• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 List of Figures
 List of Tables
 Introduction
 Physical modeling of cross-shore...
 Cross-shore transport hydrodyn...
 Concentration model
 Cross-shore sediment transport...
 Summary, conclusions and recom...
 Appendix A: Breaking wave...
 Appendix B: Moments of the velocity...
 Bibliography
 Biiographical sketch






Group Title: Technical report – University of Florida. Coastal and Oceanographic Engineering Program ; 97
Title: Hydrodynamics and profile response due to cross-shore processes in the surf zone
CITATION PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00075324/00001
 Material Information
Title: Hydrodynamics and profile response due to cross-shore processes in the surf zone
Physical Description: xii, 202 leaves : ill. ; 29 cm.
Language: English
Creator: Srinivas, Rajesh, 1964-
Publication Date: 1993
 Subjects
Subject: Coastal and Oceanographic Engineering thesis Ph.D   ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1993.
Bibliography: Includes bibliographical references (leaves 192-201).
General Note: Typescript.
General Note: Vita.
Funding: Technical report (University of Florida. Coastal and Oceanographic Engineering Dept.) ;
Statement of Responsibility: by Rajesh Srinivas.
 Record Information
Bibliographic ID: UF00075324
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 - 001950917
oclc - 31200873
notis - AKC7459

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Title Page
    Acknowledgement
        Acknowledgement
    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 Tables
        List of Tables
    Introduction
        Page 1
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    Physical modeling of cross-shore sediment transport
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    Cross-shore transport hydrodynamics
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    Concentration model
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    Cross-shore sediment transport model
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    Summary, conclusions and recommendations
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    Appendix A: Breaking wave model
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    Appendix B: Moments of the velocity vector
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    Bibliography
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    Biiographical sketch
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Full Text



UFL/COEL-TR/097


HYDRODYNAMICS AND PROFILE RESPONSE DUE
TO CROSS-SHORE PROCESSES IN THE SURF ZONE






by




Rajesh Srinivas


Dissertation


1993















HYDRODYNAMICS AND PROFILE RESPONSE DUE TO CROSS-SHORE
PROCESSES IN THE SURF ZONE











By

RAJESH SRINIVAS


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


1993













ACKNOWLEDGEMENTS


I would like to express my sincere gratitude and appreciation to my committee

chairman, Dr. Robert G. Dean, for providing me with inspiration for my work through

his zeal and love for coastal engineering. His unflagging spirits, constant accessibility

and valuable ideas went a long way in making my work easy and enjoyable. Even

after knowing him for so many years, he still never ceases to amaze me by the depth

of his knowledge. Similarly, Dr. Ashish Mehta's help in innumerable aspects is really

appreciated. My discussions with Dr. Robert J. Thieke went a long way in clearing

many nebulous facets of hydrodynamics. My thanks also go to Dr. D.M. Sheppard

and Dr. B.A. Christensen for serving on my committee. I am especially appreciative

of Dr. B.A. Christensen for consenting to serve on such short notice. I am also

grateful to Sidney Schofield for his invaluable overall help, Subarna Malakar for his

help with computing facilities, and Jim Joiner at the laboratory. Special thanks are

due to all staff, especially Helen Twedell and Cynthia Vey. Finally, I would like to

thank my friends and, most of all, my parents for their unqualified support and faith

in me.

This work was supported with funding provided by the Florida Department of

Natural Resources.















TABLE OF CONTENTS




ACKNOWLEDGEMENTS ............................

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

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

ABSTRACT .................... ................

CHAPTERS

1 INTRODUCTION ...............................
1.1 Surf Zone Hydrodynamics ........................
1.2 Sediment Transport Modeling ......................
1.3 Overwash Process and Relevance to Barrier Islands ..........
1.4 Objectives ................... ..............
1.5 Plan of Study ...............................


2 PHYSICAL MODELING OF CROSS-SHORE SEDIMENT
2.1 Similitude Considerations ...............
2.2 Laboratory Facility and Apparatus . . .
2.3 Investigation of Overwash ..............
2.3.1 A Brief Literature Review . . .
2.3.2 Scope of the Overwash Experiments . .
2.3.3 Procedure, Measurements and Test Conditions
2.3.4 Results .. .. ... ... .. .. ...
2.3.5 Discussion of Results ..............
2.4 Bar Formation Mechanisms ..............
2.4.1 Background ...................
2.4.2 A Brief Literature Review . . ..


TRANSPORT



.o.......
........


2.4.3 General Characteristics of Present Laboratory Experiments .


2.4.4
2.4.5
2.4.6


Correlation of Bar Characteristics and Infragravity Waves .
Effects of Wave Spectra and Height Distributions . .
Discussion of Results ......................


3 CROSS-SHORE TRANSPORT HYDRODYNAMICS .........
3.1 Background ..... ........... ....... .... ...
3.2 Convergence of Sediment Transport . . . . .
3.3 A Note on Breaking Waves ... ...................
3.4 Characteristics of Breaker Evolution . . . .
3.5 Cross-Shore Hydrodynamics Contributing to Suspended Transport
3.5.1 First-Order Contribution .. . .. . ...
3.5.2 Return Flow Model .......................


103
103
105
107
108
119
122
122









4 CONCENTRATION MODEL ........................... 132

5 CROSS-SHORE SEDIMENT TRANSPORT MODEL .......... 138
5.1 Suspended Sediment Transport ..................... 138
5.1.1 Contribution due to Intermittent Suspension ......... 138
5.1.2 Contribution due to Mean Cross-Shore Currents . ... 139
5.2 Bedload Transport ................. ......... 141
5.2.1 Transport due to Effects of the Bottom Boundary Layer 141
5.2.2 Transport due to Wave Asymmetry . . . .. 144
5.3 Parameterization of Constants . . . .. .. 147
5.4 Model Verification ................... ......... 147
5.5 Assessment of Model Limitations . . . .. .. 174
5.6 Discussion of Results ........................... 178

6 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS ....... 184
6.1 Sum m ary .. ................. ............ 184
6.2 Conclusions ....... ............ ........... 185
6.3 Recommendations for Further Work . . . .... 188

APPENDICES

A BREAKING WAVE MODEL ......................... 190

B MOMENTS OF THE VELOCITY VECTOR . . . .... 192

BIBLIOGRAPHY ................... ............. 198

BIOGRAPHICAL SKETCH ........................... 208













LIST OF FIGURES


1.1 The barrier beach as a complete system (from Godfrey, 1976). 6

2.1 Size distribution of sand used in the present study . ... 16

2.2 Schematic layout and cross-section of wave tank facility. .. 18

2.3 Field measurements of beach erosion and overwash, Leatherman
1979. . . . . . . . ... 22

2.4 Initial beach profile in the wave tank for each experiment. ... 25

2.5 Illustration of estimated rising and falling storm surges. ..... 31

2.6 Storm surge simulation used in Experiment E5. . ... 32

2.7 A regular wave train (Experiment E4) (a) seaward of the toe of
the beach (340 m), and (b) landward of the toe of the beach (240
m ). . . . . . . . ... .. 34

2.8 A regular wave train (Experiment E4) (a) seaward of the break-
point (176 m), and (b) just landward of the breakpoint (136 m). 35

2.9 A regular wave train (Experiment E4) (a) over the crest of the
barrier island (98 m), and (b) over the crest of the barrier island
(49 m ) . . . . . . . .. 36

2.10 An irregular wave train at the toe of the beach (Experiment E8). 37

2.11 Spectrum of an irregular wave train at the toe of the beach (Ex-
periment E8) ........................... 38

2.12 Experiments (a)E1 and (b)E2, Mean profiles at 00 and 18 hours. 40

2.13 Experiment E3, Profile B1, 00-06 hours . . ... 43

2.14 Experiment E3, Profile B1, 06-12 hours . . ... 44

2.15 Experiment E3, Profile Bl, 12-18 hours . . ... 45

2.16 Experiments (a)E3 and (b)E4, Mean profiles at 00 and 18 hours. 46

2.17 Experiment E3, profile variance at 18 hours . . ... 47









2.18 Experiment E5, (a)Mean profiles at 00 and 06 hours, (b)Mean
profiles at 06 and 16 hours, (a)Mean profiles at 16 and 24 hours. 49

