)i is generally positive within the surf zone and negative near
the breakerline, which is essentially the same as the Component II. 188

B.7 Distributions of (Tv)2 when Ho = 9cm (Test F222). The values
varied from -4.62 to 5.32 in 1/sec2. Solid lines represent positive
isolines while dotted lines represent negative values. Note that
(Tv)2 is generally negative within the surf zone and positive near
the breakerline ............................. 189

B.8 Distributions of (Tv)3 when Ho = 9cm (Test F222). The values
varied from -4.62 to 5.32 in 1/sec2. Solid lines represent positive
isolines while dotted lines represent negative values. Note that
(Tv)3 is generally positive near the breakerline. . ... 190

C.1 Filter Response Function versus Wave Number. Note the low-pass
character. ................ ................. 192

C.2 Filtered, Unfiltered and Removed High-Frequency Components of
the Marginal Distributions of the Total Torque presented in Figure
4.19. Note that the filter worked well except both end regions of
the data, in which the filtered data are affected by the finite length
of the filter ... .. .. .. .. ... .. .. .. ... ... 193

C.3 Wave Number Spectrum of the Filtered, Unfiltered and Removed
High-Frequency Components of the Marginal Distributions of the
Total Torque presented in Figure 4.19. . . .... 194













LIST OF TABLES


2.1 Profile Classification Criteria ................. .... 13

2.2 Relationship of Rip Currents Intensity to Various Factors (from
Shapard et al. (1941) ......................... 22

2.3 Factors Affecting the Occurrence of Rip Currents (from McKenzie,
1958) . . . . . . . . 24

2.4 Rip Current Generation Mechanisms. . . . 29

3.1 Description of Movable Bed Experiments. . . .. 45

3.2 Maximum Cross-Tank Differences of the Profile Elevations at 352
min during Experiment MT06 ................ .. 75

3.3 Periods Associated with Edge Waves. . . . 84

4.1 Wave Conditions for Fixed Bed Experiments . . ... 94

4.2 Jet Discharge for Fixed Bed Experiments . . ... 99

4.3 Description of Circulation Tests with and without the Presence of
the Jet . . . . . . . .. 104

4.4 Summary of Minimum and Maximum Values of the Components
Involved in Vorticity Driving Torque. Values are given in 1/sec2. 111

4.5 Summary of Total Vorticity Driving Torque based on the Vorticity
Equation. Values are given in cm2 /sec2 . . . 121

4.6 Comparison of Total Vorticity Driving Torque based on the Mo-
mentum Equation with Torque Induced by the Jet. . ... 125

4.7 Wave Period Conditions for Edge Wave Tests . . ... 126

5.1 Numerical Values of the Bar Dimensions with Their Definitions 133

5.2 Description of Circulation Tests on a Barred Beach . ... 135

5.3 Summary of Minimum and Maximum Values of the Components
Involved in Vorticity Driving Torque. Values are given in 1/sec2. 141










5.4 Summary of Total Vorticity Driving Torque based on the Vorticity
Equation. Values are given in cm2 sec2 . . ... 147

5.5 Summary of Total Vorticity Driving Torque based on the Momen-
tum Equation. ............................ 151


xvii














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

THREE-DIMENSIONAL HYDRODYNAMICS AND MORPHOLOGY
ASSOCIATED WITH RIP CURRENTS

By

TAE-MYOUNG OH

August 1994

Chairman: Dr. Robert G. Dean
Major Department: Coastal and Oceanographic Engineering

This study was conducted to develop an improved understanding and predictive

capability of the 3-D hydrodynamics and morphology associated with rip currents.

Six movable bed tests were carried out with a fairly fine sand to (1) monitor

profile evolution and the resulting equilibrium, and (2) investigate various possible

interrelationships and causes of the three-dimensionality, which included the effects

of (a) induced perturbations in the bar topography, (b) elevated water table in the

berm, and (c) an initially 3-D berm. These movable bed studies suggested that the

profiles appeared to be stable against the perturbations and there was a relatively

slow feedback between the hydrodynamics and the morphology that led to initiation

and growth of 3-D features.
Three series of fixed bed tests were performed to investigate whether or not an

existing rip current was self-reinforcing or stable on a 2-D prismatic topography,

including (1) vorticity measurements at a point within the surf zone, (2) circulation

tests with and without the presence of a jet discharge, and (3) edge wave tests by

varying wave heights and periods. It was found that rip currents were neither self-
reinforcing nor stable on a 2-D prismatic topography. Waves in the area with opposing


xviii









currents were higher due to both the refraction and the counter current. It was

these increased momentum fluxes that tended to stabilize the jet-induced cellular

circulations on a 2-D beach morphology.

Since rip currents are neither self-reinforcing nor stable on a 2-D prismatic beach,

a series of fixed bed tests was conducted to examine the effect of a 3-D bar morphology

on the tendency for cellular circulation. The results showed that rip currents were

stable on 3-D barred beach, although increased momentum fluxes of waves in the area

with opposing currents induced by the bar tended to exert a counter force against

them. It appeared that the water mass transported over the bar tended to return to

sea through deeper area in the bar morphology. This cause is believed to be due to

the greater hydraulic efficiency of flows through deeper portions of the profile, which

leads to a hydraulic/sedimentary instability which causes development of a vestigial

channel.

Finally, a simple model for rip currents on barred beaches was developed consid-

ering mass transport over the bar and the bar morphology.














CHAPTER 1
INTRODUCTION


A beach, the boundary between sea and land, is one of the most interesting places

in the world. The beach is quite complex in structure being composed of air, water

and sediment, resulting in dynamics characterized by nonlinear and nonequilibrium

processes; hence it presents an eternal challenge to the coastal engineer.

The challenge is due, in part, to so many processes, of which the underlying

physics are still obscure, occurring simultaneously on various temporal and spatial

scales with a large number of factors. One of these challenges is understanding and

predicting the three-dimensional (3-D) hydrodynamics and sedimentary features as-

sociated with rip currents.

Rip currents are seaward-flowing jet-like concentrated currents extending beyond

the breakerline, representing a major agent of surf zone water drainage, and carrying

large quantities of sediment offshore. They can occur along a long straight beach

periodically, near longshore barriers such as jetties or groins, and at relatively narrow

and deep channels in sand bars.

Rip currents constitute an integral part of the nearshore circulation pattern which

shows more or less a closed-form with a series of discrete cells along the beach, as

shown in Figure 1.1. Water carried landward through a broad portion of the breaker-

line runs along the beach and finally returns to the offshore through relatively narrow

and deep channels. The offshore velocity in a rip current can be large enough to

modify the wave field including refraction such that at the rips the wave crest lines

are displaced seaward and wave-current interaction such that the waves are higher at

the rip locations.



































Figure 1.1: Schematic Diagram of Nearshore Circulation System with Rip Currents
(from Shepard and Inman, 1950b)


Even before Shepard (1936) first proposed the name 'rip current' to describe the

seaward-flowing jet-like concentrated currents, rip currents were well-known to life

guards and to experienced swimmers, as these currents were considered responsible

for pushing swimmers outside the breaker zone at irresistible speeds; but seemed to

have largely escaped the notice of scientists at that time. Since Shepard, however, rip

currents have attracted the interest of coastal engineers because (1) they can modify

the wave field by refraction and other interaction mechanism, (2) they can change the

coastal configuration by removing and transporting significant quantities of sediment

offshore, (3) they are a potential danger especially to unwary swimmers, and (4) they

can refresh the surf zone water, thus affecting water quality in the nearshore region.

1.1 Three-Dimensional Features in Nature

If uniform waves in the longshore direction approach shore over straight and

parallel bottom contours, under some conditions beach morphology is known to be

characterized by a well-developed two-dimensional (2-D) longshore bar. In nature,


SCHEMATIC OIAGRAM OF SURFACE
I LOW IN COASTAL ANO NEAN3HOXE
CURRENT SYSTEMS
N -
~* L[NGtTh OlARROW INOICATIS (LArlyVl
U CUR r NT MA*NITUO( of THE CURRiiT


4,1 -"*, -, -,


ARENT
O "- "-.-- *. --. -. -
/ .. ..... '
" o -/ : .. ."
- MASS TRASP*iloRT ri WAVES



.. ...O. ^ t CU tR ^ -








3
however, waves are not 2-D and the beach morphology would be characterized by a

range of states including some 3-D forms that are fairly regular, and which appear

to be associated with rip currents. Figure 1.2 (from Holman and Lippmann, 1987),

which was created digitally by averaging ten-minute time exposure images, shows a

typical well-developed 2-D longshore bar and well-formed 3-D crescentic bar.

Since Shepard, Emery and La Fond (1941), who first carried out detailed field

studies, field observations were emphasized to obtain some basic idea of the depen-

dence of nearshore circulation and beach morphology on the prevailing wave condi-

tions. After obtaining a detailed description of the main features of the rip currents,

laboratory and simple analytical (including numerical) models were developed to ex-

plain those features and to determine the strength of and the spacing between the rip

currents.

Based on previous studies, it is generally accepted that nearshore cellular circu-

lation at natural beaches could be produced and maintained by the driving forces

induced by longshore variability in the breaking wave heights; however, it is not yet

entirely clear which mechanism can provide those variations in the longshore direction,

which are sufficient to drive rip currents. To quote from Sonu (1972), "Undulation

of the surf zone bed was an essential condition to the formation of the two major

patterns of wave-induced nearshore currents: circulation and meander" (p. 3245).

However, Dalrymple and Losano (1978) showed through analytical and numerical

analyses that wave-current interaction could generate stable rip current circulation

cells on a prismatic beach. Hence, a relevant question is: Can rip currents occur on

a prismatic beach?

Furthermore, there is a related question about the direction of rip current circu-

lation. It is known that circulation is shorewards near the regions of higher breaking

waves and seawards near low wave zones; but some observations showed the opposite

case (e.g., McKenzie, 1958), where the currents flowed shorewards from low wave area





























(a) Well-Developed Two-Dimensional Longshore Bar System

















(b) Well-Formed Three-Dimensional Crescentic Bar System


Figure 1.2: Bar Morphologies Created Digitally by Averaging Ten-Minute Time Ex-
posure Images. White bands indicate the shore break and regions of concentrated
wave breaking on distinct bar morphologies at the Army Corps of Engineers Field
Research Facility at )uck, North Carolina. (from Holnman and Lippmann, 1987)








5
(shoals) and seawards through higher wave area (embayments). Hence, this argument

raises the question: "Which path do rip currents voluntarily follow in Nature? Where

are they generated? From the shoals, or from the embayments?"

Another important characteristics of rip currents is the modification of wave field

through refraction. As discussed earlier, it is known that wave crests generally show a

lag in the neck of the rips due to refraction and wave heights increase due to shoaling.

But sometimes a gap in advancing breakers exists where rips move seaward (Shepard,

Emery and La Fond, 1941), which means low waves at the location of rips. This

simply raises the question: "What is the usual wave-current interaction mechanism?"

The last point of disagreement is the causes) of the three-dimensionality in na-

ture. Several mechanisms appear to dominate this interaction between the hydrody-

namics and morphology. Candidate explanations include edge waves and a hydrody-

namic/sediment instability that reinforces the nearshore system and 3-D morphology.

This argument raises the question: "Which mechanisms) can initiate and form a bar

morphology with rip currents present?"

In the present study, it was decided to conduct laboratory experiments in a nar-

row wave tank in attempts to investigate the tendency for cellular circulation in the

planform and to investigate various possible interrelationships and causes of the three-

dimensionality. Laboratory studies can isolate the selected governing parameters of

the processes and can control their effects more easily than field studies. Furthermore,

a narrow tank can remove any 3-D effects inherent to a wide tank, e.g., nonuniform

wave crests in the longshore direction or cross waves. It should be noted that a rel-

atively wide tank condition can be satisfied by reducing generated wave heights and

periods, which makes the tests for edge waves mechanism possible in a narrow wave

tank.








6
1.2 Three-Dimensional Features in a Narrow Wave Tank

When conducting movable bed tests in a narrow wave tank, it is usually assumed

that the hydrodynamics and morphology are 2-D. Both water and sand particles are

considered to remain within the plane of motion and to move horizontally back-and-

forth only. Hence, any 3-D patterns such as horizontal circulation of the water and/or

cross-shore variations of the profiles are considered as 'errors' or extraneous features in

the experiments and subsequently have not been documented extensively. However,

investigators have found evidence of three-dimensionality in narrow wave tank tests.

Bagnold (1940) first observed noticeable 3-D circular water motions and resulting

profile changes over the beach face during 2-D laboratory experiments. The beach

face was always 2-D with coarser materials. With sands, however, 3-D beach face

and resulting circular sweeping motion of the water were observed with sands always

deposited on one side or the other side of the tank over the beach face. Bagnold found

that the slope of sand deposition was 14 degrees and the other side of the tank, where

there was no deposition, retained 5 degrees slope. It should be noted that the tank

used in Bagnold's experiment was only 0.53 m wide.

Three-Dimensional morphology in 2-D wave tank tests were also observed in ear-

lier tests by the Beach Erosion Board (BEB, 1947). The experiments were conducted

in a tank approximately 26 m long, 4.3 m wide and 1.2 m deep, and with a deep water

wave height of 11.6 cm; hence, the experiments could be considered as 3-D since the

ratio of the tank width to the wave height would suggest that the experiments were

carried out in a relatively wide tank. Even though BEB considered the experiments

as 2-D, BEB measured five profiles across the tank to account for observable three-

dimensionality during the experiments and averaged to represent the mean profiles at

the measuring time. Although BEB did not document those profiles, they presented

photographs as shown in Figure 1.3, which clearly exhibited 3-D morphology during

the tests.




































(a) Bed after 1 hour Wave Operation


--
* '; U.-


(b) Bed after 10 hours Wave Operation



Figure 1.3: An Example of Three-Dimensional Morphology in Two-Dimensional Nar-
row Wave Tank Tests (from Beach Erosion Board, 1947). Note the temporal reduction
of three-dimensionality after 10 hours wave operation.









During the investigation of vertical velocity profiles, Russel and Osorio (1958)

stated; "It is probable however that the velocities would be disordered by circula-

tions in a horizontal plane, if the waves were not confined to a narrow channel" (p.