2.19 Experiment E5, Mean profiles at 06 and 24 hours. . ... 50

2.20 Experiments (a)E6 and (b)E7, Mean profiles at 00 and 18 hours. 52

2.21 Experiments (a)E8 and (b)E9, Mean profiles at 00 and 18 hours. 54

2.22 Definition sketch of a longshore bar in a beach profile. . 59

2.23 Formation and movement of a longshore bar during the 10/82
storm at FRF, DUCK, NC (from Sallenger and Howd 1989). 66

2.24 Formation and movement of the longshore bar during 9/85 storm
at FRF, DUCK, NC (from Sallenger and Howd 1989).. .. 67

2.25 Positioning of general morphological features in the air-sea tank. 69

2.26 Case 1. x = 18m (toe of beach). (a)Measured total wave sys-
tem (b)Measured long wave (c)Energy spectrum of the total wave
system (d)Energy spectrum of long waves . . .... 73

2.27 Case 1. x = 15.5 m (just seaward of the surf zone). (a)Measured
total wave system(b)Measured long wave (c)Energy spectrum of
the total wave system (d)Energy spectrum of long waves . 75

2.28 Case 1. x = 15 m. (just inside the surf zone) (a)Measured total
wave system(b)Measured long wave (c)Energy spectrum of the
total wave system (d)Energy spectrum of long waves . .76

2.29 Case 1. x = 14 m (well inside the surf zone).(a)Measured total
wave system(b)Measured long wave (c)Energy spectrum of the
total wave system (d)Energy spectrum of long waves . .77

2.30 Case 1. x = 11.6 m nearshoree). (a)Measured total wave sys-
tem (b)Measured long wave (c)Energy spectrum of the total wave
system (d)Energy spectrum of long waves. . .. . 78

2.31 Case 1 Evolution of the bed profile 0-4.5 hours. . .. 79

2.32 Case 1: Sediment transport rates at different times for Case 1. 80

2.33 Numerical (line) and analytical (symbols) solutions for a long wave
with a frequency of 0.10 Hz on a planar (1:19) beach . .83

2.34 Case 1 (a) Measured and predicted IG wave envelope, (b) Initial
and Final (4.5 hours) bed profiles . . . .. 85

2.35 Case 2 (a) Measured and predicted IG wave envelope, (b) Initial
and Final (4.5 hours) bed profiles . . . .. 86









2.36 Case 3 (a) Measured and predicted IG wave envelope, (b) Initial
and Final (4.5 hours) bed profiles . . . .. 87

2.37 Case 4 (a) Measured and predicted IG wave envelope, (b) Initial
and Final (4.5 hours) bed profiles ............... 88

2.38 Change in bar position with changes in position of nodes and antin-
odes. . . . . . . . .. 89

2.39 Case 5, Multifrequency waves. Total and long waves and associ-
ated energy spectra at x = 18 m (toe of beach) . .... 91

2.40 Case 5, Multifrequency waves. Total and long waves and associ-
ated energy spectra at x = 12 m nearshoree). . . .... 92

2.41 Case 5 WHPD, Initial and Final bed profiles. . ... 93

2.42 Case 6 WHPD, Initial and Final bed profiles. . ... 94

2.43 Case 7 WHPD, Initial and Final bed profiles. . ... 95

2.44 Case 8 WHPD, Initial and Final bed profiles. . ... 96

2.45 Case 9 WHPD, Initial and Final bed profiles. . ... 97

2.46 Wave Height Probability Distribution Function for Cases 1 and 2. 99

2.47 Wave Height Probability Distribution Function for Cases 3 and 4. 100

3.1 Comparison of mass flux predictions and measurements (from Nadaoka
1986). ................... ............ 113

3.2 Turbulent intensities immediately below the trough level (from
Nadaoka 1986). ................... ....... 114

3.3 Irrotational and rotational velocity components in a breaking wave
(from Nadaoka 1986). ....................... 115

3.4 Suspended transport regions. . . . ... . 121

3.5 Mass flux distribution in cases without overtopping. ...... ..126

3.6 Mass flux distribution in cases with overtopping. ...... 126

3.7 Measurements of radiation stress and the mean water line gradi-
ents (from Stive and Wind 1982). . . . ... 129

4.1 Measured levels of tke (from Svendsen 1987). . . ... 135

4.2 Predictions of production, dissipation and flux of tke, Experiment
El. ................... ............... 137









5.1 Experiment El: Actual suspended sediment transport and redis-
tributed suspended sediment transport due to the weighting func-
tion . . . ... . . . .. 150

5.2 An example cumulative probability function for random waves at
the toe of the beach (x=18 m): Experiment E8. . ... 151

5.3 Experiment El: initial profile and model prediction compared with
the measured final profile ................... 154

5.4 Experiment El: initial profile and model prediction (without bed-
load) compared with the measured final profile . ... 156

5.5 Experiment El: initial profile and model prediction after 14 hours
of wave action compared to the measured final profile (after 4.5
hours) . . . . . . . .. 157

5.6 Experiment E2: initial profile and model prediction compared with
the measured final profile ................... 158

5.7 Experiment E3: initial profile and model prediction compared with
the measured final profile ................... 160

5.8 Experiment E4: initial profile and model prediction compared with
the measured final profile ................... 162

5.9 Experiment E4: initial profile and model prediction (no bedload)
compared with the measured final profile. .... . .. 163

5.10 Experiment E5: initial profile and model prediction compared with
the measured final profile ................... 165

5.11 Experiment E5: measured profile before the advent of the storm
(1.5 hours) and the model prediction after 4 hours (peak storm
tide) compared with the measured profile after 4 hours . 166

5.12 Experiment E6: initial profile and model prediction compared with
the measured final profile ................... 167

5.13 Experiment E6: initial profile and model prediction (no bedload)
compared with the measured final profile . . .. 169

5.14 Experiment E7: initial profile and model prediction compared with
the measured final profile ................... 170

5.15 Experiment E8: initial profile and model prediction compared with
the measured final profile ................... 172

5.16 Experiment E9: initial profile and model prediction compared with
the measured final profile. ................... .. 173

5.17 Model prediction for Experiment El with the friction factor in-
creased by a factor of 10. ....................... 176









5.18 Experiment El, measured profiles and model prediction with bed-
load mechanisms only. ................. ......... 177

5.19 (a)Measured local changes in elevation after 1.5 hours, and mea-
sured profiles for Experiments (b)E5 and (c)El. . ... 179












I













LIST OF TABLES


1.1 Storm surge prediction for a Category 5 hurricane at 20 locations
in Florida . . . . . . .. 7

2.1 Comparison of various approaches for determination of basic scale
ratios of coastal movable bed models (from Coastal Hydraulic
Models, CERC, 1979) ..................... 12

2.2 Experimental conditions of tests (E1-E9) of overwash study (pro-
totype units) .......................... 29

2.3 Variation in the magnitude of storm surge parameters. . 30

2.4 Bar formation criteria ........................ 61

2.5 General features of bar formation investigation experiments ... 68

2.6 Characteristics of experiments with biharmonic waves . 72

2.7 Characteristics of experiments with non biharmonic waves. 90

5.1 Parameters required in the numerical model. . . ... 147

5.2 Test conditions of Experiments E1-E9 (model units). . 153














CHAPTER 1
INTRODUCTION


A challenging aspect of many coastal and estuarine problems is the elucidation
of nearshore sediment transport as beaches are constantly evolving in response to
time-varying waves, tides, winds and nearshore currents. The increasing use of the
coastal zone has made the quantitative understanding of the causative mechanisms
of beach change and the nature of beach response essential for coastal engineers to
predict the evolution of beaches. Thus, the aspects to understanding beach behavior
involve both the prediction of nearshore hydrodynamics and the coupled prediction
of sediment transport causing beach response.
The most dynamic region in the ocean floors is the surf and runup zone. This
is the region where incoming waves break and run up the beach foreshore. Typical
widths vary from tens of meters to about a thousand meters depending on the sea
state and the bottom morphology. The bottom is characterized by sediments and
rocks of all sizes, shapes and constituents. It is not surprising that under these
circumstances there is no universal model to explain sediment transport mechanisms
and related bedforms in the cross- shore direction. In the present .work, an attempt
is made towards quantitatively accounting for some of the mechanisms causing beach
change in order to develop a simple physics-based cross-shore sediment transport
model inculcating recent developments in modeling surf zone hydrodynamics and
bottom boundary layer approximations.
1.1 Surf Zone Hydrodynamics

Waves and related phenomena in shallow water are of particular interest to coastal
engineers as they act as external forcing that shape the beach. The steepening and
deformation of waves in the nearshore region due to non-linearity, dispersivity, bottom
topography, etc., are generally well understood. However, their eventual breaking in








2
shallow water results in a number of problems in water wave mechanics which have
not been resolved rigorously and unambiguously. Specifically, in terms of sediment
transport modeling, the correct representation of surf zone hydrodynamics is most
essential as greatest morphological changes occur here. The surf zone is characterized
by motions of different types and scales including turbulence, large-scale coherent
vortical motions, infragravity waves, horizontal (rip currents) and vertical (undertow)
circulation patterns. There have been considerable advances in identification and
modeling of the majority of these surf zone flows, but the interactions are not well
understood and no single unified model exists capable of predicting all possible flows;
for example, the rate of spreading of turbulence from the free surface (due to wave
breaking), the rate of decay and the interaction of this turbulence with the bottom are
still poorly understood. Another poorly understood region is the zone immediately
shoreward of the breakpoint (transition zone) where loss of wave momentum does not
translate instantly into a pressure gradient. Turbulence produced by wave breaking
is often modeled as a wake or a mixing layer, but it is quite possible that breaking
induced turbulence is another unique type of free shear flow. Thus, some of the
related modeling is quite heuristic due to the intrinsic complex nature of turbulence.
1.2 Sediment Transport Modeling

It is generally convenient to divide sediment transport in the nearshore into two
components: longshore (shore-parallel) sediment transport and cross-shore (shore-
normal) sediment transport. Gradients in sediment transport cause changes in the
beach planform and profile. Although precise sediment transport modeling requires
accounting for both components of sediment transport, it is possible to judge the
relative importance of one with respect to the other from a rough knowledge of the site.
Longshore sediment transport determines beach planform evolution and is especially
important in the vicinity of sediment sinks (inlets), littoral barriers (including jetties
and groins) and beach nourishment fills and at sites with strong variations in wave
direction and longshore variations of wave height. Cross-shore sediment transport
determines beach profile change primarily for beaches located away from structures









and inlets. The time scales of beach change are also quite different, with major
planform evolution being on the scale of years while strong cross-shore transport and
substantial profile change can occur during a storm with associated time scales of
hours to a few days. A storm with energetic wind (short period) waves accompanied
by augmented tide levels often results in substantial cross- shore reconfiguration of the
beach profile. Broadly speaking, augmented water levels and high waves result in dune
and beachface erosion, with the eroded sediment being transported and deposited
offshore with the formation of a longshore bar. The advent of milder waves after
the storm results in post-storm recovery as the eroded sand slowly moves onshore.
Recent cases emphasizing the vulnerability of coastal communities to storm damage
were extensive beach erosion along the central Caribbean and eastern Mexico during
Hurricane Gilbert and along the northeast Caribbean and South Carolina during
Hurricane Hugo. The present work solely addresses the facet of cross-shore sediment
transport.
In contrast to numerical, modeling of beach planform evolution, which has been
actively studied for about five decades, cross-shore sediment transport (numerical)
modeling is relatively recent (~ 20 years). Cross-shore sediment transport mod-
els are, for example, essential for identifying especially susceptible areas in times of
storms and have safety implications for humans and property and the establishment
of coastal "setback lines." Cross-shore sediment transport models can be broadly
classified into two groups: closed loop and open loop models. Closed loop sediment
transport models have either an explicit or implicit assumption of a target ("equilib-
rium") profile and consider transport to be the result of and proportional to variation
from this equilibrium (e.g., Moore 1982, Kriebel and Dean 1985, Larson and Kraus
1989). The assumption of an equilibrium beach profile implies that changes in a beach
profile will diminish and eventually die out if the beach is exposed to constant forcing
for an infinite time. Equilibrium beach profiles are generally based on assumptions
of equal energy dissipation per unit volume or per unit area. Equilibrium beach con-
cepts are very useful and comparatively simpler to use as they mask the details of
specific wave-sediment interactions; however, most models in use predict only mono-









tonic beach profiles. In contrast to closed loop models, open loop models do not have
a target profile. They generally consider detailed mechanics of the flow and sediment
concentration profiles and variations of related quantities to compute sediment trans-
port and resultant changes in the profile. A standard drawback of such an approach
is the lack of model stability due to the lack of any explicit stabilizing mechansims. In
the present study, a rational, physics-based open loop cross-shore sediment transport
model is developed. The model accounts for both suspended and bedload sediment
transport. Effects of intermittent suspension, turbulence and momentum transfer due
to wave breaking, augmented mass flux in the surf zone, the bottom boundary layer,
wave asymmetry and gravity have been accommodated. Unlike most of the previous
cross-shore sediment transport models, the present model was formulated requiring
the fewest possible conditions as input: for a given beach, only the wave conditions
at the toe of the beach are required. The model computes the wave field, the required
hydrodynamics, the sediment transport and depth changes across the beach. No local
information is required as the profile response unfolds. It is mentioned that the ex-
tensive modeling required for a comprehensive model can easily lead to an unwieldy
set of components that obfuscate the essential physics of the total sediment transport
process. With this in mind, each of the processes was modeled as simply as possible.
1.3 Overwash Process and Relevance to Barrier Islands

A variety of cross-shore sediment transport models is available for predicting dune
erosion due to storms; however, the facet of overtopping and resultant overwash of
sediment has been almost completely ignored. Prediction of overwashed sand, one of
the focal points of the current study, is especially relevant for barrier islands. Over-
wash is one of the principal processes by which sediment is transported across the
barrier island. Overwash occurs when storm surges allow waves to overtop the beach
and push sand across the beach and dune zones. This results in the deposition of
sand above the normal high tide mark and the creation of barrier flats. The frequency
of occurrence of overwash depends on the frequency and magnitudes of storms and
the barrier island profile. The magnitude of overwash depends on the exposure and







5
orientation of the barrier island, wave energy, tidal range and the ecological response
of barrier island vegetation to the overwash process. The magnitude of overwash is
particularly high when storms coincide with times of high astronomical tides. Over-
wash is the process by which barrier islands maintain their relative elevations to keep
pace with rising sea levels.
Barrier islands are long, narrow, low-level offshore islands generally parallel to
the coastline. These islands are generally characterized by a beach and dunes on the
ocean side and salt marshes and estuaries on the mainland side and are bounded by
tidal inlets (natural or man- made). Figure 1.1 displays most of the geomorphological
features commonly present in barrier beaches. Most of the U.S. Atlantic coast south
of Long Island and the coast along the Gulf of Mexico is composed of barrier islands.
Gierloff-Emden reported in King (1972) that barrier islands compose over 13% of the
world's coastline. In Florida, barrier islands represent about 50% of the shoreline.
It is crucial to recognize that of all coastal island types, barrier islands are one of
the most unique, dynamic, fragile and vulnerable landforms. Long-term forcing
affecting their equilibrium include sea level rise, land subsidence and longshore drift,
while short-term forcing include storm effects. During storms, barrier islands act as
a physical barrier, protecting the mainland and bays behind them by absorbing the
brunt of the attack of waves and storm surges. However, many of the barrier islands
themselves are highly developed human habitats and protection of their beaches is a
major concern at many locations.
The National Hurricane Center, Coral Gables, Florida, has estimated the mag-
nitude of the storm surge for Category 5 hurricanes making landfall normal to the
shoreline at 20 locations in Florida. Hydrographs were predicted with the use of
SLOSH model. The locations, estimated peak surge elevation and rates of rise and
fall of the storm surge are presented in Table 1.1. The peak storm surge ranges from
3.2 m and 8 m. As the maximum crest elevation of most barrier islands typically
varies between 1.5 m and 4.5 m above mean sea level, low-level segments of the is-
lands may frequently be totally inundated under storm surges whereas islands with
higher crest elevations may experience substantial overtopping only under extreme

















o~eq



ae,



Dto
t'jo



190/




4*/ ,


00 I7
B-L1 o0


I-I--i,-t-
r= S2.i ,i


aj O N
^'~e~


O19h











Table 1.1: Storm surge prediction for a Category 5 hurricane at 20 locations in Florida

Peak Surge Rising Receding
Location Elevation Rate Rate
(m above MSL) (m/hr) (m/hr)
Pensacola Beach 3.8 1.8 5.8
Ft. Walton Beach 3.4 1.2 1.1
Panama City Beach 4.0 1.1 1.0
St. George Island 4.3 0.7 0.8
Wakulla Beach 8.0 2.8 1.3
Cedar Key 6.5 1.5 1.7
Clearwater Beach 6.1 1.8 4.4
Tampa Bay 7.8 2.3 1.4
Sarasota 5.7 1.9 2.2
Ft. Myers 6.9 1.7 2.1
Naples 6.6 1.4 2.3
Key West 3.2 0.6 0.6
Key Largo 3.4 0.9 0.7
Miami Beach 3.2 0.9 0.6
Palm Beach 3.7 1.0 0.9
Ft. Pierce 4.1 1.0 1.6
Cocoa Beach 4.4 1.0 1.1
Daytona Beach 4.0 0.6 1.2
St. Augustine 5.1 0.9 1.2



storm conditions.