183). Bagnold (1963) has observed when the channel width in Russel and Osorio's

experiments exceeded a certain multiple of the water depth, that the wave drift along

the bed, which was otherwise uniform across the channel section, showed signs of

instability, becoming greater on one side than on the other. Bagnold suggested that

in wider channels, horizontal circulation would appear and a random scattering of

sediment would tend to be superimposed upon a smaller forward drift, which might

result in 3-D morphology.

3-D morphology over the entire surf zone in relatively narrow wave tanks have

been noted by Kriebel et al. (1986a) and documented by Hughes and Fowler (1990).

There are several possible causes of 3-D flows and morphology in a wave tank,

some of which could also be representative of those occurring in nature: (1) instabil-

ity of 2-D flows on 2-D morphology, (2) organized longshore wave motions that could

induce edge waves in nature or in a tank or cross-tank waves under laboratory condi-

tions, and (3) a feedback between the hydrodynamics and morphology that reinforces

3-D morphological features under certain stages of profile development.

1.3 Objectives

This study was conducted to understand and predict 3-D hydrodynamics and

morphology associated with rip currents. As previous studies were not yet entirely

clear to explain rip current generation, the following questions were addressed as the

first step:


(a) Can rip currents occur on a prismatic beach?

(b) Which path do rip currents voluntarily follow in Nature? Where are they gen-

erated? From the shoals, or from the embayments?









(c) What is the usual wave-current interaction mechanism?

(d) Which mechanisms) can initiate and form a bar morphology with rip currents

present?

For these questions, it was decided to review the previous studies extensively to

address the questions in a more orderly fashion to determine the scope of present

study. And then, as explained earlier, both fixed and movable bed tests were con-

ducted in two narrow wave tanks of the Coastal and Oceanographic Engineering

Laboratory of the University of Florida.

At first, movable bed experiments were designed (1) to monitor profile evolution

and the resulting equilibrium, and (2) to investigate various possible interrelation-

ships and causes of the three-dimensionality. For 3-D morphology, the following were

examined:

(a) Effects of an induced perturbation in the bar topography,

(b) Effects of an elevated water table in the berm, and

(c) Effects of an initially 3-D berm.

Upon knowing the main features of profile evolution with rip currents present, the

next objective was to investigate the tendency for cellular circulation on a prismatic

beach and to measure following:

(a) Cumulative rotation at a point within the surf zone as influenced by waves and

a landward directed jet, and

(b) Wave height distributions in the presence of a jet-induced circulation

The final objectives were to (1) investigate the tendency for cellular circulation

on a barred beach through wave tank experiments, and (2) develop a simple model

for rip currents on barred beaches.








10
1.4 Scope of Study

Chapter 2 provides a comprehensive review of previous studies on 3-D cellular

circulation and morphology both in nature and in narrow wave tanks. Also included

are previous studies on profile evolution and the resulting equilibrium.

Chapter 3 summarizes the experimental facilities, conditions and experimental

cases for movable bed laboratory studies, and presents the results of the generation

and development of 3-D morphology and the resulting equilibrium of the profile in a

narrow wave tank.

Through a series of fixed bed wave tank experiments, Chapter 4 discusses the

generation and existence of 3-D flows on a prismatic beach with a fixed bed. The

method to analyze the test results are presented and followed by the conclusions.

In Chapter 5, 3-D flows on a barred beach are studied through wave tank exper-

iments, and a simple model for rip currents on barred beaches is developed.

Finally, conclusions from this study and recommendations for future efforts are

presented in Chapter 6.














CHAPTER 2
LITERATURE REVIEW


2.1 Introduction

Considerable research has been carried out during the past 50 years, and has

provided a wealth of knowledge in understanding and predicting quite complex beach

processes associated with rip currents. This chapter is devoted to exploring and

acknowledging some of those very major contributions.

This chapter starts with reviews focused mainly on laboratory studies of beach

profile evolution and the resulting equilibrium profile, which seems to be logical in

the present study since laboratory experiments were selected to investigate the three-

dimensionality associated with rip currents under 2-D controlled wave conditions. As

appropriate, previous studies addressing the physical mechanism will be reviewed.

Next, a brief review is made of the literature describing 3-D flows and morphology

in a narrow wave tank. These are followed by a comprehensive review describing field

studies on rip currents which have established the terminology and main features of

rip current systems. Finally, an extensive review on analytical and numerical models

to investigate various characteristics and causes of the three-dimensionality associated

with rip currents are presented.

2.2 Profile Evolution and Equilibrium Profile

A beach profile is the result of the natural forces (both "destructive" and "con-

structive") acting on the sand composing the beach. The destructive forces including

gravity act to flatten the profile by transporting sediments seaward; while the con-

structive forces act to move sand onto the beach, resulting in a steep beach. Hence








12
for sediment particles of a given size and for the given wave conditions, there will be

an 'equilibrium' profile as a balance of destructive versus constructive forces. If any

of these forces are altered, the beach responds and evolves toward a new equilibrium.

The equilibrium beach profile is an idealized profile, but is very useful in predicting

qualitatively the evolution of a particular beach profile for changes in waves and

sediment conditions, or for given initial conditions. In the field, the equilibrium profile

is considered to be 'dynamic' as the tide and incident wave field change continuously

in nature and therefore the profile changes shape as well. In the laboratory, however,

it is relatively easy to establish an equilibrium profile, by running a steady wave train

onto a beach for a long time. After the remolding of the initial profile, a 'final' profile

results, which changes little with time. This is the equilibrium profile for that beach

material and wave conditions in the laboratory. Hence, as a beach profile approaches

an equilibrium, the incident wave energy is dissipated without any significant profile

changes and the time-averaged sediment transport rate converges to zero at all points

along the profile.

Considerable laboratory research in a 2-D narrow wave tank has been directed

toward determining the relationship between dominant forces and complex processes

of beach profile evolution and resulting equilibrium profile (e.g., Rector, 1954; Saville,

1957; Kriebel et al., 1986a and 1986b; Larson and Kraus, 1989, etc.). Based on those

studies, it was generally accepted that storm wave conditions cause offshore transport

of sand resulting in an eroded beach face and an offshore breakpoint bar, while normal

conditions cause onshore transport resulting in a developed berm and no offshore bar,

and coarser sands result in steeper profiles while finer sands result in milder ones.

Due to its uniqueness and importance on the cross-shore hydrodynamic and sed-

iment transport processes, the longshore bar has been the focus of many previous

studies. However, an understanding of the profile evolution, the rates at which the

profile changes occur, becomes equally important recently since the beach recovery







13
processes have been paid attentions to achieve the overall stability of the beaches

following severe erosion events, the storm.

Based on the bar formation, profile classification criteria in terms of wave steep-

ness, sediment size, sediment fall velocity and beach slopes, etc. were proposed to

predict the behavior of the profile. Some of these criteria are summarized in Table 2.1;

while more detail review is given in Kriebel et al. (1986a).


Table 2.1: Profile Classification Criteria

Researchers) Bar Formation Criteria Scales
Johnson (1949) Ho/Lo > 0.03 small
Rector (1954) Ho/Lo > 29.4(Dso%/Lo)0- small
Saville (1957) Ho/Lo > 0.025 small
Ho/Lo > 0.0064 large
Dean (1973) Ho/wT > 0.85 small
Sunamura and Horikawa (1974) Ho/Lo > C(tan/ )-0.27(D5o%/Lo)067 small
Kriebel et al. (1986a) Ho/Lo > Arw/gT small, large
Larson and Kraus (1989) Ho/Lo < 0.0007(Ho/wT)3 large
Dalrymple (1992) gH2/w3T > 9000 10400 large
where, in this table
Ho = Deep water wave height
Lo = Deep water wave length (=gT2/2r)
T = Wave period
g = Gravitational acceleration
tan = Initial beach slope
D50% = Median diameter of sand
w = Sediment fall velocity
A, C = Constants


As presented in Table 2.1, the empirical constants determined based on the large

scale experiments are always much smaller than those based on the small scale ex-

periments. It appeared that the constants in the small scale experiments contained

scale effects due to the use of relatively larger sand sizes (Kriebel et al., 1986a).

Based on small-scale model tests, Rector (1954) described the behavior of the

bar as follows. The bar generated rapidly on an initially planar beach and moved








14
onshore during early times and remained stationary at later times. It was then that

the equilibrium shape of the profile started to take form. Bottom ripples formed

rapidly at the offshore area of the wave breaking zone and progressed steadily onshore;

eventually they lost their identities at the bar. Rector noted that waves sorted the

sands continuously during the evolution process to the equilibrium profile; hence the

median diameter of the sand in the bar area was always larger than that of the original

sand.

Dean (1973) developed a heuristic model based on the suspension of sediments

induced by wave breaking and possible types of sediment fall trajectories. Assuming

instant suspension of the sand particles under the passing of wave crests and set-

tlement during one wave period, Dean suggested that the direction of net sediment

transport would depend on the ratio of the fall time of a sand particle to the wave

period. Net offshore transport would occur if the suspended particle required a time

longer than one half the wave period to fall back to the bottom, and vice versa. As-

suming that the suspension height is proportional to the wave breaking height, Dean

finally expressed the onshore/offshore transport criteria as


Ho
S= 0.85 (2.1)
wT
Although Dean presented the criteria for the direction of sediment transport only,

his model can be easily extended to predict the sediment transport rate for determin-

ing the evolution process of the beach profiles (e.g., Dally and Dean, 1984). It is

worth noting that the role of the sediment size and wave period become clear in the

formation of the different profile shapes.

Dean's heuristic model also can be extended to explain the bar formation by

increasing wave heights with a constant period, as shown in Figure 2.1 (Dean, 1985).

When small waves act on a beach profile, they break in shallow water resulting in

deposition of the suspended sediment landward of its suspension point as the fall time










4 NO BAR p BAR



., 4 V: "3 3







(a)t SF< T4 < tF

Figure 2.1: Bar Formation with Increasing Wave Height (drawn based on Dean, 1985).
Here, T is the wave period, and tF is the fall time of the sediment, defined as the
ratio of the suspended height to the fall velocity of the sediment.

is still less than one-quarter of the wave period (T/4). With increasing wave heights,
the waves break in deeper water, the sediment is suspended to a higher elevation
above the bed and thus the fall time increases. If the fall time is longer than T/4 but

still less than T/2, the sediment still experiences a net onshore movement but it is
influenced by offshore velocities under the wave trough. If the fall time is equal to be
T/2 at some wave height, the sediment will fall back to the same location where it was
suspended. For larger waves, the sediment will experience a net offshore displacement
as the fall time increases further, thus causing a bar to form.
Bruun (1954) first showed and Dean (1977), after analyzing more than 500 profiles,
presented equilibrium beach profile by the form


h(x) = Ax 213 (2.2)

where h is the water depth at a distance z which is oriented in an offshore direction
with the origin at the mean water line and A is a profile scale factor which depends on
sediment size. Dean demonstrated that this form of the profile could be interpreted in
sediment size. Dean demonstrated that this form of the profile could be interpreted in








16
terms of uniform wave energy dissipation per unit water volume. Later Dean (1987)

presented the relationship between the parameter A and the sediment fall velocity,

W, as



A = 0.067w0.44 (2.3)

where A is given in m4 while w in cm/sec. This relationship is surprisingly linear on

a log-log plot.

Kriebel et al. (1986a, 1986b) performed comprehensive small-scale laboratory

experiments to: (1) test the validity of the model scaling law proposed by Dean

(1985) using an undistorted Froude similarity with sediment scaled according to fall

velocity, (2) investigate the effects of initial profile shape (not slope) on the equilibrium

profile configuration, (3) examine the onshore/offshore sediment criterion given in

Equation (2.1) (Dean, 1973), and finally (4) investigate the beach recovery process

following severe erosion events.

Based on comparisons with large scale results of Saville (1957), the model scaling

law provided good agreement for erosive wave conditions, but moderate agreement

for acceretive waves mainly due to wave reflections. It appeared that the initial

profile shape was very important in determining the profile evolution and resulting

equilibrium as the concave profile was found to have more realistic wave shoaling

and breaking characteristics. Results for the sediment transport criterion indicated

that Dean's original criterion included scale effects and suggested a higher value than

that given by the right hand side of Equation (2.1). For the post-storm recovery

experiments, the storm-generated bar did not migrate landward easily under normal

waves of constant height, while berm formed rapidly. However, the bar migration

occurred in a related experiment as wave conditions were finely tuned such that the

waves always broke just landward of the migrating bar.









Kraus and Larson (1988) documented all the experimental data obtained at the

Large Wave Tank of the Coastal Engineering Research Center (CERC, successor orga-

nization to the BEB). Based on these data, Larson and Kraus (1989) described general

characteristics of cross-shore transport and derived empirically-based transport rate

equations to develop a numerical model, called SBEACH.

2.3 Three-Dimensionality in a Narrow Wave Tank

It will be most appropriate to start this section with a contribution by Bagnold

(1940). Through a series of wave tank experiments and with very careful observations,

Bagnold presented a pioneering description of noticeable 3-D circular motions over

the beach face during 2-D experiments using both rounded pebbles with a median

diameter of 7 mm and sands of diameter ranging 0.5 to 3 mm under regular waves.

The width of the tank was only 0.53 m, as discussed earlier.

With coarser material like shingle, Bagnold observed that a 2-D beach was always

formed with a straight shoreline parallel to the wave crests. When more material was

added on one side of the tank, this soon became distributed evenly over the width of

the mobile portion of the beach. However, the beach changed to 3-D forms with fine

materials such as sands and sands always deposited on one side or the other side of

the tank over the beach face, resulting in a circular sweeping motion across the tank

instead of moving directly up and down. As presented earlier, Bagnold found that

the slope of sand deposition was 14 degrees and the other side of the tank, where

there was no deposition, retained 5 degrees slope.