Barrier islands often form a continuous beach extending, say, 3 km to 80 km

between adjoining tidal inlets. Typical inlet widths are between 100 m and 1 km. The

bay area (i.e., the waterway between the mainland and the barrier island) is connected

to the sea only through these relatively narrow inlets. Hence, there is a substantial

phase lag between the bay water level and the rapidly rising sea water level during

storms. The differential hydrostatic head could be on the order of meters depending

on the intensity and duration of the storm. If the island is already inundated, this

gradient alone creates strong currents over the crest of the barrier island from the sea

side to the bay side resulting in considerable erosion. Waves, in combination with

these currents, further increase the erosion rate. It is interesting to note that the

erosion of barrier islands can also take place with currents from the bay side to the

sea during falling storm tides as torrential rains accompanying storms pile up large

quantities of storm water within the bay area that cannot be quickly drained to the








8
sea through the narrow tidal inlets. A study of Hurricanes Carla (1961) and Cindy
(1963) by Hayes (1967) showed that channels were cut in the barrier islands in Texas
to a level below mean sea level. Significant amounts of sediment were lost from the
barrier islands to the offshore by the flow of bay waters to the sea across the barrier
island.
If barrier islands can be considered to be in long-term equilibrium, then storms
can be considered to be episodic perturbations that result in considerable cross-shore
reconfiguration.
1.4 Objectives

With the preceding discussion in mind and after a literature review revealed the
lack of predictive tools to estimate overwashed sand volumes under overtopping con-
ditions, it was decided to conduct experiments to simulate the effects of overtopping
and overwash at barrier islands in the "air-sea" wavetank facility at the Coastal and
Oceanographic Engineering Laboratory of the University of Florida. A laboratory
provides a tightly controlled' environment where important parameters and their ef-
fects may be isolated and studied, which is not readily possible in the field.
A physical model of the barrier island was developed with an initially horizontal
crest and planar beach slope. The objectives of the present investigation involved
monitoring the changes in the bed profile and identifying the resulting principal mor-
phological features produced as a result of a variety of wave and tidal conditions.
Longshore transport was minimized by using only unidirectional waves traveling nor-
mal to the shoreline. A common feature noted in all tests was surf zone erosion. As
longshore bars were commonly generated, the next key objective was the elucidation of
causative mechanisms, at least for the present conditions, for the pervasive longshore
bars. Additional experiments were conducted for this purpose. Once the fundamental
forcing were properly identified, the next objective was the modeling of hydrodynam-
ics associated with cross-shore sediment transport and modeling concentration profiles
associated with suspended load in the surf zone incorporating the additional effects of
turbulence in stirring sediment. Equations for mean cross-shore flow were formulated








9
using recent experimental evidence. Bedload mechanisms causing onshore transport
were also included as tests with overtopping conditions exhibited washover deposits
over the crest of the barrier island. Finally, the ultimate objective was the formu-
lation of a fairly comprehensive, physics-based sediment transport model including
the above features and having the capabilities of predicting overwash and surf zone
erosion and developing longshore bars.
1.5 Plan of Study

The following chapters document the investigation of the issues of overwash at
barrier islands, longshore bar formation mechanisms, modeling of surf zone hydrody-
namics and concentration profiles and the formulation of an "open loop" cross-shore
sediment transport model having the capacity for both onshore and offshore trans-
port. The sediment transport model was finally tested against data obtained from
present laboratory experiments conducted to examine overwash. The format of the
present investigation is slightly different from that prevalent: instead of having an
all-encompassing literature review for all the above aspects right in the beginning, it
was considered more logical to have literature reviews at the beginning of each of the
above aspects as they were considered sequentially.
The investigation starts with Chapter 2, which documents the present physical
modeling of the cross-shore sediment transport processes. Similitude considerations
for the construction of the physical model of a barrier island and the experimental
methodology of the present investigation including apparatus and procedure of exper-
imentation are addressed. The laboratory investigations of overwash and longshore
bar formation mechanisms are chronicled, and primary forcing and morphological
signatures are identified and discussed.
Chapter 3 is devoted to modeling the relevant hydrodynamics that are associated
with cross-shore sediment transport. Contributions to suspended transport arise from
both first and second order (in wave steepness) wave effects. The formulation of
undertow is examined and the choice of boundary conditions in different regions, as
incoming waves shoal and break, are elucidated and inculcated.







10
The issue of representation of suspended sediments is discussed in Chapter 4
and the shear velocity due to breaking waves is evaluated taking into account the
additional stirring effects of turbulence.
In Chapter 5, the equations for the numerical model of cross-shore transport
process are formulated. Simple expressions for suspended and bedload transports are
developed. The predictive capabilities of the model are tested using data from the
overwash experiments. A discussion of model results, including limitations of the
model, follows.
Finally, Chapter 6 presents a summary and documents the main conclusions of
the present study.














CHAPTER 2
PHYSICAL MODELING OF CROSS-SHORE SEDIMENT TRANSPORT


2.1 Similitude Considerations

In order to achieve similarity between the model and the prototype in beach
profile studies, several criteria have been recommended depending upon the princi-
pal phenomenon to be studied and the predominant active forces. Often, practical
considerations such as the type and size distribution of bed material available for
laboratory tests, size and capabilities of the available test facilities, funds and time
available for study and the degree of accuracy desired are the governing constraints
in laboratory investigations.
Some of the important similitude criteria recommended for scale model studies
are based on the following:

Froude Number

Densimetric Froude Number

Reynolds Number

Bed Shear Velocity

Friction Factor

Kinematic Condition (ratio of horizontal to vertical displacement of sediment
particles)

Fall Velocity

The Coastal Engineering Research Center, U.S. Army Corps of Engineers (1979),
conducted a comprehensive review of literature on similitude criteria for beach ero-
sion investigations. A summary is presented in Table 2.1. The main conclusions were













Table 2.1: Comparison of various approaches for determination of basic scale ratios
of coastal movable bed models (from Coastal Hydraulic Models, CERC, 1979).



Source Basic relations Method of derivation

Goddet and Jaffry no = /17/20f8/5 Sediment motion due to
(1960) combined action of waves
n,, = /3/20o-3/5 and currents


Valembois = n,1 Kinematic of motion of
(1960) suspended sediments
n.,n3 = 1 Similitude of D.

p= n3,no Modified relation of initiation of
sediment motion: D. = KRI19


Yalin nD = -3/4,t/2 Dimensional analysis
(1963)
nlIn3o =1


Bijker nyonD-1 = pn,, Similitude of F,
(1967) lote: This relation was
0- equilibrium beach profiles noted to be an error.


Fan and Le Mehaute nrn3 = 1 Similitude of sediment transport
(1969) characteristics, i.e., F. and R.
ny, = 3A-3/2 or no = A'11/-1

Q equilibrium beach profiles


Noda non ;, = 0.ss5 Similitude of sediment transport
(1971) characteristics, i.e., F. and R.

A =1.32 -0.386

0 equilibrium beach profiles








13
as follows. Complete similitude of all dynamic processes involved in the movement
of coastal sediment is impractical. Similitude of certain dynamic processes fixes the
relation between model and prototype linear dimensions, material characteristics and
other factors. Therefore, no particular set of scale model laws for coastal sediment
models was recommended. Each of the scale model laws given in Table 2.1 was be-
lieved to have its own special area of application, and the selection of the appropriate
set of equations for a particular problem largely depends on the experience and ex-
pertise gained by the particular group of laboratory personnel performing mobile bed
scale model tests.
Kemp and Plinston (1968) suggested a distortion relation for beach profile erosion
study:
A = (2.1)

where
S model length
prototype length
model depth
prototype depth
0.45 < a < 0.65.

Noda (1972) has given a detailed account of scale model relationships for movable
bed models. Data from experiments utilizing a number of materials and grain sizes
suggested that the following relations need to be satisfied for reasonable similitude

A = (p)132(n) -0.386 (2.2)

nD(nn)1.85 = /0.55 (2.3)

where

nD = ratio of sediment diameter in model to that in prototype

ny = ratio of relative specific weight of sediment in model to that in prototype

whereas data from experiments using sand suggested

nD = /A0.55 (2.4)

A = y1.32 (2.5)









when n, = 1.
Dean (1973) and Kohler and Galvin (1973) have identified the importance of the
dimensionless fall velocity parameter (H/wT) (now called the Dean number) as a
criterion for berm-bar formation where H and T are the wave height and period,
respectively, while w, is the sediment fall velocity. Dean (1973) also noted the rele-
vance of this parameter in modeling beach systems. Dalrymple and Thompson (1976)
conducted a series of beach profile experiments in the laboratory and confirmed that

n( )=1 (2.6)
wT
where n stands for the ratio of model to prototype, is the most promising scale
relationship for modeling of beach processes. From earlier tests on dune erosion with
two types of sand, van de Graaff (1977) found that the results of experiments with
different sands compared very well using the Dean number concept. The movable bed
model tests on dune erosion conducted by Vellinga (1978a,b) at the Delft Hydraulics
Laboratory have found that equal Dean number values in model and prototype lead
to geometrically similar beach profile development in the model.
It would be apparent from the above review of various similitude criteria that
for the scale model study of beach profiles, dimensionless fall velocity criterion (Dean
number) is the most appropriate and hence has been adopted for the present study.
It is noted that disregarding exact Reynolds number similarity can potentially cause
different flow conditions to exist in the model and the prototype. Since gravity is the
predominant force for free-surface water waves in the ocean and in the laboratory,
Froude similarity also needs to be achieved simultaneously, i.e.,

Vm = v. (2.7)


where V = velocity and d = depth; m and p denote model and prototype respectively.
This directly leads to the time relationship for geometrically similar scale models as

Tm m(2.8)

where 1 denotes the length scale.







15
According to Stokes' law, fall velocity, ws, of a sediment particle is given by

1 D2g (b 7) (2.9)
w, (2.9)
18 v 77

where

D = diameter of sediment particle

g = gravitational acceleration

v = kinematic viscosity of fluid

7, = specific weight of sediment
7f = specific weight of fluid

For the present study the prototype sediment diameter (Dp) was considered to be 0.5
mm. This corresponds to medium-sized sand which occurs on several barrier islands.
Size gradation analysis of sand available for the model study showed that the median
diameter (Dm) was 0.2 mm (Figure 2.1). Based on the standard relationship (e.g.,
Vanoni 1975) for fall velocity, ws,p ~ 0.09 m/sec and ws,m ~ 0.023 m/sec.
The dimensionless fall velocity criterion (Equation 2.6) specifies that

H H
S )= ( ) (2.10)
wT wT

whereby
Hm p (2.11)
H, Tm Wsp
Therefore, using Equation (2.8) and substituting for the fall velocities,

in /P 1 (2.12)
Ip Vlm, 4

whence
Ir 1
S= 1- (2.13)
,I 16
Hence, a geometrically similar scale of 1:16 was adopted for the present study. Thus,
all length and time scales in the prototype were 16 and 4 times those in the model,
respectively.
















GRAVEL SAND SILT


coarse


medium


fine


coarse


medium


fine


CLAY

%


%
100

90

80

70

60

50

40

30

20

10

0
1


1 u.A


U.Z U.1 U.Ub U.U4 U.U2
GRAIN SIZE (mm)


U.u1 U.Uuo


U.UUZ U.UU1


0


Figure 2.1: Size distribution of sand used in the present study.


10


- -- --- ---- -- --fj-- ---- ---- ---- --- 70U
90

- -80

1 70

- - -- ---- -- ---- --- -- ---- 0

50

___ --- -- __ --- ___ --- 40
40
Sample 1
Sample 2


- -- ------ -- -------- -- ------- __- 20

-- -- -- --I----- ____________ -~__ ______ -0
10

10

n ^ r r r A ~


U a


GRAVEL


SAND


SILT








17
2.2 Laboratory Facility and Apparatus

All experiments were conducted in the air-sea tank facility at the Coastal and
Oceanographic Engineering Laboratory of the University of Florida. The tank was
approximately 37 m long, 2 m wide and 1.9 m deep (Figure 2.2). A concrete block
wall (splitter wall) had been placed along the tank centerline dividing it into two
tanks each approximately 0.9 m wide. One outer wall was constructed of glass panels
and all experiments were conducted in this side of the tank thereby facilitating direct
observation. A wave generator was located at one end of the wave tank with hydraulic
drive pistons at two elevations allowing piston, flap or a combination of motions to be
generated. The paddle of the wavemaker was made of wood and was driven by a two-
level rod and bearing system connected to a hydraulic power unit. The wavemaker
was capable of generating regular or irregular waves. Wave signals for operating the
wavemaker were generated using a SeaSim Function Generator and a Pegasus Servo
Controller/Amplifier or an IBM-compatible PC. The wavemaker was fronted by wave
screens to prevent cross-tank variation. The splitter wall along the tank centerline
was separated from the wave maker by approximately 2 m; at the downwave end of
the tank (beyond the beach), the splitter wall was composed of concrete blocks with
horizontal openings, thereby allowing circulation around the splitter wall in cases of
overtopping. A sloping frame with artificial "horse hair" and permeable nylon bags
filled with pebbles was located at the downwave end of the tank side which was not
used for the experiments. The toe of the beach of the barrier island was about 21 m
from the wavemaker. The barrier island and beach were 18 m in extent.
Rails were located along the top of the tank and an electrically operated trolley
was mounted on the rails for transporting a carriage containing a measuring equip-
ment package along and across the wave tank. A resistance wave gage was used for
measuring wave height and period. The gage was mounted on the carriage and it
could be moved to any location within the tank for wave measurements. The wave
gage was calibrated each time before data acquisition in order to eliminate errors
caused by changes in water temperature or other factors.




























Flow


Wave, p
Board 8


CROSSSECTION


* Steel Framework
.1.9cm Thick Plate Glass

SStill Water Level
in Tank


Figure 2.2: Schematic layout and cross-section of wave tank facility.







19
An additional apparatus was required for later experiments (Section 2.4) investi-
gating the role of long waves in causing/affecting bar formation. This was a mechani-
cal filter in the form of a manometer and stilling well arrangement which recorded long
waves ("surf beat" or infragravity waves) while damping the short, primary waves.
This approach was first used by Dally (1987b) and consisted of three 5 m sections of
plastic tubing of increasing cross-sectional diameter joined together and connected to
a fourth section which acted as a stilling well. The open end of the tube with smallest
diameter served as a wave pressure sensor when placed along the bed and a resistance
wave gage was mounted inside the stilling well. This gage recorded the long waves of
the total wave system.
An automatic bed profiler mounted on the carriage was used for measuring the
beach profiles at various time intervals during the course of an experiment. An electric
motor drove the carriage at a constant speed along the length of the wave tank and,
simultaneously, the bed sensor automatically moved up or-down, closely following the
bed profile by maintaining a fixed gap, adjustable from 0.5-3 mm, between the tip of
the sensor and the bed. The direction of travel of the carriage could be reversed and
the carriage speed varied to suit the requirements of data acquisition.
Bed elevation data, as a function of distance measured with respect to a pre- de-
fined coordinate system, were stored on computer hard disks and magnetic diskettes.
A DEC PDP/11 (LSI 1103) computer was used in the overwash experiments to acquire
data, while later, more refined experiments to investigate bar formation mechanisms
used an IBM-compatible 386 PC with the GLOBLAB program for data acquisition,
display and analysis. A Data Translation 16 channel A/D converter was connected to
all the data sources and the computer. The wave data were also stored on magnetic
diskettes and were subsequently processed using either a VAX 8350 computer or an
IBM- compatible PC and plotted using a laser plotter.
Since the effects of storm waves with overtopping conditions were to be examined,
it was expected that sand from the island would be transported to the lee of the barrier
island. Hence, a spout was provided on the leeside and arrangements were made for
collection and weighing of the sand washed over the crest of the barrier island.