Rector (1954) performed laboratory studies in the same tank used by BEB (1947),

of which size is 25 m long, 4.3 m wide and 1.2 m deep, but with four different sizes of

sands. The median diameters of the sands were 0.22, 0.46, 1.20 and 3.44 mm, in which

the sand of 1.20 mm was a mixture of 0.46 and 3.44 mm sands. Considering 2-D tests

with width being of little importance, Rector tested those sands simultaneously by

dividing the tank longitudinally into four equal widths. Rector also utilized full and








18
half widths of the tank. Although Rector did not note 3-D topography, some of his

photographs clearly showed the cross-tank variations of the beach profiles. Rector's

experiments demonstrated that the three-dimensionality inside a wave tank strongly

depended on the width of utilized tank as well as on the size of the sand.

Maruyama and Horikawa (1977) performed laboratory experiments in a wave

basin (6 m long, 1.2 m wide) in order to investigate the generation mechanism of rip

current using regular waves with a period of 0.96 seconds and heights of 0.8 and 1.5

cm. They measured wave heights across the tank, which were smaller at the center

of the tank where the rip currents flowed offshore than those near both side walls,

resulting in a circulation from high to low waves. This variation of the wave height

remained unchanged even with strong rip currents with the maximum velocity of 6.8

cm/sec under about 1 cm wave height experiments. As pointed out by Maruyama and

Horikawa, this tendency is contrary to the usual wave-current interaction mechanism.

But the measured wave height distributions across the tank agreed well with the

calculated wave heights by superimposing the cross waves into the incident waves.

Maruyama and Horikawa concluded that rip currents would occur due to the interac-

tion between incident waves and the synchronous progressive cross waves having crests

at certain angles to the wave maker and therefore cross waves should be suppressed

in a laboratory experiment to simulate a natural coast.

However, cross waves are subharmonic standing waves with crests at right angles

to the wave maker, of which energy are supplied by the wave maker through depth

independent second-order pressures (Garrett, 1970; Mahony, 1972). Maruyama and

Horikawa also pointed out that synchronous cross waves observed in their experiments

were physically differerit from subharmonic cross waves predicted theoretically by

Garrett and Mahony and that the mechanism was not yet definite how the wave

maker supplied the energy to cross waves in their experiments.








19
At this stage, it is worth noting that cross waves are usually observed in wave

tanks where the wave maker is substantially wider than the length of the waves

generated; which is another good reason to select a narrow wave tank in investigating

three-dimensionality.

During the small-scale laboratory experiments, as presented earlier, Kriebel et al.

(1986a) first noted 3-D cross-tank variations of the profiles over the entire surf zone,

noticeable in the seeming lack of volume closure in several of the profiles. Hence,

Kriebel et al. took several profiles across the tank and averaged to represent mean

profiles. The tank used was approximately 30 m long, 1.3 m deep, and 0.9 m wide.

Barnett and Wang (1988) conducted 2-D laboratory tests in the same tank used

by Kriebel et al. (1986a) using regular waves and a fine sand with a median diameter

of 0.15 mm. Barnett and Wang took two profiles at approximately one-third the cross-

tank distance from each of the flume walls to represent mean profiles. They noted

that these variations were observed periodically and exhibited a temporal reduction

such that, by the end of most of the tests, the cross-tank variations appeared to be

negligible. They considered that possible causes are wall boundary layer producing

wave refraction, uneven bed compaction, and reflected wave interaction with incident

waves.

From a series of 2-D laboratory tests in a wave tank of 1.83 m width, Hughes and

Fowler (1990) observed that noticeable cross-tank variations occurred after the profile

reached a quasi-equilibrium condition and documented these variations by measuring

three profiles across the tank, as shown in Figure 2.2 which were measured after 1650

waves (equivalent to 1 hour wave run) in their experiment T03.

It was thought that these cross-tank variations have been caused by a small

misalignment of the revetment in the flume which in turn caused reflection of waves

from the exposed concrete revetment since similar variations were not present in the

prototype scale tests of Dette and Uliczka (1986). After another test with increased









1.5
-- -- CENTER PROFILE
1.2 -----GLASS SIDEWALL PROFILE
O -- CONCRETE SIDEWALL PROFILE
--- ---- INITIAL PROFILE
Z
S 0.9


a 0.6

0
0.3


0.0
-2.0 -1.0 -0.0 1.0 2.0 3.0 4.0 5.0 6.0
DISTANCE (m)


Figure 2.2: Cross-Tank Variations of the Profiles after 1 hour Wave Run (modified
from Hughes and Fowler, 1990). Note 3-D morphology inside the surf zone and near
the bar area.

wave height by approximately 10 percent (their experiment number T04), Hughes and

Fowler noted that increased wave heights test exhibited a similar cross-tank profile

variations as the test approached. equilibrium, but apparently made the variations a

little more severe than observed in the previous test (Test T03).

Hughes and Fowler described that these variations did not materialize until after

the profile was close to an equilibrium, which might indicate that the profile was

more susceptible to cross-tank perturbations when the profile had reached a quasi-

equilibrium state. If the profile was not close to equilibrium, the onshore/offshore

transport of sand seemed to overwhelm any cross-tank-induced sediment transport.

Hughes and Fowler then related this trend to the field data of Howd and Birkemeier

(1987), and stated "A prestorm breakpoint bar that exhibited nonuniform along-

shore variation became quite linear and moved offshore during the storm. Near the

end of the storm, when presumably a near-equilibrium had been reached, alongshore

variation in the bar began to reappear" (p. 37).












** *



-iJH












S"O*r UNE
S ZO C 0.*' "'* *
i I OC


from the land. Shepard et al. described the general characteristics of rip currents,

s.oar UNC

Figure 2.3: Constitutive Elements of a Rip Current System: the feeder currents flows
of water parallel to the shore; the neck, the main seaward-flowing current extending
beyond the breaker zone; and the rip head, in which the rip current lose its identity
as the water spreads out. (from Shepard, Emery and La Fond, 1941)

2.4 Rip Currents in Nature

Shepard et al. (1941) reported the first scientific observations of rip currents, and

recognized them as a main feature of the nearshore circulation system, which returned

the water piled onto the beach by the waves and carried seaward fine sediments derived

from the land. Shepard et al. described the general characteristics of rip currents,

their relation to coastal and shoreline configuration, and the constitutive elements of

a rip current system, as shown in Fig 2.3.
By measuring waves (height, period and direction), winds, longshore currents,

and tides, Shepard et al. related rip current intensity (its definition was not clear in

their paper, but it appeared to be represented by the flow velocity in the rip neck) to

those factors, and the results are summarized in Table 2.2.

It will be interesting to note that Shepard et al. defined zero intensity of rip

current when wave height was 0.6 m (2 ft), as shown in Figure 2.4; which would











Table 2.2: Relationship of Rip Currents Intensity to Various Factors (from Shapard
et al. (1941)
Factors Observed Relations
Wave Height Largest rip current intensities corresponded
with the largest waves (see Figure 2.4).
Wave Period No pronounced relation was observed.
and Steepness
Longshore Rip current appeared to vary with the direction
Currents and intensity of the currents, but completely
satisfactory relation was not well defined.
Rip currents subsided with large waves, and strong
Winds rips did not occur on the windy days when waves
were small. Rip currents also appeared to be small
when wind was blowing along the coast.
Rip currents were more pronounced at low tide,
Tides but no evident relation of the rips to the spring
and neap tides was observed.


suggest that wave height must be larger than 0.6 m for rip currents to form. If waves

were smaller than 0.6 m, then rip currents would disappear.

Another important result was the existence of the channels in the path of a rip

current, which were largely confined to the surf zone and deeper than their surround-

ings. The floor of the channels was found to be decidedly irregular mainly due to the

strong rip current. Shepard et al. noted that the position of the channels varied rel-

atively rapidly as well as the positions of rip currents, as stated "three days after the

survey, the inner channel had completely disappeared and no appreciable rip could

be observed in the locality" (p. 355).

Shepard and Inman (1950a) investigated the nearshore circulation system near

areas where diversified submarine topography occurs off relatively straight shorelines

and found that the nearshore circulation system was definitely influenced by the

wave divergence at the heads of submarine valleys and by the wave convergence over

submarine ridges. Longshore currents adjacent to the shore diverged from areas of
















ca

C,
'1


'U
C
I-'
C!)


fC& MARCH APPl. MAY 41:C
S(-- WAVS & roDC (--) RIPCUARCtHr3

Figure 2.4: Measured Wave Height and Rip Current Intensity (from Shepard et al.,
1941). These data were obtained daily. Note the direct relationship between these
two variables. Note the definition of zero intensity of rip current when wave height
was 0.6 m (2 ft); which would suggest that wave height must be larger than 0.6 m
for rip currents to form.


wave convergence and flowed seaward as rip currents at areas of wave divergence.

This work implied the importance of the longshore wave height variations caused by

wave refraction due to irregular offshore bottom topography.

Shepard and Inman (1950b) performed a comprehensive series of field measure-

ments, and described the general circulation system on most beaches including two

straight beaches with parallel bottom contours. It was found that the direction of the

longshore currents was primary dependent not only on the angle of wave incidence to

the shoreline, but also on the longshore distribution of the wave set-up, greater in the

zones of higher breakers along the beach. The longshore currents commonly flowed

away from the zones of highest breakers toward the rip current. Although Shepard

and Inman did not note why there were those variations of the set-up in the longshore

direction on uniform beaches, they concluded that cellular circulation systems could

occur and be maintained even under normal wave incidence on straight beaches with

parallel contours.


N 1 A -2
a_, ___ ', ,, \4



_____"ijirI!V f V








24
McKenzie (1958) observed rip current systems on beaches with smooth offshore

topography but undulatory surf zone topography of alternate shoals and channels,

and categorized main factors affecting the occurrence of rip currents as summarized

in Table 2.3.


Table 2.3: Factors Affecting the Occurrence of Rip Currents (from McKenzie, 1958)

Factors Importance Observation(s)
Size and Regularity Determine the strength Small and numerous rips appeared
of waves of rip currents under moderate waves; while larger
but fewer rips were developed under
large waves.
Tides Affect the position Falling tide caused the change of
of rip currents channel angle with the beach, or
gradually moved channel into
new position with the same angle.
Wave Control wave angle Rips tended to turn into the waves
Direction and determine the rip within the surf zone, and tended to
currents direction turn away from the waves
outside the surf zone.
Coastal Control wave angle No direct relationship was observed
Configuration and wave energy between the rips and the distribution
distribution by wave of wave energy.
refraction


As listed in Table 2.3, McKenzie could not find any direct relationship between the

rip currents and longshore wave energy distributions, i.e., wave height distributions;

instead, he observed that rip currents "do not, as might be expected, seek that part of

the beach with least energy concentration but tend to move seaward in the vicinity of

greatest wave activity" (p. 107). This argument seemed to contradict the circulation

system flowing from higher energy zones to lower ones, as observed by Shepard and

Inman (1950a). However, this could be explained by the difference in the nearshore

zone topography, i.e., difference between undulatory offshore but planar surf zone

as in the observation by Shepard and Inman and smooth offshore but undulatory








25
surf zone topography as in McKenzie's observation, and also by considering both the

correlation between the circulation and the surf zone topography and wave-current

interaction at the location of rip currents, as will be discussed later.

Bowen and Inman (1969) performed field studies on the beach having smooth

offshore topography and planar surf zone bed in order to confirm their laboratory

results, which showed that the rip currents occurred at alternate antinodes of standing

edge waves of the same frequency as the incident waves. Bowen and Inman measured

incoming wave heights, the breaking wave heights and water depth, the width of the

surf zone and also the spacing of the rip currents to confirm whether or not these were

equal to the longshore wavelength of the edge waves, and found that rather regular

spacing was in good agreement with the calculated longshore wave length of an edge

wave of a particular mode. Bowen and Inman suggested that stationary interaction

between incident waves and synchronous edge waves resulted in periodic longshore

variations of breaking wave heights, which could drive such regular circulations on

plane beaches.

Sonu (1972) observed wave-induced nearshore circulation and meandering cur-

rents on a beach with smooth offshore topography and surf zone undulations under

essentially uniform breaking wave heights. By measuring the spatial distribution of

the horizontal velocities, the current patterns, the wave set-up in the surf zone, and

the time series of velocities inside the rip channels, he observed that the currents near

the shoreline moved from shoal areas of lower waves to rip channel areas of higher

waves, of which pattern seemed to contradict Shepard and Inman (1950a) but to

agree with McKenzie (1958).

Sonu then found that the current patterns followed precisely the same spacings

as the undulation wavelength; he concluded that for uniform waves the surf zone

undulation was an essential factor to the cellular circulation. By observing that

floating balls followed the directions of the measured gradient of water surface, Sonu








26
demonstrated that the currents were not driven by the gradient of the wave heights,

but were driven by the gradient of the mean water surface, which were caused by

radiation stresses.

2.5 Rip Current Models

In this section, a brief description will be given some rip current models which

explained various characteristic features of rip currents as observed in the field. Those
features include the width change of the rip neck, the rate of velocity decrease in the

current, the formation of rip head, and the turning of rip currents into the direction

of wave approach. These models consider that rip currents were already generated

by the merging of feeder currents.

Arthur (1962) first theoretically examined the dynamics of rip currents using the

steady-state shallow water continuity and momentum equations, in which the pressure

gradient term was the only remained driving force term after neglecting friction and

the Coriolis force terms. Arthur then eliminated the forcing term by employing the

vorticity equation and explained a relatively narrow, concentrated pattern of the rip

current by the conservation of vorticity along a stream line extending from shallow

to deeper water. Arthur noted that the friction would tend to broaden streamlines

of rip current. He also implied the importance of refraction effects of rip currents

on the incident wave field and noted that this interaction might be important in the
dynamics of rip currents.

Tam (1973) proposed a simple mathematical model which reduced a rip current

to an identical 2-D incompressible jet after assuming steady-state conditions, shallow

water approximations, energy dissipation mainly by horizontal mixing, and boundary

layer approximation for a narrow rip current. Tam also considered that the gradients
of the radiation stresses were balanced by the slopes of the mean sea level within the

narrow rip current; hence he assumed that the radiation stresses could be negligible

as long as the rip current was already formed and driven by the feeder currents.