20
2.3 Investigation of Overwash

2.3.1 A Brief Literature Review

Several field studies have been conducted regarding geological processes, ecological
aspects and management plans for barrier islands (including Fisher 1968, Swift 1975,
Godfrey 1976 and 1978, Godfrey and Godfrey 1976, Leatherman 1977; Davis et al.
1979 and Stauble 1989).
Studies of the overwash process have been conducted almost exclusively by geolo-
gists. Early qualitative descriptions of the overwash process in the field were reported
in Johnson (1919) and Lobeck (1939). Price (1947) noted the importance of storm
surge for and defined specific terms associated with the overwash process. Hayes
(1967) discussed the effects of Hurricanes Carla (1961) and Cindy (1963) on barrier
islands in Texas. Godfrey (1970) studied the effects of the overwash process at the
Outer Banks, North Carolina (NC) and concluded that overwash was a major cause
of shoreline recession between Beaufort and Ocracoke Inlets. He also noted the fact
that overwash allowed the barrier island to maintain its dynamic equilibrium with a
rising sea level. Dolan (1972) examined barrier islands in NC where foredunes had
been constructed to lend stability. He concluded that this stabilization, which pre-
vented the overwash process from occurring, resulted in a decrease of beach width.
Dolan and Godfrey (1973) examined the effects of Hurricane Ginger (1971) on stabi-
lized and unaltered barrier islands of the Outer Banks, NC. There was severe erosion
seaward of the crest of the foredune at Cape Hatteras (stabilized) and severe erosion
of the dune at Core Banks (unaltered). Core Banks gained sand on the bayside of the
foredune line while the stabilized barrier islands did not. From pre- and post-storm
survey data, they concluded that unaltered barrier islands were better suited to with-
stand severe hurricanes. Surveys conducted about ten months after the hurricane
showed the profile at Core Banks actually gained sand due to post-storm recovery.
Leatherman (1977) reported that Assateague Island, Maryland, experienced an over-
wash deposit of the order of 2.8 m3 per m width of dune during the storm of March
1975.








21
Leatherman (1979b) documented field observations at two sites: (i) Assateague
Island, Maryland, along the mid-Atlantic coast for the December 1974 storm and (ii)
Coast Guard Beach, Nauset Spit, Cape Cod, Massachusetts, for the February 1978
storm. Figure 2.3 shows the storm-induced changes along the centerline profile. At
Assateague Island, the beach was characterized by medium-sized sand (0.3 mm) and
a beach foreshore slope of 5 degrees. The mean tidal range was 1.1 m. During the
storm of December 1, 1974, breaking waves of about 2.7 m were observed from the
shore. The calculated significant wave height was 5 m in deep water, and the storm
surge was 0.8 m. The beach experienced erosion of 10.2 m3 per m length of beach.
The dune lost 7.1 m3 per m of beach sand and the dune crest was displaced 4.6 m
landward. Dune erosion averaged from several profiles was calculated to be 5 m3 per
m of beach. An important conclusion drawn from the analysis of sand samples was
that there was no evidence of beach sediment coarsening nor steepening of the beach
profile as a result of the severe storm.
The sediments at Nauset Spit were medium-sized sand (0.4 mm), and the beach
slope was rather steep (11 degrees). The mean tidal range was 2 m. During the
storm of 6-7 February 1978, the significant deep-water wave height was about 5 m.
The nearshore breaker heights exceeded 3 m, and the maximum storm surge was
about 1.2 m. Comparisons are made here with respect to the winter (2/5/78) profile
(Figure 2.3). As a result of this storm, the berm crest receded about 20 m with
a loss of about 30 m3 per m of beach. Large quantities of sediment were pushed
across the berm by overwash surges and deposited as an overwash fan. The volume
of overwashed sand was about 102 m3 per m of beach. The overwash deposition
thickness was up to 1.7 m above the living marsh and penetration distances extended
up to 140 m landward of the dune line.
Williams (1978) conducted the only previous laboratory investigation of overwash.
The experiments were conducted in a wave tank which was 30 m long, 2.5 m wide and
1.5 m deep. Only monochromatic waves were generated. The beach was composed of
reasonably uniformly sorted sand with a median grain size of 0.21 mm. The barrier
island was simulated with an initial profile slope of 1:15 on the seaward side and 1:40
























DISTANCE FROM BASELINE (m)


Beach erosion and overwash deposition following the 1 December 1974
northeasterly storm at Assateague Island, Md.


E
Z 3.00 -
0
2.50 -
4
2.00 .

1.50 -

> 1.00 -

S0.50

40 35


30 25 20 15 10 5 0 5w 10 15 20 25 30 35
DISTANCE (m)

6 -7 February 1978 northeasterly storm resulted In severe beach erosion
and overwash deposition at Coast Guard Beach, Nauset Spit, Ma.


Figure 2.3: Field measurements of beach erosion and overwash, Leatherman 1979.


E 3.0

() 2.5

W 2.0
0
S1.5
z
0 1.0

> 0.5
w a
-'VI


130







23
slope landward of the beach crest. Each test comprised three phases. The first phase
was the formation of an equilibrium profile. This generally required a period of six
to ten hours. After the formation of the equilibrium profile, the water level in the
tank was increased gradually in the second phase to a level at which overwashing of
the beach crest commenced due to wave runup. In the third phase, the storm surge
level was increased further by about 10 to 25% of the vertical difference between the
dune crest-elevation and the water level at which overwash commenced. The tests
were then carried out until overwash had occurred to the point that the resulting
deposits prevented further overwash. The washover deposits exhibited some three-
dimensionality in the relatively wide (2.5 m) tank. In all, 22 tests were conducted and
the results from the best 10 tests were utilized to evaluate two proposed relationships
for predicting the washover volumes. It was found that the predictive relationship
was better for larger washover volumes. The best fit line agreed with the laboratory
data to within approximately 50%.
The first model considered the overwash transport rate, q,, to be proportional to
the excess runup raised to an exponent a, i.e.,

= -(A(t) A.)" (2.14)

where q, is the volumetric sediment discharge rate per unit width and K1 is a dimen-
sional coefficient. A(t) is the excess runup in the elapsed time defined as the difference
in elevation between the potential runup and the crest of the dune or structure, A.
is the critical excess runup defined as the minimum height which the potential runup
must exceed the crest of the dune for sand to be transported and T was the wave pe-
riod. The second model expressed the overwash sediment transport rate as a rapidly
increasingly function for small values of excess runup and asymptotically approaches
zero for larger values of runup:

qs = (A(t) A.)e-K3(A()-A) (2.15)

where K2 and K3 were dimensional coefficients.
A non-linear least-squares fit was used to determine the coefficients for both the







24
relationships. No attempt was made to apply the predictive relationship to proto-
type events because the method required data on the time- varying storm surge and
assumed that the dune height was constant during the event.
The values of the coefficients were quantified as follows:

Model I: K1 = 0.09 a = 0.04 A. = 0.4
Model II: K2 = 0.24 K3 = 0.66 A. = 0.32

Other laboratory studies with particular emphasis on overwash are not available.
The results of field investigations and model studies are often used to calibrate and
supplement the analytical expressions developed for achieving predictive capabilities.
Theoretical developments relative to overwash and beach erosion may be classified in
two areas, namely, hydrodynamics of breaking waves and sediment-wave interaction.
Hydrodynamics associated with wave breaking inside the surf zone have been stud-
ied by several'researchers including Dally (1980), Dally and Dean (1984), Svendsen
(1984a, b), Dally et al. (1985), Stive and Battjes (1985), Stive and Wind (1986) and
Stive (1988). Models of sediment-wave interaction have been given by Kemp (1960),
Inman and Bagnold (1963), Meyer (1972), Dean (1973), Swart (1976), Bowen (1980),
Bailard (1981), Bailard and Inman (1981) and Trowbridge and Young (1989) among
others. Pertinent models for wave-induced hydrodynamics and sediment transport
are reviewed later as required, in Chapters 3, 4 and 5.
2.3.2 Scope of the Overwash Experiments