27
For a plane beach, Tam found the linearly proportional width (this contradicts

Arthur, 1962) and inversely proportional maximum velocity to the distance from the
shoreline, resulting in constant flow rate, and described the rip head formation by

imposing a sudden increase in the plane beach bottom slope in deeper water depth,

which resulted in dramatic broadening of the width and reducing of the maximum

velocity, thus forming a rip head.

Wind and Vreugdenhil (1986) presented a numerical model to generate a rip
current due to the interaction of longshore current with a longshore barrier such as

groin and then compared the numerical results with the results of experiments in a

closed basin with fixed bed. Their numerical model included all the terms in the

depth-integrated momentum equations and the continuity equation, and investigated

the relative importance of convection, diffusion and bottom friction in the flow over

a sloping bottom.

They demonstrated that the combined effects of the bottom topography and con-

vective terms caused the convergence of rip current streamlines over a seaward sloping

bottom, which agreed with Arthur (1962). When convective terms were excluded from

the momentum equations, the rip current disappeared. They also found that the ef-

fect of bottom friction was to decelerate the rip current with diverging streamlines,

as discussed by Arthur (1962). For a given forcing, the total circulating flow rate was

regulated by the bottom friction rather than the magnitude of the viscosity for the

lateral shear stresses or convective term, which would be expected from the angular

momentum balance of the circulating water mass. The lateral shear stresses were

found to be responsible for closed streamlines outside the surf zone.

2.6 Rip Current Generation Models

2.6.1 Introduction

Since field studies have recognized a longshore variation in the radiation stresses

field and the wave-induced set-up as the main driving forces in the formation of rip







28
currents, various analytical and numerical models were developed based on several

mechanisms to explain the longshore wave height variability resulting in the variation

of the radiation stresses field. The two factors are usually considered: (1) longshore

variation in the breaking wave height, and (2) longshore variation in the bottom

topography.

In the present analysis, the various mechanisms are divided into two categories:

(1) prismatic and (2) non-prismatic topography models. The distinction between the
two is that prismatic models can explain the occurrence of a rip current on a planar

beach, while non-prismatic model needs undulatory topography inside the surf zone

to generate and maintain a rip current. It should be noted in present classification

that the mechanisms by the presence of coastal structures were not included, since the

special interest here was to investigate whether or not rip currents could be caused

by interaction of the beach topography with the incident waves. Similarly, Dalrymple

(1978) classified the models into (1) wave interaction and (2) structural interaction

according to the same criteria as the present study, but included the interaction with

coastal structures.

Prismatic topography models require hydrodynamic longshore perturbations on a

prismatic beach to provide the longshore variability of wave heights, which are enough

to drive the rip currents. For the case of normally incident waves on a straight

beach with fixed bed, no horizontal circulation is expected with uniform set-up in

the longshore direction. However, the prismatic model considers that the wedge-

shaped 3-D beach is very sensitive to instabilities in the longshore direction; hence the

beach could not maintain the uniform state against longshore perturbations, which are

considered mainly due to the wave-wave interactions (Bowen, 1969; Bowen and Inman,

1969, Sasaki and Horikawa, 1975; Dalrymple, 1975) or wave-currents interactions

(LeBlond and Tang, 1974; Dalrymple and Losano, 1978) or some instability inherent

to the nearshore hydrodynamics (Hino, 1974).











Table 2.4: Rip Current Generation Mechanisms

(a) Prismatic Topography Models
Mechanisms Representative Researcher(s)
Wave wave interaction
Synchronous edge wave Bowen (1969), Bowen and Inman (1969)
Infra-gravity wave Sasaki and Horikawa (1975)
Intersecting wave trains Dalrymple (1975)
Wave current interaction LeBlond and Tang (1974)
Dalrymple and Losano (1978)
2-D Instability with movable bed Hino (1974)

(b) Non-Prismatic Topography Models
Mechanisms Representative Researcher(s)
Undulatory bottom topography Bowen (1969), Noda (1974)
Mei and Liu (1977), Schmidt (1986)
Bar morphology Dalrymple (1978)
without sedimentary feedback Deigaard (1986)
Bar morphology Dalrymple, Dean and Stern (1976)
with sedimentary feedback Deigaard (1990)


Non-prismatic topography models need undulatory bottom topography (Bowen,

1969; Noda, 1974; Mei and Liu, 1977; Schmidt, 1986) or 3-D bar morphology with rip

channels (Dalrymple et al., 1976; Dalrymple, 1978; Deigaard, 1986, 1990) to provide

the driving forces which generate rip currents. Table 2.4 lists a number of the various

models according to the present classification.

Before presenting details, it would be better to start by reviewing Bowen's work

(1969) since his model first theoretically approached the rip current problem and
furthermore could be classified as either prismatic or non-prismatic model since it

was not clear in his analytical and numerical examples whether or not a longshore

variation of the radiation stresses field was induced by the bottom topography's effects
on the wave field.







30
Bowen first presented a theoretical model to generate rip currents on a planar

beach under normally incident waves having a longshore variation in wave height.

Considering two possible mechanisms for such longshore perturbations: (1) a long-

shore undulation of the surf zone bed, and (2) the interaction of synchronous edge
waves with the incident wave field, Bowen demonstrated that cellular circulations

were driven by a longshore variation in the radiation stresses field in the surf zone,

resulting in the currents flowing from higher to lower waves.

Considering that Bowen assumed a linear relationship of local wave heights to

the total water depth even at the location of the rips, the circulation would flow from

the embayments of higher waves to the shoal areas of low waves, which seemed to be

contradictory to most field studies carried out on undulatory beaches.

2.6.2 Prismatic Topography Models

Bowen and Inman (1969) found that progressive or standing edge waves with

the same frequency as the incident wave (synchronous edge waves) could generate a

nearshore circulation and presented the rip current spacing as,



L, = L, = L, sin[(2n + 1)03] (2.4)


where, Lr is the rip current spacing, Le the edge wave length, Lo = gT2/27, the deep

water wave length, g the gravitational acceleration, / the planar beach slope and n

is the mode of the edge wave, which is equal to the number of zero crossings of the

water surface elevations in the offshore direction. The spacing of rip currents is not

dependent on the wave heights but strongly dependent on the incident wave period,

which was in good agreement with their field observations but appeared to contradict

most of field studies (e.g., Shepard et al., 1941), and has a maximum value of deep

water wave length for the case of very steep beaches and/or high mode edge waves.








31

As given by Equation (2.4), it is always possible to select a combination of wave

period, edge wave mode numbers and beach slope, which can nearly match the ob-

served spacings; this would be a reason why the edge wave model is so attractive.
However, Guza and Davis (1974) have shown that only subharmonic edge waves could

be excited on a plane beach through a nonlinear resonant mechanism. These subhar-

monic edge waves were different from those suggested by Bowen and Inman (1969)

and could not produce rip currents. Guza and Davis also have shown that surging

conditions might be required for an edge wave model to be effective in causing rip

currents.

Hino (1974) proposed a rip current generation model based on stability analysis

of the steady-state uniform beach system on an initially plane beach but allowing a

feedback between the movable bed and the flow field, and found that the system was
hydrodynamically unstable for infinitesimal longshore perturbations, resulting in the

most preferred spacing of rip currents of about four times the surf zone width,



L, 4 Xb (2.5)

where Xb is the surf zone width, the distance from the shoreline to the breakers. Hino

showed that these spacings agreed well with the observed data. Although this model

allowed a sedimentary feedback for the growing and maintenance of rip currents, it

could generate rip currents on an initially planar beach by hydrodynamic instability;

hence, Hino's model was classified as prismatic topography model in the present study.

LeBlond and Tang (1974) questioned Bowen's (1969) assumption that rip currents

were sufficiently small so that their interaction with the field was negligible, and first

applied energy equation including advection, wave-current interaction and dissipation
terms. Together with the shallow water continuity and momentum equations and

the fixed bed consideration, LeBlond and Tang posed an eigenvalue problem for the
circulation cells inside the surf zone and performed a perturbation analysis. However,







32
in solving the posed eigenvalue problem it was necessary to assume that rip currents
would be most likely to occur where the relative rate of energy dissipation is least,
i.e., LeBlond and Tang have looked for the longshore wave number that minimized

the ratio of energy dissipation rate to the total kinetic energy present in a rip current

system.
The resulting circulation pattern was found to be essentially the same as in the
uncoupled case where wave-current interaction was neglected, with a somewhat mod-

ified wave field such that the energy coupling with the currents attenuated the waves

in that area (this contradicts the usual wave-current interaction considerations, espe-
cially on a prismatic beach where there is no undulatory bottom topography, i.e., no
differences in water depth along the longshore direction.), but the currents predicted

by the coupled case were weaker due to hydrodynamic feedback, as excepted. How-

ever, their computed values of the longshore wave number were too small and did

not compare well with available data. Furthermore, Dalrymple and Losano (1978)
later found that LeBlond and Tang's work contained a significant numerical error,
and concluded that their results were invalid.

Sasaki and Horikawa (1975) analyzed rip current spacings given by Bowen and

Inman (1969) and by Hino (1974) according to the deep water surf similarity param-
eter, which is defined as the ratio of beach slope to the square root of deep water
wave steepness, and found that these two models predicted the spacings which were
always smaller than those observed in the field for the very mild beaches and could be

applied only on beaches with steep and medium slopes; hence Sasaki and Horikawa
proposed an infra-gravity wave model for the gentle beaches with spacings given by



tanf tan #
L, = 157 ( ta- )2 Xb (0.22 > tn > 0.08) (2.6)
VHo//Lo .XHo/Lo









in which Ho/Lo is the deep water wave steepness. However, the mechanism to generate

rip currents was actually the same as that of edge wave except with the forcing given
by infra-gravity wave.

Dalrymple (1975) has shown on an open coast that intersecting wave trains of

the same period could cause rip currents. If two wave trains of the same period

intersect, they superimpose and cancel each other spatially, resulting in periodically

spaced nodal lines along the shoreline; at these lines, rip currents occur with a spacing

determined by the deep water wave length and directions of the waves, as follows:



L, = o (2.7)
sin 01 sin 02

where 01 and 02 are the deep water wave angle of the two wave trains. It was noted

that this model had no theoretical maximum spacing but a minimum of one half the

deep water wave length. Dalrymple also carried out laboratory experiments to verify

this model and the observed results agreed well with the predicted spacings. The

spacings of rip current were strongly dependent on the incident wave period but had

no relationship with the wave heights or the surf zone width, which was similar to

the relationship proposed by edge wave mechanism.

Assuming an existing rip current, Dalrymple and Losano (1978) developed two

analytical models to provide steady rip current system on a prismatic beach based

on a hydrodynamic feedback through wave-current interaction. It was noted in their

models that the energy equation was considered indirectly by a linear relationship

between the wave height H and the total water depth (h + 77) as



H = n (h + ) (2.8)

where h is the still water depth, r is the set-up, and n is a breaking index of the order

of unity (about 0.8).







34
The first model extended previous studies by LeBlond and Tang (1974) to include

only the changes of the local wave length in the presence of rip currents, yet no rip

currents occurred. Dalrymple and Losano then included the refraction of the waves

on the currents in the second model, and found that this refraction caused the waves

to impinge on the beach obliquely by forcing the incident waves to slow over the

rip, thus generating longshore currents flowing from regions of high wave energy and

set-up towards regions of low energy, i.e., the base of the rip, as suggested by Bowen

(1969).

They presented the non-dimensional rip current spacing as a function of one

parameter, defined as the ratio of the bottom slope to the friction, and later Dalrymple

(1978) proposed an approximate equation



1
A X +2.8 (2.9)
AD

where AXb 2rXb/L, is the non-dimensional rip current spacing, AD = nKr tan Pl[f(8+

3,c2)], is the breaking index and f is a Darcy-Weisbach (constant) friction coeffi-

cient. Equation (2.9) predicts that the rip current spacing increases with increasing

wave height as observed in the field. The spacing given in Equation (2.9) also increase

with more smooth bottom, which is not clear in the field since it is difficult to define

the bed smoothness in the field.

It was noted that work done by the currents against the radiation stresses ap-

peared to reduce the wave energy at the location of rip currents. As discussed earlier,

however, this mechanism seems to contradict the usual wave-current interaction such

that the opposing current tends to increase the wave height due to the wave refraction

and interaction on a counter current.









2.6.3 Non-Prismatic Topography Models

Noda (1974) developed a numerical model to obtain a steady-state nearshore

circulation pattern considering the effects of bottom topography on an incident wave

field, and found that, for an undulatory bottom, wave-bottom topography interaction

changed the incident wave field according to bottom undulation, thereby causing

spatial variation of the radiation stresses field, and that this variation of the radiation

stresses field inside the surf zone ultimately derived the nearshore circulation flowing

from the shoals to the embayments.

Although Noda obtained unrealistically large value of the maximum current ve-

locity, numerical examples of his work to various bottom topography have verified

the driving mechanism for the nearshore circulation due to the bottom topography's

effects on the wave field. It was noted that a feedback between circulation currents

and movable bottom should be provided to develop an equilibrium bottom configu-

ration for a given wave forcing. Noda also pointed out that wave-current interaction
would tend to modify the incident wave field, resulting in a more uniform breakerline

as observed by Sonu (1972), thus reducing spatial variation of wave heights, hence

consequently reducing the magnitude of the circulation velocity.

Dalrymple et al. (1976) suggested a nearshore circulation model on a 3-D long-
shore bar crest-trough morphology, with the main driving forces given by the gradients

in the set-up values behind the bar. Dalrymple et al. considered that these gradients

in set-up could be induced both by wave reflection from the submerged sand bar and

mass transport over the bar, and presented the circulation flows to regions of lesser
set-up at rip channels. It was noted that by roughly considering sedimentary feedback,

they could obtain minimum rip current spacings on the barred coastlines. Although

no details were given, the basic idea seemed to be correct. The detail formulations of

the hydrodynamics are given in Dalrymple (1978).








36
Mei and Liu (1977) developed a linear analytical model for the nearshore circu-

lation driven by the effects of periodically varying topography confined within and

near the surf zone. Assuming a small depth deviation from a plane beach, Mei and

Liu found that the circulation pattern would be determined based on two effects:

(1) variations in the set-up and in the tangential and transverse components of the

radiation stresses to the wave direction which would tend to drive rip currents from

the shoals to the embayments, and (2) variations in an additional component of the

radiation stresses, representing the flux in the wave direction of the transverse com-

ponent of momentum, which would tend to drive rip currents from the embayments

to the shoals.

Relative magnitude of those two effects was controlled by both the bottom to-

pography and the ratio of the surf zone width to the longshore wave length of the

topography variation. However, Mei and Liu found that the circulation was always

shorewards near the shoals and seawards near the embayments if the bottom undu-

lations were entirely confined within the surf zone. They also obtained a counter-

rotating circulation in a small region near the shoreline.

Dalrymple (1978) presented a model to include the effect of wave reflection from

the bar as suggested by Dalrymple et al. (1976), and examined mean currents behind

a longshore bar by considering (1) the continuity equation, which states that the mass

transport over the bar crest should equal the increase in flow in the longshore trough

between the bar and the beach, (2) the equation of motion within the trough, which

is driven by the set-up differences, and finally (3) the momentum equation, which

includes the radiation stresses and the reverse effect of momentum flux due to wave

reflection by the bar.

By considering the differences between the set-up corresponding to uniform con-

ditions without net flow (designated as potential set-up) and the set-up with net flow

(designated as actual set-up), Dalrymple found that the mass transport over the bar







37
increased continuously toward the rip channels, resulting in the longshore current
velocity increasing from zero at the midpoint between two rip channels to the maxi-

mum value at the locations of the rip channels. In driving his equations, Dalrymple

imposed no mass transport condition (i.e., actual set-up = potential set-up) at the

center point of the bar, which seemed to be physically incorrect since mass transport
at that point might occur depending on the length of the bar. If the bar length is

short, then water would be transported over that point. The symmetric condition for

the longshore velocity (i.e., zero longshore velocity) would be enough at that point.

Expecting that the set-up would be zero at the rip channels, Dalrymple obtained

the minimum stable spacing of the channels as a function of the wave steepness and
sediment size through bottom friction effects as well as several geometric parameters

representing 3-D bar morphology. Dalrymple noted that, in addition to wave-current

interaction, the sedimentary feedback mechanism should be incorporated into this

hydrodynamic model. Even though some equations appears to be incorrect, the basic
idea to consider the momentum equation near the bar area seems to be correct to

describe the mean currents behind the longshore bar.

Deigaard (1986) presented an analytical model to calculate the longshore currents

behind the bar, which was similar to Dalrymple's model (1978) but the reflection from
the bar was not taken into account. Deigaard assumed that the flow rate over the

bar was simply determined by the energy loss caused by the differences between the

potential set-up and the actual set-up, and expressed the flow rate as;



q = h V2g(o 7) (2.10)

in which q is the flow rate, h the mean water depth over the bar crest, j0 the potential

set-up, and J the actual set-up. Equation (2.10) considers that the total head loss in

set-up values is fully contributed to the velocity head loss, thus neglecting unknown

loss of internal energy which is usually involved in wave breaking process. Hence,







38
Equation (2.10) tends to overestimate the flow rate, resulting in decreased longshore

velocity. In this aspect, the momentum equation would be better application to the

problem of determining the flow rate. This will be discussed in details later.

Deigaard also considered both the momentum equation within the trough ne-

glecting bed friction and the continuity equation. By allowing mass transport at the

center point of the bar, which depended on the length of the bar, he then obtained

the longshore current velocity as a function of potential set-up and geometric pa-

rameters such as the length of the bar and cross sectional area of the trough. His

results demonstrated the same trend as Dalrymple's model as the velocity increased

and approached the maximum magnitude toward the rip channels.

However, his momentum equation, as presented in Equation (2.11), appeared to

be incorrect since he neglected the first order term, i.e., the bed shear stress, and
considered only the second order convective acceleration term. Furthermore, this

second order term was considered incorrectly. This will be discussed later.



d + ) = 0 (2.11)


Deigaard suggested the minimum stable spacings of rip channels by considering

that the longshore velocity in the trough approached the possible maximum longshore

velocity beyond certain distance from the center of the bar, which were of the order

of two or three times the ratio of cross sectional area of the trough to the mean water

depth over the bar crest.

Schmidt (1986) carried out experimental investigations on the hydrodynamics

of wave-induced circulation over bar-channel topography which simulated a periodic

form parallel to the coast superposed on a regular offshore sloping bottom. By measur-

ing the distribution of wave heights, mean currents and time-dependent wave-induced

vorticity, Schmidt concluded that this circulation associated with the bar morphol-







39
ogy might be interpreted as a self-maintenance mechanism. During the experiments,

Schmidt observed a shoreward-directed flow over the bar crest and a return flow from

the trough regions, and concluded that higher breaking waves over the bar crest in-

duced a larger set-up driving the flows to bar trough areas of lower waves and smaller

set-up. But he could not observe the counter-circulation in a small region near the

shoreline as obtained theoretically by Mei and Liu (1977). This effect was considered

to be due to the absence of lateral mixing in the theoretical considerations by Mei

and Liu.

Deigaard (1990) presented a model to explain the formation of rip channels on

a barred coastline by performing a linear stability analysis. The equilibrium state

was characterized by a uniform bar system under normally incident waves along the

beach with no net current. The flow was described using essentially the same method
as Deigaard (1986), However, in determining the flow rate over the bar crest, he

included the momentum exchange inside the surf zone, resulting in an increase in the

magnitude of the longshore velocity, thus reducing rip current spacings compared to

those suggested by Deigaard (1986).

Deigaard then provided a perturbation to the longshore bar, which was periodic

in the longshore direction, causing longshore variations in the set-up, finally resulting

in a net circulation with shoreward flows over the bar crest, longshore currents in the

trough and rip currents in the channels. By considering sediment transport due both

to bed slope of the perturbation and to linearly-varying cross-shore transport with

the water depth in the surf zone, Deigaard obtained the spacing of the rip channels, at

which the perturbation would grow or decay in time with the maximum rate. When

Deigaard considered a specific example, he could obtain the spacing of the order of

about twice the surf zone width, which was defined as the distance from the shoreline

to the bar crest.








40
It was noted that low period oscillations of the cross-shore discharge over the bar

crest was necessary to obtain a linear theory; however, it is very questionable how

he derived his cross-shore flow rate. Furthermore, his sediment transport equation,

which showed a linearly varying transport rate with water depth, also seems to be

incorrect.














CHAPTER 3
LABORATORY STUDIES ON THREE-DIMENSIONAL MORPHOLOGY


3.1 Introduction

As reviewed in Chapter 2, there are several possible causes of 3-D flows in a wave

tank, some of which could also be representative of those occurring in nature: (1)

Instability of 2-D flows on 2-D morphology, (2) Organized longshore wave motions that

could induce edge waves in nature or in a tank or cross-tank waves under laboratory

conditions, and (3) A feedback between the hydrodynamics and morphology that

reinforces 3-D morphological features, resulting in cross-tank profile variations under
certain stages, especially when the profile approached an equilibrium with overall

stability.

In the present study, as discussed earlier, movable bed experiments in a narrow

wave tank were carried out to (1) monitor profile evolution and the resulting equi-

librium, (2) provide experimental repeatability, and (3) investigate various possible

interrelationships and causes of the three-dimensionality, which included:


(a) Effects of induced perturbations in the bar topography, including deepening of

the bar trough, asymmetric area seaward of the bar, and removing half the bar

crest,

(b) Effects of controlled water table levels in the berm, which were maintained

higher than the mean sea level, and

(c) Effects of an initially 3-D berm.







42
It should be noted that present experiments were performed with the fine sands

which have been utilized during previous tests, thus have been subjected to continuous

submergence. This prolonged submergence appeared to allow microorganism active

although the experiments were carried out in winter season, resulting in unpleasant

odors and black-colored cohered-looking sands inside the beach, especially near the

tank bottom. Hence, one experiment was designed to investigate the effects of mi-

croorganism inside the beach on the profile evolution. Since the breaks between wave

runs to measure profiles appear to retard the development of steady-state for a given

beach system, an additional test was performed to examine the effects of continuous

wave run without intermissions on the occurrence of the three-dimensionality.

Based on the results of these experiments, the mechanisms) which can initiate

and form a bar morphology with the presence of rip currents will be discussed. Also,
by observing the path of rip currents during the experiments, it was examined whether

rip currents were generated from the shoals or from the embayments.

3.2 Laboratory Facilities and Experimental Conditions

A total of 6 experiments was carried out in the tilting flume of the Coastal and

Oceanographic Engineering Laboratory of the University of Florida. This tank is 15.5

m long, 0.9 m high and 0.6 m wide, and is equipped with a piston type wavemaker

with a mechanically controlled motion and with one glass wall panel and one steel

wall.

The planar beach of initial slope 1:18 was formed of well-sorted fine quartz sand

with a mean diameter of 0.21 mm (2.25 in < unit), a sorting coefficient of 0.58 and

fall velocity of approximately 2.3 cm/sec. The grain size distribution include sizes

ranging between 0.1 to 0.5 mm. The water depth in the horizontal portion of the

tank was 0.275 m. Regular waves with a period of 1.5 sec and wave height of 0.11 m

were utilized, and were measured by a capacitance-type wave gage. Figure 3.1 shows

a schematic diagram of the initial profile and other experimental details.











43







0











EE

C.)d




0





00

Ob
II C
C)



< A


E5


















II
-o



















a to CD

CD1 zQ -q q
J 0o

II I I-
(, rA 1c0



-o z







C)


cn )
ze

cj 5-


~Q:L NYI


I I I I
(ui EIAIVSN~ 3OVNLV3







44
The profile was measured manually by a point gage modified by replacing the

point with a small, rectangular foot (7.5 cm by 2.5 cm) which provided a flat surface

to rest on the sand. In order to avoid consolidation at the measuring point, the gage

was constructed of light aluminum. Three profiles, designated as B1, B2 and B3, were

measured over the entire length of the beach to document the three-dimensionality

at various times. As shown in Figure 3.2, profile B1 was 0.15 m from the glass side

wall while profile B3 was 0.15 m from the steel side wall. Profile B2 represented the

center line profile along the tank.


Wave

Steel Side Wall

Profile B3

0.6 m Profile B2 (Center Line)

Profile B1


Glass Side Wall

Figure 3.2: Three Profiles B1, B2 and B3 across the Tank

The profiles were documented at locations spaced 0.1 m along each of these lines,
and then these three profiles were averaged to represent the mean profile at the

measuring time. Since three profiles were not sufficient to document 3-D features

when a fairly deep and narrow channel appeared near one of the tank walls, the

profile elevations at both sides of the tank were measured additionally to document

the maximum cross-tank variations of the profile.

The desired water table level in the berm was maintained by excavating 2-D

depressions across the tank. These excavations were connected to the constant head

reservoir through plastic tubes so that water was siphoned out of or into the excavated







45
holes to maintain the desired water table level. During the experiments, this method

has worked very well. However, bubbles appeared sometimes inside the tubes due

to prolonged experimental duration; at which time, they were removed by allowing a

small amount of flow from the excavated holes to the reservoir, or vice versa.

3.3 Description of Movable Bed Experiments

Table 3.1 lists experiment identification number, total wave run duration, water

table level conditions, and brief descriptions of each experiment. Each experiment

was defined as a collection of sequential profiles for an initially planar beach subjected

to regular waves.


Table 3.1: Description of Movable Bed Experiments
Exp. Duration Water Table Note
No. (min) Level* (cm)
MTO1 0-476 0.0 Reference test
MT02 0-407 0.0 Biological effects (quick start)
MT03 0-545 0.0 Wave run duration effects
(run waves without intermission)
0-821 Perturbations in the bar topography
MT04 (0-69) (no change)
(69-138) 0.0 (bar trough is deepened)
(138-352) (asymmetric offshore scour area)
(352-821) (remove half of bar crest)
MT05 0-1166 +11.0 Initially 3-D berm
with elevated water table level
MT06 0-1166 +16.5 Highly elevated water table in the berm
Zero refers to the mean sea level (MSL). Hence, positive
value represents the water table level above MSL.



The six experiments were defined as: (1) Reference test (Experiment MT01),

(2) Repeat tests (Experiment MT02 and MT03), (3) Perturbation tests (Experiment

MT04 MT05 and MT06).









Reference Test

The first movable bed experiment (Experiment MT01) was designed to monitor

the profile evolution and to determine whether or not three-dimensionalities might

occur, hence providing a reference for future experiments.

The profiles were surveyed at intervals of 23 min during initial stages to document

rapid evolution of the profiles and were increased later up to 69 min depending on the

rate of profile change. The same intervals were used in the subsequent experiments

to compare the profiles at the same elapsed times.

Experimental Repeatability

Experiments MT02 and MT03 were carried out to (1) provide experimental re-

peatability of Experiment MTO1 and (2) investigate the possible effects of experi-

mental conditions on the three-dimensionality occurred at Experiment MT01, which

included the effects of the microorganism inside the beach and the effects of continu-

ous wave run.

Experiment MT02 was conducted to investigate the effects of microorganism, of

which presence could be perceived by unpleasant odors and black-colored cohered

sands located near the tank bottom, as discussed earlier. Since the biological film

inside sand was believed to be disturbed after long wave run, Experiment MT02

started with the remolding of the initial profile immediately after the last wave run

of Experiment MT01.

The purpose of Experiment MT03 was to investigate the effects of required

time for the beach system to reach steady-state on the occurrence of the three-

dimensionality. In this experiment, hence, the wave was run continuously without

intermissions to measure profiles.

Perturbation Tests

Experiments MT04, MT05 and MT06 represent the main attempts in the present

study to investigate the three-dimensionality.







47
Experiment MT04 was carried out to investigate the effects of induced pertur-

bations in the bar topography, which included (1) deepening of the bar trough, (2)

asymmetric area seaward of the bar, and (3) removing half the bar crest, and was

continued further to investigate resulting equilibrium.

Experiment MT05 started with an initially 3-D berm superimposed on a planar

initial profile to investigate whether or not resulting 3-D flows in the beach face would

facilitate the occurrence of three-dimensionality. This experiment also included the

effects of elevated water table in the berm.