The objective of this stage of the present laboratory study was to measure changes
in the profile of a barrier island due to storm waves with various sea levels including
those which cause overtopping and inundation and concomitant overwash.
The topography of barrier islands prone to overwash can vary substantially,
though low-relief barrier islands will be more prone to substantial overtopping dur-
ing storm surges. The present laboratory study was not intended to be site-specific.
Instead, a hypothetical barrier island with an arbitrary crest width of 122 m and a
beach slope of 1:19 was considered for simulation. All dimensions in the overwash









4.0-

2.0-

g 0.0-
z
I -2.0-

I -4.0-

-6.0-

-8.0-

-10.0- i
0 100 200 300
DISTANCE (M)

Figure 2.4: Initial beach profile in the wave tank for each experiment.

study (only) are in prototype units unless otherwise mentioned. As discussed in Sec-
tion 2.1, a geometrically similar scale of 1:16 was adopted for the present study. The
laboratory studies were conducted in a wave tank facility which was described in
Section 2.2. The wave direction was always normal to the beach. Experiments were
conducted for different sea water levels and both regular as well as irregular waves
were simulated. For each experiment, the initial beach profile was linear from the
crest of the barrier island to the toe (as shown in Figure 2.4). This provided a com-
mon reference profile for comparison of profiles obtained under different experimental
conditions.
Vegetation on the barrier island could have a significant effect on the magnitude
of erosion and overwash at some of the field sites, however, this factor was not taken
into account in the present study and all the experiments reported here were carried
out to represent barrier islands with no significant effects of vegetation. Also, the
ecological aspects related to erosion and deposition have not been considered in the
present study. The bay water level was the same as the sea water level in the present









study.
The nominal characteristics of the prototype for the nine experiments conducted
in this stage were as described below:

Initial crest elevation of barrier island The entire island had an elevation of
1.9 m above the still water level for all the experiments.

Initial beach profile Linear with 1:19 slope, constant for all tests.

Water depth at toe of beach 7.3 m below mean sea level.

Sediment Fine sand with a median diameter of 0.2 mm (see Figure 2.1). No
shells or protective armor layer were included.

Still water level The following water levels were used to simulate storm con-
ditions:

1. Mean Sea Level (MSL), referred to as zero.

2. 1.9 in above MSL (same as the island crest): "marginal" overtopping.

3. 3 m above MSL (causing complete inundation): "moderate" overtopping.

4. 3.5 m above MSL (causing complete inundation): "severe" overtopping.

5. Time-varying water level with peak surge of 3.4 m.

Incident waves (storm conditions):

1. Regular waves with a height of 2.6 m and a period of 8 seconds.

2. Irregular waves with a mean period of 8 seconds and a range of 7.6-8.4
seconds (narrow-banded spectrum) with a maximum height of 2.6 m.

Time of wave action 18 hours.

2.3.3 Procedure, Measurements and Test Conditions

As previously mentioned, in the following description of the overwash experiments,
unless noted otherwise, all quantities are presented in prototype units. Thus, all the







27
model data have been converted to equivalent prototype values in all beach profile
plots for convenience of interpretation. Experiments were conducted in the wave tank
for examining the reconfiguration of an initially horizontal crested barrier island with
a planar beach subjected to regular and irregular waves and different water levels.
The initial profile of the barrier island was first laid out on the glass walls of
the side of the wave tank. This outline helped in the construction of the profile. A
vertical scale was affixed on the glass side wall at the position of the toe of the beach
for monitoring the water level and for rough measurements of wave heights.
The barrier island was molded to conform to the initial profile, as specified in
Figure 2.4, with the help of trowels, shovels and the human hand. Compaction of
sand was achieved by spraying water on the sand and stepping on the sand repeatedly
until the profile was smooth. The next step was filling the wave tank to the desired
level with water using the city water supply.
The wave gage was calibrated before the start of each experiment by immersing
known depths of the resistance wire on the gage in water and recording the corre-
sponding voltages on the computer. A least-squares procedure was utilized to fit
a straight line through the calibration points and establish the voltage to depth of
immersion (linear) relationship.
The laboratory measurements included the following:

Each experiment was started with a remolded linear profile from the crest of
the island to the toe of beach as shown in Figure 2.4. The crest of the barrier
island was horizontal and the entire profile was measured at the beginning of
each experiment.

Under wave action, the initial linear profile was changing with time during the
course of an experiment. The resulting beach profiles were measured in the wave
tank at intervals of 30 minutes (model units) using a bed profiler which provided
data on bed elevation as a function of distance. The number of measured bed
profiles for each experiment ranged from at least 2 to a maximum of 9, depending
upon the reach and the variability of bed forms. Two profiles, designated as B1








28
and B2, were measured covering the entire length of the barrier island and the
beach. Profile B1 was 0.25 m from the glass side wall while profile B2 was 0.25
m from the splitter side wall. In addition, for some of the experiments, where a
three-dimensional bed pattern was noticed visually, an additional seven profiles
were measured over a smaller area of the tank where the three-dimensional
feature was evident.

Wave heights were measured at various locations along the flume.

Wave induced surface currents over the barrier island were measured using
weighted floats in those cases where the barrier island was submerged.

The weight of sand transported over the crest of the island was measured every
30 minutes (model units) by collecting it in a bucket and weighing it on a plat-
form balance. These measurements were made only in those tests when the crest
of the island was totally submerged with accompanying overwash. However, the
maximum amount of sand collected over the extent of any experiment was only
~ 18 kg as most of the transported sand was in suspension which caused it to
be transported over and across the sand trap. The measured weights were thus
discounted and are not mentioned hereafter.

In all, nine experiments were conducted during the course of the study. The ex-
perimental conditions of these tests are summarized in Table 2.2. These experiments
were divided into the following three groups.
Group 1 Experiments El to E4
Under this group, the effect of raising the sea water level from MSL to complete
inundation of the barrier island (as can often occur under high storm surges) was
studied. These experiments were conducted with the water level at MSL, 1.9 m
above MSL which corresponded to the crest level of the barrier island, 3.0 m above
MSL (1.1 m inundation of island) and 3.5 m above MSL (1.6 m inundation of island),
respectively. Regular waves with nominal dimensions of 2.6 m height and 8 seconds
period were allowed to impinge upon the beach and each experiment was conducted











Table 2.2: Experimental conditions of tests (E1-E9) of overwash study (prototype
units).


Water Level Wave Characteristics
Expt. No. Duration Level Type Height Period
(hrs) (ft) (ft) (sec)

1 0--18 MSL Regular 7.0 8.0 '

2 0--18 +6.3 Regular 8.5 8.0

3 0--18 +10.0 Regular 8.5 8.0

4 0-22 +11.5 Regular 8.5 8.0

5 0--6 MSL Regular 8.5 8.0
6--8 +0.5
8--10 +2.90
10--12 +6.82
12--14 +10.24
14--16 +11.30
16--18 +10.24
18--20 +6.82
20--22 +2.90
22--24 +0.50