Experiment MT06 was carried out to examine the effects of highly elevated water

table level in the berm on the profile evolution and resulting 3-D morphology.

3.4 Results and Discussions

3.4.1 Reference Test (Experiment MT01)

During the early stages (t < 242 min), as suggested by the criteria presented in

Table 2.1, the offshore bar formed quickly from a linear profile and remained station-

ary. However, the berm also started to accrete slowly at the initial times and more

rapidly at the later times. A small bar appeared between the main offshore bar and

the berm. This bar moved landward continuously and finally remained stationary

just landward of the berm. The profiles appeared to approach an intermediate equi-

librium with overall 2-D conditions. The mean profiles during early stages at elapsed

times 23, 69, 161, and 242 min with the initial profile are presented in Figure 3.3.

As shown in Figure 3.4, the mean profile inside the surf zone at 242 min was

in good agreement with the equilibrium profile, presented in Equation (2.2) using

the profile scale parameter presented in Equation (2.3); this indicated that, after 242

min, the profile really approached an equilibrium for the given forcing.

After the profile approached an equilibrium and a level of profile stability had

occurred at 242 min, a weak counter-clockwise 3-D circulation occurred after about

270 min, flowing from the steel side wall to the glass side wall inside the surf zone.




















0.15



0.10



-0.05



S-0.

w

Z -0.05



S-0.10
0

Z -0.15
0
O 0

r -0.20


-0.25
S TANK BOTTOM

-0.30 I I '
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

DISTANCE FROM. TANK END (m)


Figure 3.3: Mean Profile Evolution during Early Stages of Experiment MT01. Elapsed
Times = 0 (Initial Profile), 23, 69, 161 and 242 min. Note that the profile approached
an equilibrium and a level of profile stability had occurred at 242 min.








49
0.15
S........ mean profile at 242 min.
S0.10 -
-- equilibrium profile. (y=Ax-2/3)
o 0.05 ........
.M.S.L.

> -0.05
0
S-0.10

O -0.15
[--
S-0.20 ...

-0.25 TANK BOTTOM "'"............

-0.30 i 1 I I I I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)


Figure 3.4: Comparison of the Mean Profile at 242 min during Experiment MTO1
with the Equilibrium Profile Proposed by Dean (1977). Note the similarity between
two profiles inside the surf zone.


This flow initiated a new stage of profile evolution. However, only small changes

occurred between 242 and 297 min since the circulation was not sufficiently strong

to transport the sediments. Figure 3.5 shows the mean profiles at elapsed times 0

(initial profile), 242, 297, 352' 407 and 476 min.

After 297 min, the sedimentary feedback appeared to reinforce the circulation

sufficient to transport sands landward. As shown in Figure 3.5, the area seaward

of the bar eroded with a substantial deepening and the eroded sand was deposited

immediately landward of the bar trough, thus changing this area from mildly erosional

to strongly depositional.

Furthermore, this area changed from overall 2-D conditions to 3-D features with

higher parts near the steel side wall, as shown in Figure 3.6 which presents three

profiles Bl, B2 and B3 to document three-dimensionality occurred after 476 min.

Bar started to move landward with counter-clockwise rotation of approximately 20

degrees about the direction of wave propagation. The bar trough became shallower


















0.15
476 min.
--- 407 min.
0.10 -- 352 min.

--- 297 min.
0.05 -- 242 min.
SIY \. --.....- initial profile


C;1 -0.00 -M.S.L.
0 .0 0 ... .............. ............ ..._....__...__..._........ ...



Z -0.05


'-0.10



z -0.15
0


-0.20



-0.25 \
TANK BOTTOM

-0.30 I I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

DISTANCE FROM TANK END (m)







Figure 3.5: Mean Profile Evolution after the Profile Approached an Equilibrium dur-
ing Experiment MT01. Elapsed Times = 0 (Initial Profile), 242, 297, 352, 407 and 476
min. Note the substantial erosion of the area seaward of the bar and the deposition
of the area immediately landward of the bar trough. Note also landward movement
of the bar.









0.15
S mean profile profile B3
0.10 initial profile ----. profile B2

0.05 --- profile BI

1.4 M.S.L.
0.00 0 .0 -...... .... ...... ..........................................-,...... -, ............ ................ ...- -. .. .......



O -0.10
-0.05




0
S-0.20

S- 0.25
5 TAqNK BOTTOM

-0.30
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)

Figure 3.6: Initial Profile and Three Profiles B1, B2 and B3 and Mean Profile at 476
min during Experiment MT01. Note three-dimensionality inside the surf zone and
near the bar area, which is 3-D morphology associated with rip currents, and also
that the centerline profile B2 is almost the same as the mean profile.


at the later times as sand was deposited over the area landward of the bar. This

profile morphology was reminiscent of a bar morphology with a rip current present.

After 476 min, the maximum cross-tank difference of the profile elevation at the

depositional area inside the surf zone was estimated to be 6.0 cm.

3.4.2 Experimental Repeatability

Experiment MT02

As explained earlier, Experiment MT02 started with the remolding of the initial

profile right after the last wave run of Experiment MT01, at which time biological

film inside sand was believed to be disturbed.

The trend of the profile evolution was generally the same as Experiment MT01,

as shown in Figure 3.7, thus providing the experimental repeatability rather than

proving the effects of microorganism.


I

















0.15
407 min.
----- 352 min.
0.10 -- 297 min.
207 min.
-.--*- initial profile
0.05


-0 M.S.L.
'l 0.00 .. ....... .... ................. ..................... ..

Z -0.05




S-0.10



Z -0.15 1 \



S-0.20






-0.30 I I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

DISTANCE FROM TANK END (m)








Figure 3.7: Mean Profile Evolution after the Profile Approached an Equilibrium dur-
ing Experiment MT02. Elapsed Times = 0 (Initial Profile), 207, 297, 352, and 407
min. Note the substantial erosion of the area seaward of the bar and the deposition of
the area immediately landward of the bar trough, which occurred during Experiment
MT01 (see Figure 3.5), thus providing experimental repeatability.









0.15
Experiment MT03
0.10 -- Experiment MT02
0.05 ------ Experiment MT01

M.S.L.
0 .0 0 ...... ................ ... ........................................... ............. .......................... ._... : _._ ._s... .... .. ......
-o.o0 ....... .............

-0.05 -

0 -0.10

Z -0.15 .
O
E -0.20 "\^
-0.20

S-0.25 TANK BOTTOM

-0.30 i I I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)

Figure 3.8: Comparison of the Mean Profile at 207 min during Experiment MT03
with the Mean Profiles at the Same Time during Experiments MTO1 and MT02. Note
the similarity between those three mean profiles.


Although the three-dimensionality occurred slightly earlier at about 240 min than

that during Experiment MT01, no clear conclusions could be drawn to the effects of

microorganism on the occurrence of the three-dimensionality, which might be due to

low temperature during this experiment, as explained earlier.

Experiment MT03

Experiment MT03 was performed to investigate the effects of required time for

the beach system to reach steady-state, as discussed earlier. Hence, the wave was

operated continuously without intermissions for the first 207 min. After 207 min,

however, the wavemaker malfunctioned, resulting in interruption of the continuous

wave run.

As shown in Figure 3.8, the mean profile at 207 min was amazingly the same as

those during Experiments MT01 and MT02. Also, three-dimensionality occurred at

almost the same time (240 min) as Experiment MT02. These facts implied that the

effect of continuous wave run was unexpectedly small.







54
Up to 476 min, the profiles evolved in the same manner as previous experiments.

Counter-clockwise circulation occurred and transported sands from the area offshore

of the bar to the depositional area immediately landward of the bar trough. As sand

was deposited, the circulation seemed to be reinforced again.

When the experiment was conducted continuously beyond 476 min, strong circu-

lation occurred, resulting in substantial onshore transport of the sands from the area

seaward of the bar, thus causing the landward movement of the bar and rapid build

up of the berm with another peak which moved seaward. Figure 3.9 shows the mean

profiles at elapsed times 0 (initial profile), 207, 352, 476 and 545 min.

This depositional area changed from overall 3-D feature to overall 2-D one, as

shown in Figure 3.10, except a very narrow deep channel near glass side wall of tank,

where the maximum depth was found to be about 5.0 cm below the mean profile.

The overall slope of the profile at 545 min was estimated to be 1:10, which was

defined as the slope between the seaward end of the profile and the peak of berm. The

slope of the beach face was estimated to be 1:7, which was approximately the same as

that of the area seaward of the bar. After 545 min, wavemaker again malfunctioned,

resulting in termination of this experiment.

3.4.3 Perturbation Tests

Experiment MT04

Experiment MT04 was carried out to investigate the effects of induced perturba-

tions in the bar topography on the occurrence of three-dimensionality inside the surf

zone, and continued further to investigate resulting equilibrium.

During the first 69 min of wave operation, the trend was the same as previous

experiments as the morphology was dominantly 2-D. As a first perturbation to the

bar topography, the bar trough was deepened by approximately 4 cm after 69 min of

wave run, as shown in Figure 3.11, to investigate whether or not the morphology is

stable against the perturbations during the initial phases of the profile evolution.















0.15



0.10



0.05






-0.05 -



-0.10



-0.15



-0.20



-0.25
TANK Bi

-0.30
0.0 0.5 1.0


1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

DISTANCE FROM TANK END (m)


Figure 3.9: Mean Profile Evolution during Experiment MT03. Elapsed Times = 0
(Initial Profile), 207, 352, 476 and 545 min. Note rapid change during 476 to 545
min with landward movement of the bar and another peak of the berm









0.15
-0- profile along rip channel profile B3
E 0'.-- initial profile ------ profile B2

S0.05 '_ --- profile Bl

^ O O ............. :,............ ,- .............................................................. .. ..... .................. .... ............................. ........... .... ... ... ........................
S............ .
-0.00 *-..- M.SL.-.

> -0.05 -.*...
0 ....... .. ..
-0.10 -

-0.15 -
E.-

-0.20 -

-0.25 ........
0.25 TANK BOTTOM

-0.30 I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)

Figure 3.10: Initial Profile and Three Profiles (BI, B2 and B3) and the Profile along
Rip Channel inside the Surf Zone at 545 min during Experiment MT03. Note overall
2-D conditions inside the surf zone except a very narrow deep channel near glass side
wall.

During 69 to 138 min, the profile surprisingly returned back to the pre-modified

profile at 69 min, as shown in Figure 3.12. The deepened 2-D bar trough completely

filled in and the profile morphology was dominantly 2-D; which implied that the

profile morphology was stable against the perturbation given by deepening of the bar

trough.

After 138 min wave run, the area seaward of the bar, which was almost 2-D,

was modified by relocating sand from the steel side wall to the glass side wall, as

shown in Figure 3.13, resulting in asymmetric offshore area of the bar. However, the

mean profile remained approximately the same. The maximum cross-tank difference

of the profile elevation in this area at the two sides of the tank was about 6.0 cm.

This asymmetric offshore area was expected to change wave shoaling and breaking

characteristics over the bar region, hence resulting in longshore variations of the

breaking wave heights.


1


















0.1 modified mean profile
........ pre-modified mean profile

-0.0 ............... M.S.L.


-0.1


-0.2

(a) Comparison of Mean Profiles
S-0.3 I i i
O 0. --- pre-modified profile B3
------ pre-modified profile B2




-0.1

.! t -0.2

W- _(b) Three Profiles before Modification-- ..
-0.3 -- I Ii I
0.1 modified profile B3
------ modified profile B2
-0. --- modified profile B1 M.S.L.
-0.0.


-0.1


-0.2
(c) Three Profiles after Modification -...
-0.3 i I i' I 'I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

DISTANCE FROM TANK END (m)




Figure 3.11: Induced Perturbation to Deepen the Bar Trough at 69 min during
Experiment MT04: (a) Comparison of the Modified Mean Profile with Pre-Modified
Mean Profile, (b) Three Profiles before Modification, and (c) Three Profiles after
Modification


















0.1


-0.0


-0.1


-0.2


-0.3

0.1


-0.0


-0.1


-0.2


-0.3

0.1


-0.0


-0.1


-0.2


-0 -3


0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

DISTANCE FROM TANK END (m)


5.0 5.5 6.0


Figure 3.12: Comparison of Pre-Modified Profile at 69 min with Pre-Modified Profile
at 138 min during Experiment MT04: (a) Comparison of Mean Profiles, (b) Three
Profiles before Modification at 69 min, and (c) Three Profiles before Modification at
138 min.


--- pre-modified mean profile at 69 min.
........ pre-modified mean profile at 138 min.

M.S.L.





-------------- ---------------i----------------------



(a) Comparison of Mean Profiles


--- pre-modified profile B3

------ pre-modified profile B2
--- pre-modified profile B1 M.S.L.







-

(b) Three Profiles before modification at 69 min.
I I I I I I I
pre-modified profile B3
------ pre-modified profile B2

.'.'. --- pre-modified profile B1 M.S.L.
. _.....................t.......... .......................




-..



(c) Three Profiles before modification at 138 min. -'- .
f 1 I I I I I I I I I


v.*
















0.1 -- modified mean profile
........ pre-modified mean profile

-0.0. .- M.S.L.
0 .0 .......o .. ..... ..................................... .... ... ....... .... ... ... ... ... .


-0.1


-0.2
(a) Comparison of Mean Profiles
-0.3 I i i
S .1- pre-modified profile B3
------ pre-modified profile B2
S--- --- pre-modified profile B1 M.S.L.
S-0.0


-0.1
oE

I -0.2
S(b) Three Profiles before Modification -" .-.
-0.3 I I
0.1 --- modidied profile B3
------ modified profile B2
S '* --- modified profile B1 M.S.L.
-0.0 ---...................---- --... .............



-0.2


(c) Three Profiles after Modification R'-"--. ..
-0.3 I 2 I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

DISTANCE FROM TANK END (m)





Figure 3.13: Induced Perturbation to Provide Asymmetric Area Seaward of the Bar
at 138 min during Experiment MT04: (a) Comparison of the Modified Mean Profile
with Pre-Modified Mean Profile, (b) Three Profiles before Modification, and (c) Three
Profiles after Modification. Note the dominantly 2-D profile before modification and
the asymmetric area seaward of the bar after modification.







60
As shown in Figure 3.14, again the profile returned to pre-modified 2-D profile

morphology at 138 min within an hour after resumption of wave action. The mean
profile at 207 min agreed well with the pre-modified mean profile at 138 min, as

shown in Figure 3.14(a). And the perturbed area seaward of the bar was changed

to the pre-modified 2-D one. These again demonstrated the stability of the profile

morphology against the perturbations.

At this stage, it will be interesting to consider the direction of the sand transport

during 138 min to 207 min. During this time, sands could be transported either (1)

directly from the glass side wall to the steel side wall by gravity and/or 3-D circulation

confined in the area seaward of the bar, or (2) by overall 3-D circulation starting at

the higher perturbed area, passing over the bar, circulating inside the surf zone in

clockwise direction, and returning to the lower perturbed offshore area.

By considering the clockwise rotation of the bar by approximately 20 degrees, as

shown in Figure 3.14(c), the sands appeared to be transported by overall 3-D circula-

tion as described above; this was exactly what was observed during the experiment.
It appeared that modification of the area seaward of the bar caused different

characteristics of the wave breaking at two sides of the tank (wave breaking occurred

at first in the higher perturbed area), thus producing nonuniform distributions of the

set-up across the tank, resulting in the clockwise 3-D circulation. At the beginning,

this 3-D flow appeared to be weak to transport sands; however, it was sufficiently
strong to rotate the bar. As the bar was rotated, the 3-D flow was reinforced by the

sedimentary feedback. This 3-D flow then started to transport sands from the higher

perturbed area to the area immediately landward of the bar trough. Small portion of

those sands were transported landward continuously and built up the berm slightly,

while main portion of the transported sands were carried back to the lower perturbed

area seaward of the bar, resulting in the pre-modified 2-D offshore area.









61






0.1 ........ modified mean profile at 138 min.
-- mean profile at 207 min.
M.S.L.
-0.0 ...... ......................... ........................... .. ......


-0.1


-0.2
S (a) Comparison of Mean Profiles .
-0.3 I I
v --- modified profile B3
cc 0.1
------ modified profile B2
S --- modified profile B1 M.S.L.
v> 0 .0 ...................... ............................................................... ..... ....... . .. ...... .... ....
-0.0

O
E-



(b) Three Profiles after modification at 138 MIAl & -.
-0.3
0.- profile B3



----- profile B2

---- profile B1 M.S.L.
-0.1
S-0.2

(b) Three Profiles after modification at 138 min.
-0.3 i I---








0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)
Figure 3.14: Profile Evolution from 138 in to 207 in during Experiment MT4:
--(a) Comparison of the Modified Mean Profile at 138 in with Mean Profile at 207
____ --- profile B1 M.S.L.



-0.1


-0.2
(c) Three Profiles at 207 min. -'
-0.3 I I I I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)





Figure 3.14: Profile Evolution from 138 mm to 207 min during Experiment MT04:
(a) Comparison of the Modified Mean Profile at 138 min with Mean Profile at 207
min, (b) Three Profiles after Modification at 138 min, and (c) Three Profiles at 207
min.







62
During 207 to 297 min, the 3-D flows remained weak to cause strong onshore

transport of the sands from the 2-D area seaward of the bar and the profile was

dominantly 2-D except the bar area rotated clockwisely by about 20 degrees.

However, during 297 to 352 min, fairly strong 3-D circulations started to occur,

thus causing a rapid landward sand transport, increasing the three-dimensionality

inside the surf zone, as shown in Figure 3.15. In this figure, the mean profile at 352

min appeared to agree well with that at 297 min. However, the three-dimensional
features appeared inside the surf zone at 352 min, which were associated with a fairly

strong 3-D circulation and a rapid net landward sand transport. It is noted that the

rotation of the bar unchanged and the angle remained as about 20 degrees.

After 352 min of wave run, half of the bar crest was removed to fill the bar trough,

resulting in a linear profile without prominent bar near the steel side wall, as shown

in Figure 3.16. This was designed to impose an extreme three-dimensionality into

the bar crest, thus accelerating the development of the 3-D features already existed

inside the surf zone.
The bar crest again recovered its pre-modified shape from the imposed 3-D feature

over a testing time of approximately one hour, resulting in a smaller rotational angle

(less than 10 degrees), as shown in Figure 3.17. During the recovery, the other part

of the profile remained almost the same as the pre-modified one, and no distinct

circulation was observed.

After overall recovery occurred approximately at 400 min, the bar started to move

landward with increasing clockwise rotation due to reinforcing 3-D circulation and the

area seaward of the bar eroded substantially, resulting in the deposition of sand at the

area immediately landward of the bar trough and the increase in clockwise rotation

of the bar crest. This morphology and hydrodynamics are strongly reminiscent of the

morphology associated with rip currents, as shown in Figure 3.18.









63




0.1 -...... mean profile at 297 min.
mean profile at 352 min.



-0.1 ............


-0.2

(a) Comparison of Mean Profiles .
0.3 ,- ,1
S 0.1 --- profile B3
------- profile B2
--- profile Bl M.S.L.

-0.0

o

E- -
S-0.2 "-S,
W (b) Three Profiles at 297 min. '-..
-0.3 -- I
0.1 profile B3
------ profile B2
-0 .0 --- profile Bl M.S.L.
0.0 ........ ................ ... M L


0 1 % / ,


-0.2
(c) Three Profiles at 352 min.
-0.3 I I -
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)





Figure 3.15: Profile Evolution from 297 min to 352 min during Experiment MT04:
(a) Comparison of the Mean Profile at 297 min with Mean Profile at 352 min, (b)
Three Profiles at 297 min, and (c) Three Profiles at 352 min. Note the erosion of the
area seaward of the bar and deposition of the area immediately landward of the bar
trough. Note also the differences in the three-dimensionalities between two elapsed
times.
















0.1


-0.0


-0.1


-0.2


-0.3
0.1


-0.0


-0.1


-0.2


-0.3

0.1


-0.0


-0.1


-0.2


-0.3


0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

DISTANCE FROM TANK END (m)


5.5 6.0


Figure 3.16: Induced Perturbation to Remove Half Part of the Bar Crest at 352 min
Wave Run during Experiment MT04: (a) Comparison of the Modified Mean Profile
with Pre-Modified Mean Profile, (b) Three Profiles before Modification, and (c) Three
Profiles after Modification


modified mean profile
........ pre-modified mean profile
M.S.L.
................ ............. ................................................... ....... ..... ........................... ..... .... ....................................... ......... .. ..... M








(a) Comparison of Mean Profiles
Ipre-modified profile
--- pre-modified profile B3
------. ------ pre-modified profile B2

--- pre-modified profile BI M.S.L.








(b) Three Profiles before Modification
imodidied profile B3
-- modified profile B3
.------ modified profile B2

-\ --- modified profile BI M.S.L.




--~




(c) Three Profiles after Modification
i-I I I I I















0.1 ........ pre-modified mean profile at 352 min.
mean profile at 407 min.
M.S.L.
0.0 -- ....- ........- ..... ...... ................... ..................................... ------------ ------------- -- ------ ---------------- ----
-0.0 ..............l.......


-0.1


-0.2

(a) Comparison of Mean Profiles
S-0.3
C 0.1 --- pre-modified profile B3
------ pre-modified profile B2
-\ ---- pre-modified profile B1 M.S.L.
> 0. ..................0 ---- .............................. ................... ..... ..... ............... .


-0.1 zw
0
--o.1 ,,,



-0.2
(b) Three Profiles before Modification at 352 min-- s .
S -0.3 i I I I
0.1 profile B3
------ profile B2

--- profile Bl M.S.L.
-0.0 ....... --
0.1








-0.3 1 ----------file
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

DISTANCE FROM TANK END (m)





Figure 3.17: Profile Evolution from 352 min to 407 min during Experiment MT04:
-... -b-- -.,,


















(a) Comparison of the Pre-Modified Mean Profile at 352 min with Mean Profile at
407 min, (b) Three Profiles before modification at 352 min, and (c) Three Profiles at
407 min. Note the complete recovery of the bar crest with a smaller rotational angle
(less than 10 degrees).








66
Figure 3.18 presents isolines of profile elevations at 545 min, which were taken

at intervals of 1 cm by placing blank yarn along the waterline as the water was

lowered. As shown in this figure, weakly 3-D berm formed responding to clockwise

3-D circulation. Also a deep and narrow channel appeared near steel side wall, which

had the same characteristics as described by Shepard et al. (1941) as the floor of the

channels was found to be decidedly irregular mainly due to the strong rip current.

Also the depositional area occupied a large portion of the surf zone, which also can be

observed in the field near shoal areas. It can be seen that the bar rotated clockwise

as the results of clockwise 3-D circulation flowing from the depositional area to the

channel. The maximum cross-tank difference of the profile elevations between the

two sides of tank was estimated to be 4.0 cm at 545 min, which was slightly smaller

than that during Experiment MT03.

The profile seemed to approach an overall 2-D equilibrium up to 614 min with a

clockwise rotated bar crest except slight deposition of sand at the area just seaward of

berm. The maximum cross-tank difference in the profile elevations remained almost

constant as 4.5 cm even though the channel, shown in Figure 3.18, became more

distinct and clear.

During 614 min to 821 min, the area seaward of the bar maintained its slope as
1:7 with actually no changes. The berm built up rapidly in the same manner as the

profile at 545 min during Experiment MT03, as shown in Figure 3.9. However, the

slope of the beach face remained almost constant as 1:7, which was approximately

the same as that of the area seaward of the bar. The overall slope of the profile after

821 min was about 1:10, which was actually the same as that of final profile during
Experiment MT03.

In summary, this experiment was carried out to investigate the effects of induced

perturbations in the bar topography on the profile evolution and resulting equilibrium.

When profile modifications such as deepening of the bar trough, asymmetric area




























(a) Isolines at Shoreward Area


(b) Isolines near the Bar Region


Figure 3.18: Isolines of Profile Elevations at 545 min during Experiment MT04.
These photographs showed: (1) the weak 3-D bcrm, (2) deep and narrow channel
near steel side wall, (3) depositional area occupying large portion of the surf zone,
and (4) clockwise rotation of the bar. Elevation contours were established by placing
back yarn at waterline during lowering of water level.







68
seaward of the bar, and removing half the bar crest were imposed on the 2-D profile

sequentially at 69, 138 and 352 min, respectively, it was found that the profiles were

stable against those perturbations and returned to the previous 2-D profiles before

modification when waves were resumed.

The 3-D flows appeared after 160 min and started to rotate the bar by about 20

degrees. These 3-D flows were then reinforced by a sedimentary feedback, resulting in

a rapid net landward sand transport. This stage was reminiscent of the morphology

associated with rip currents (see Figure 3.18).

The profiles seemed to approach a 2-D equilibrium up to 614 min with rotated

bar crest line except slight deposition of sand at the area landward of the bar trough.
After 614 min, the bar started to move seaward with fairly smaller rotation angle

(less than 10 degrees). The overall slope of the profile after 821 min was estimated

to be 1:10, which was actually the same as that of the final profile of Experiment

MT03. The slope of the beach face was estimated to be 1:7, which was approximately
the same as that of the area seaward of the bar.

Experiment MT05

Experiment MT05 was conducted with an initially planar profile perturbed by a

3-D berm to investigate whether or not resulting 3-D flows in the beach face would

facilitate the occurrence of the three-dimensionality, and was continued further to

investigate profile equilibrium. Figure 3.19 shows the initial profile with the 3-D

berm for Experiment MT05. The elevation difference at the two sides of the tank

was about 4.0 cm. This experiment also investigated the effects of an elevated water

table in the berm (+11.0 cm above Mean Sea Level).
During the first 23 min, the initially 3-D berm changed to fairly 2-D without

inducing any noticeable 3-D circulation inside the surf zone, which indicated that the

beach morphology was again stable against perturbations during the initial phases of

the experiment.








69

0.15
_-- mean profile
S 0--- profile B3
S 0.05 ------ profile B2
0.0 -- -- profile B1
-0.00 --- ............. M.S.L.

> -0.05
0
-0.10 -

O
S-0.15
E-
S-0.20

-0.25 TANK BOTTOM

-0.30 1 i I it
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)


Figure 3.19: Initial Profile with 3-D Berm Area for Experiment MT05


The profile seemed to approach an equilibrium at 207 min. The results were

almost the same as those of previous experiments, which implied that neither the

effect of elevated water table level in the berm nor that of an initially 3-D berm was

significant in this fine sand experiment.

3-D features appeared to start during 207 to 242 min, which was almost the same

as the previous experiments. After 297 min, the bar rotated in counter-clockwise

direction about 20 degrees and maintained its angle up to 407 min although 3-D

circulation appeared to be reinforced by sedimentary feedback continuously. The

three-dimensionality inside the surf zone continuously increased up to 407 min. The

maximum cross-tank differences in profile elevations inside the surf zone were esti-

mated to be 5 cm at 407 min. The deepest part was located along the glass side wall

of the tank, which could be expected from the counter-clockwise rotation of the bar

crest, and this deep channel resembled a rip channel morphology.








70
0.15
profile B3
S 0.10 .---- profile B2

S0.05 ,- --- profile BI
....-............- initial profile
S ........... .... .M.S.L.
> -0.00
S-0.05 .....

S-0.10 A

S-0.15 i

r -0.20

-0.25 X
-0.25 TANK BOTTOM -
-0.30 i 1 1 --
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)
Figure 3.20: Initial Profile and Three Profile Bi, B2 and B3 at 476 min during
Experiment MT05. Note dominantly 2-D morphology.


During 407 to 476 min, the profile changed to a fairly 2-D, as shown in Figure 3.20,

which appeared to be associated with a fairly strong 3-D circulation. This strong 3-D

circulation transported sands from the area seaward of the bar to the area immediately

landward of the bar trough and distributed sands evenly over that area across the

tank. However, the return channel near the glass side wall of the tank remained with

approximate dimensions of 6 cm depth below the mean profile and 8 cm width.

During 476 to 614 min, the 3-D circulation has been continuously reinforced

by the sedimentary feedback, resulting in very strong onshore transport. As strong

landward transport occurred continuously, the channel finally filled in while the profile

remained in a fairly 2-D. This strong landward transport resulted in the landward

movement of the bar and a rapid build up of the berm with another peak which

moved seaward, as shown in Figure 3.21.

The overall slope of the profile after 545 min was approximated as 1:10, which

resembled those of final profiles during Experiment MT03 and Experiment MT04.









0.15
S614 min.
S0.10 -- 545 min.
S0.05 ---- 476 min.
.. ............... initial profile
cii -M.S.L.
S -0.00 -- ........ ............. .. .................M .S.L............................. ...... ....... ......... .

> -0.05 *".
O
0 -0.10 \

S-0.15 -
E-\
-0.20 -

-0.25 TANK BOTTOM -- ----

-0.30 I I 1
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)
Figure 3.21: Mean Profile Evolution during Experiment MT05. Elapsed Times = 0
(Initial Profile), 476, 545 and 614 min. Note rapid change during 545 to 614 min
with landward movement of the bar and another peak of the berm. However, the
overall shape of the profile was surprisingly unchanged.


The slope of the berm was estimated to be 1:7, which was again approximately the

same as that of the area seaward of the bar. Even though the profile changed sub-

stantially during 545 to 614 min, the overall shape of the profile at 614 min remained

approximately the same as that at 545 min, as shown in Figure 3.21.

During 614 to 890 min, the new berm built up continuously, resulting in steeper

slope of about 1:5. The area seaward of the bar eroded substantially due to landward

transport with a slope of 1:5.5, which was again similar to that of the berm. The

bar moved offshore at the initial times and, at the later times, remained stationary

and changed to almost 2-D feature with rotation angle less than 10 degrees. As

time approached 890 min, profiles appeared to approach an another intermediate

equilibrium.

During 890 to 1028 min, the berm eroded slightly at the initial times and main-

tained its form with a slope of about 1:5, as shown in Figure 3.22. The bar moved








72
0.15
1028 min.
S010 --- 959 min.
0.05 /.--- 890 min.
...... ---- initial profile
c oo M.S.L.
0.00 .......-.........-.......> .................... . .. ........_ M ...
S-0.00 --r

> -0.05 -
0
< -0.10 o-

-0.15 .

> -0.20

-0.25 '*'
-0.25 TANK BOTTOM "

-0.30 1 1 1 1I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)
Figure 3.22: Mean Profile Evolution during Experiment MT05. Elapsed Times = 0
(Initial Profile), 890, 959 and 1028 min. Note the back-and-forth movement of the
bar, otherwise the profiles approached an equilibrium.


back-and-forth with increased rotation angle of about 15 degrees. However, the pro-

files appeared overall 2-D. The slope of the area seaward of the bar changed from

1:5.5 to 1:4.5. The bar moved onshore if slope was near 1:4.5, while the bar moved

offshore if slope was near 1:5.5; these implied the equilibrium slope of 1:5.

After 1028 min, the profile approached an equilibrium with overall 2-D morphol-

ogy except the oscillation of the bar.

Experiment MT06

Experiment MT06 was carried out with a more highly elevated water table in the

berm (+16.5 cm) since moderately elevated water table during Experiment MT05

appeared to produce no effects on the profile evolution and 3-D morphology.

Up to 138 min, the trend was the same as the previous experiments as the profile

approached an overall 2-D equilibrium. Berm built up rapidly with onshore transport

at the initial times. Bar moved offshore at the initial times and moved onshore back

at the later times.








73
From 138 min to 207 min, the bar remained stationary. At the later stages (about

180 min), the bar rotated quickly and a 3-D feature appeared immediately landward

of the bar trough. At 207 min, the bar rotated approximately 25 degrees. The three-

dimensionality at this experiment occurred earlier (about 180 min) than previous

experiments, which might imply that the elevated high water table accelerated the

beach profile evolution as it caused more active transport by reducing the stability of

the bottom particles.

During 207 min to 242 min, the bar remained stationary. However, as the bar

trough became shallow and the area seaward of the bar eroded mildly, weak on-

shore transport continued and the overall three-dimensionality inside the bar region

increased continuously.

During 242 min to 476 min, as shown in Figure 3.23, the bar moved slightly

onshore at the initial times and stayed stationary at the later times. The bar trough

deepened considerably and rapidly during the first 30 min and maintained its depth

later. The area seaward of the bar eroded continuously and the sand eroded was

carried up and deposited on the depositional area immediately landward of the bar

trough. Up to 352 min, the overall three-dimensionality increased continuously. Ta-

ble 3.2 presents a summary of the maximum cross-tank differences of the profile

elevations at the two sides of the tank at 352 min. As strong onshore transport

continued during this time, the depositional area continued to grow up and to move

onshore, resulting in a deep channel across the tank at about the mean water line at

476 min.

During 476 min to 614 min, the depositional area moved continuously landward,

as observed in the previous experiments. However, it should be noted during this time

that the overall shapes of the profiles amazingly agreed well with those of Experiment

MT05, as shown in Figure 3.24 which presents a comparison of mean profiles at 614

min.











0.15

0.10

0.05

-0.00

-0.05

-0.10

-0.15

-0.20

-0.25


-0.30 1 I
0.0 0.5 1.0 1.5


2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0


DISTANCE FROM TANK END (m)

Figure 3.23: Mean Profile Evolution during Experiment MT06. Elapsed Times = 0
(Initial Profile), 242, 352 and 476 min. Note the deep channel across the tank at
about the mean water line at 476 min.

0.15
Experiment MT06
010 ----- Experiment MT05



S o.oo -................ ................. _

> -0.05 -
O


Z
o 0

S-0.15

-0.20

-0.25 -
-0TANK BOTTOM

-0.30 I I I I I I


0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
DISTANCE FROM TANK END (m)


5.0 5.5 6.0


Figure 3.24: Comparison of the Mean Profile at 614 min during Experiment MT05
with that during Experiment MT06. Note good agreement of the overall shape.











Table 3.2: Maximum Cross-Tank Differences of the Profile Elevations at 352 min
during Experiment MT06
Region Location Maximum
(m) Difference (cm)
berm 0.5 2.0
shoreline 0.9 3.5
depositional area 1.8 4.5
bar trough 2.3 6.0
bar crest 2.5 3.5


During 614 to 683 min, the depositional area finally attached to the berm, result-

ing in a large increase in the size of the berm and another peak of the berm moving

seaward, as shown in Figure 3.25. Also the 3-D profile returned to a fairly 2-D one

except the bar rotation of about 15 degrees and a narrow deep channel on the glass

side wall of the tank. The water depth of the channel was estimated to be 7.0 cm,

which was about 3.5 cm below its surroundings. The slope of the area seaward of the

bar at 683 min was estimated to be 1:4.7, which was much steeper than that of the

beach face (about 1:7.3).

During 683 min to 890 min, the bar moved onshore very quickly at the initial

times since the slope of the area seaward of the bar was steeper than 1:5, as presented

in the results of Experiment MT05. Hence, the back-and-forth movement of the

bar around the slope of 1:5 was expected. However, the slope of the offshore area

continuously reduced to 1:6.5 at 752 min, and finally to about 1:11 after 890 min,

as shown in Figure 3.26. Also the slope of the beach face reduced from 1:4 at 752

min to 1:11 at 890 min continuously. Even the bar moved onshore, strong offshore

transport occurred at the initial times, which resulted in erosion of the berm area and

deposition of the offshore area of the bar. During this time, the bar moved onshore

slightly and profile remained fairly 2-D. After 890 min, the profile approached an

equilibrium with the overall slope of about 1:12.











0.15
683 min.
0.10 ----- 614 min.

S 0.05 ----- initial profile

M.S.L.
0 .0 0 .................................... ... .. .......... ... ... ...... ... ................ -- -..................
-y 0.0 0** ---- :*---- -- -- -- .---...--.---. ..-*...- --.--- ---. --. *..------.

> -0.05

-0.10 -
z
o
S-0.15 -

W 0.20

-0.25
-025 TANK BOTTOM -

-0.30 I I
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)
Figure 3.25: Mean Profile Evolution during Experiment MT06. Elapsed Times = 0
(Initial Profile), 614 and 683 min. Note the large berm with peak moving seaward at
683 min.


It appeared that the elevated high water table had accelerated the beach profile

evolution at the initial times as it facilitated sediment transport by destabilizing the

bottom particles, resulting in earlier occurrence of the three-dimensionality than the

previous experiments. Then the profile evolved as the same way as the previous

experiments without introducing any significant effects of the highly elevated water

table. However, when the profile became steeper, the elevated high water table level

seemed to affect the profile evolution, resulting in the milder equilibrium slope.

















0.15



0.10



0.05


-0.00



-0.05


-0.10



-0.15



-0.20


-0.25 '
TANK BOTTOM

-0.30 I I i
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
DISTANCE FROM TANK END (m)









Figure 3.26: Mean Profile Evolution during Experiment MT06. Elapsed Times = 0
(Initial Profile), 683, 752, 890 and 1166 min. Note that the profile approached an
equilibrium with reduced overall slope.







78
3.5 Summary and Conclusions

3.5.1 Summary

A series of movable bed tests was carried out in a tank approximately 15.5 m

long, 0.9 m high and 0.6 m wide. The beach was formed of sand of median diameter

0.21 mm to an initial slope of 1:18. Regular waves of 0.11 m height and 1.5 sec period

were used in the experiments. Based on the profile classification criteria, presented

in Chapter 2, the bar would form under above experimental conditions. Profiles were

documented at various times using a modified point gage by measuring three profile

lines along the tank centerline and at quarter positions across the tank. The profiles

were documented at locations spaced at 0.1 m along each of these lines.

Six experiments were carried out to investigate various possible interrelationships

and causes of the three-dimensionality. The following were examined: (1) Effects of

an induced perturbation in the bar topography, (2) Elevated water table in the berm,

and (3) An initially 3-D berm.

Experiment MTO1 was conducted to investigate whether or not 3-D features

might occur inside the surf zone and to provide the reference for future tests.

At the initial stages, the bar formed quickly as expected, but also the berm built

up. Profiles approached an equilibrium at 240 min with overall 2-D conditions. After

about 270 min, 3-D circulation occurred inside the surf zone after a level of profile

stability had occurred at 242 min. This 3-D flows were generally weak to transport
the sands at the initial times. However, later they were reinforced by sedimentary

feedback so that they could transport the sediments onshore, thus initiating a new

stage of profile evolution, which was reminiscent of a bar morphology with a rip

current present.

Experiment MT02 was conducted to investigate the effects of microorganisms

inside the beach subjected to prolonged submergence. Hence, this experiment was

started immediately after the last wave run for Experiment MT01, at which time







79
the biological film inside sand was believed to be ineffective in clogging the sands.

Generally the trend of the profile evolution was similar to that during Experiment

MT01, which provided the experimental repeatability rather than proving the ef-

fects of microorganisms. Although three-dimensionality at this experiment occurred

slightly earlier at 240 min than that at Experiment MT01, no clear conclusions could

be drawn to the effects of microorganisms.

Experiment MT03 was designed to investigate the effect of required time for the

beach system to reach steady-state conditioned with continuous wave run. Hence,

the wave was run without intermission during 207 min. After 207 min, however,

the wavemaker malfunctioned, resulting in interruption of the experiment. Three-

dimensionality at Experiment MT03 occurred at the same time (240 min) as Exper-

iment MT02, which implied that the effect of continuous wave run was unexpectedly

small.

This experiment was continued beyond 407 min to investigate equilibrium of the

profile evolution. After 407 min, the area seaward of the bar eroded continuously

and the eroded sand was deposited immediately landward of the bar trough. This

depositional area changed from an overall 3-D to 2-D character except for a very

narrow deep channel near one side of tank, the maximum depth of which was found

to be about 5.0 cm below the mean profile.

Experiment MT04 was carried out to investigate the effect of induced perturba-

tions in the bar topography on the profile evolution and resulting equilibrium. Profile

modifications such as deepening of the bar trough, asymmetric area seaward of the

bar, and removing half the bar crest were imposed on the 2-D profile sequentially at

69, 138 and 352 min, respectively. Surprisingly, the profiles returned to the previous

2-D profiles when waves were resumed; hence, the profiles were stable against the

perturbations during the initial stages of the profile evolution.







80
The 3-D flows appeared after 160 min and started to rotate the bar by about

20 degrees. These 3-D flows were then reinforced by a sedimentary feedback, result-

ing in a rapid net landward sand transport. This stage was reminiscent of the bar

morphology associated with rip currents (see Figure 3.18).

The profiles seemed to approach a 2-D equilibrium up to 614 min with rotated

bar crest line except slight deposition of sand at the area landward of the bar trough.

After 614 min, the bar started to move seaward with a fairly small rotation angle less
than 10 degrees. The overall slope of the profile after 821 min was estimated to be

1:10, which was actually the same as that of the final profile of Experiment MT03.

The slope of the beach face was estimated to be 1:7, which was approximately the

same as that of the area seaward of the bar.

Experiment MT05 was carried out to investigate the effect of an initially 3-D
berm with moderately elevated high water table in the berm. During the first 23 min,

the 3-D berm changed to approximately 2-D without introducing any noticeable 3-

D circulation inside the surf zone; this again indicated that the morphology was

stable during mne initial phases of the experiment. The magnitude of the berm,

however, was somewhat larger than that of previous experiments due to initially

deposited sand. The profile seemed to approach an equilibrium up to 207 min and

the results were almost the same as those of previous experiments, which meant that

the effects of moderately elevated high water table level was negligible for these fine
sand experiments.

Three-dimensionality appeared to start during 207 to 242 min, which was almost

the same as the previous experiments. From 242 to 545 min, the bar rotated again 20

degrees and maintained its angle up to 407 min. The maximum cross-tank difference

of the 3-D features inside the surf zone was about 5.0 cm and occurred at 407 min.

The deepest profile was located at the narrow channel on one side of the tank. During

407 to 476 min, 3-D depositional area changed to a fairly 2-D one. The overall slope




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