6 0--22 MSL Random 7.0 7.6

7 0--18 6.3 Random 7.0 8.0

8 0--18 +10.0 Random 7.0 8.0

9 0--18 +11.5 Random 7.0 8.0










Table 2.3: Variation in the magnitude of storm surge parameters.
Condition Minimum Maximum
Peak storm surge 3.2 m 7.8 m
Rising rate 0.6 m/hr 2.3 m/hr
Receding rate 0.6 m/hr 5.8 m/hr


over a duration of 18 hours of prototype time which is equivalent to 4.5 hours model
time. The duration of test was based on two criteria: 18 hours represent a fairly
long duration for a severe storm, and the model beach profiles were seen to attain
quasi-equilibrium and not significantly change beyond this test duration.
Group 2 Experiment E5
Experiments under Group 1 and Group 3 were conducted under conditions of a
steady storm surge level for 18 hours. In nature, the maximum storm surge level may
not last longer than one or two hours. Three examples of storm.surge estimates made
by the National Hurricane Center are shown in Figure 2.5 where zero hours denotes
the instant of landfall. At Tampa Bay, the rate of rise of water level is 2.3 m/hour
and the rate of fall is 1.4 m/hour. At Pensacola, the rate of rise (1.8 m/hour) is
slower than the rate of fall (5.8 m/hour) whereas the rates are equal for Key West
(0.6 m/hour). The range of variation in the magnitudes as seen from Figure 2.5 is
presented in Table 2.3. For purposes of preliminary study, equal rising and receding
rates of 0.39 m/hour and a peak storm surge of 3.5 m above MSL were considered
for simulation. Only one experiment was conducted which consisted of simulation
of a storm surge hydrograph instead of a steady storm surge level. The effect was
simulated by a series of stepped increases and decreases of the water level with each
time step lasting two hours. The beach was first allowed to reach near-equilibrium by
subjecting it to waves at MSL conditions for 6 hours before the onset of the storm.
The storm surge simulation (after the aforementioned 6 hours) used in Experiment
E5 is shown in Figure 2.6.
Group 3 Experiments E6 to E9
Under this group, irregular waves were used with nominal dimensions of significant
wave height and mean zero crossing period equivalent to 2.1 m and about 8 seconds,












I 9
Ca
3 Tampa Bay (ENE -15 mph C5)
ME


I--



0 3 I ML

S9- b
(^ Pensacola Beach (N 15 mph C5)
E

w, 6

3-
Iw
OC
cc 3
O



- 9
0 Key West NN -12 mph C5)
HOURS AFTER LANDFALL

0-s 3


0
I--







o- 7- 12 MSL
-48 -36 -24 -12 0 12 24
HOURS AFTER LANDFALL


Figure 2.5: Illustration of estimated rising and falling storm surges.



















4.0-





Li.1
3. 0-
/




0






S 4 12 16 20 2
TIME (HOURS)
TIME (HOURS)


Figure 2.6: Storm surge simulation used in Experiment E5.







33
respectively, .i.e., the wave heights and periods were maintained to be as close as
possible to those of Experiments E1-E4 for comparison of results. The same storm
surge levels were simulated for the irregular wave experiments as described previously
for experiments involving regular waves, namely MSL, 1.9 m above MSL which
corresponds to the crest elevation of the barrier island, 3.0 m above MSL and 3.5 m
above MSL.
2.3.4 Results

Wave data
An example of the evolution of a typical wave train in the wave tank is presented
in Figures 2.7, 2.8 and 2.9. The data are for Experiment E4. Waves are symmetric
towards the toe of the beach and develop vertical asymmetry as they approach break-
ing. After breaking, the waves are markedly asymmetric and resemble the classic
"saw-tooth" shape over the crest over the barrier island.
Typical examples of an irregular wave train and the associated energy spectrum
at the toe of the beach for Experiment E7 are presented in Figures 2.10 and 2.11.
Bed profile data
As mentioned before, 2-9 profiles were measured every 30 minutes. The mean
profile was calculated using all measured profiles. The following discussion-references
the mean profile unless otherwise mentioned. The landward end of the barrier island
was taken as the zero reference for measurements of distance. The seaward crest of
the barrier island was then at 122 m and the toe of the beach at 288 m.
Sources of error in beach profiling. The automatic bed profiler needed calibration
for each profile and this involved the voltage output corresponding to two "known"
elevations which were chosen as those of the water surface and the bed far offshore
(at 122 m) which was considered to be unaffected by the wave action. However, due
to leakage, etc., the water level could not be monitored as effectively as desired and,
also, the bed level at 122 m was noticed to change slightly with time. These are two
possible sources of error in the bed profiles in terms of elevation. A combination of
magnets embedded in the wheels of the trolley and a "Hall-effect" sensor established



























80.0
80.0


I
80.0

TIME (SEC)


120.0
120.0


I
120.0


16I
160.0


I
160.0


I
200.0
340 M


200.0
210 M


Figure 2.7: A regular wave train (Experiment E4) (a) seaward of the toe of the beach
(340 m), and (b) landward of the toe of the beach (240 m).


2.50


1.50


S0.50

CD
_ -0.50

L -1.50
_J
LLI
-2.50


2.50

1.50

Z O.SO
S0.50

-- -0.50
cr
LL -.50
_J
LLJ


I
40.0


I0.
40.0


i


240.0


I240.0
240.0


-VVV-VVVVVVVVVVVVVVVVvvvvvvvvvvv


-V v vvvvvvvvvvvvvvvvvvvvvVAY














1.50

S0.50

S-0.50
cr
L -1.50
-_
LI
-2.50





2.50

1.50

S0.50
CD

cr
-0.50

CI
LJ -1.50
-J
LJ
-2.50


I
80.0

TIME (SEC)


I
120.0


160.0
160.0


120.0.


160.0
160.0


I
200.0
176 M


I
200.0
136 M


Figure 2.8: A regular wave train (Experiment E4) (a) seaward of the breakpoint (176
m), and (b) just landward of the breakpoint (136 m).


-Il


2.50


80.0
80.0


1q0.0


40.0


i


240.0


240.0


;y I \\ \\ 1Ak


1-J1J A A
UWA-V-JA













1.50

0.50
-C
S-0.50
Cr_
L -1.50
-I
LLJ
-2.50




2.50

1.50

7 0.50

-0.50
cE
J -1.50
-I
LLJ
-2.50


80.0
TIME (SEC)


120.0
120.0


10.0
160.0


210.0


200.0
49 M


Figure 2.9: A regular wave train (Experiment E4) (a) over the crest of the barrier
island (98 m), and (b) over the crest of the barrier island (49 m).


2.50


i I I I I I I
0.0 0.0 80.0 120.0 160.0 200.0 2q
98 M


0.0
ttO.O


___ _


4 h N N L h N NN 1r h a N N h N N t N fn h


i;" ""~**"l;"i~

























































I I I 1


0 0
0 0n
0

(N) NOI1UAE\1~


E~i~


--------t~-L


I -,


~-C~C~-


~


~
-e~T=


c~r~


l I

















10.0


8.0


6.0


4.0


2.0


0.0
0.0


0.5


1.5


2.0


FREQUENCY (Hz)


Figure 2.11: Spectrum of an irregular wave train at the toe of the beach (Experiment
ES).









the horizontal position of the bed sensor. Slippage of the trolley wheels on the rails
can cause errors in the prediction of the horizontal position.
Computations of net volume change. In the following, net volume changes in the
profile are documented. The procedure of computation was as follows. All the mea-
sured profiles at the beginning and end of each experiment were separately averaged
to obtain representative mean profiles. The net volume change, V, was then computed
as
V = (zt=s zt=o)dx (2.16)

where Zt=18 and zt=o were the mean local measured elevations at times t = 18 (final)
and t = 0 (initial) hours. Of course, only portions of the profile affected by wave action
show any change. The corresponding averaged change, Va,, was then computed as

V,,e = V/L,, (2.17)

where L,, was the affected length of the profile.
Experiment El
The initially linear-sloped beach was subjected to 2.1 m high monochromatic
waves of 8 seconds period for 18 hours with the water level at MSL (no overtopping).
This allowed ascertaining the response of the 1:19 planar beach to characteristic storm
waves but without any storm surge and helps in interpreting the results of cases with
overtopping. Swash excursions caused some deposition in the range 150-160 m and
prominent deposition (- 0.7 m) up to 170 m, see Figure 2.12. The region in the range
175-220 m experienced erosion (the maximum being ~ 0.8 m at x =220 m). There
was accretion up to a maximum of about 0.8 m in the range 220-235 m followed by
very mild changes in the offshore.
Swash mechanisms deposited a prominent, narrow, triangular berm with the sand
being supplied from the region seaward of the MSL shoreline. The mean profile
exhibited a 1.5 m high steep-sided longshore bar with its crest at 223 m and trough
at 219 m. The crest of the bar was just seaward of the breakpoint (confirmed visually)
and the height of the bar was defined as the difference in the elevations of the crest
and the landward-side trough. The longshore bar formed within the first 2 hours
























6
EXPT:El INES 0I0 RS .-I--- IlNES 1 HRS


2

--------------- -------------

S-2 -

I-. -
cr
UJ -6 --- 'SEA MTEII LEVEL 10.00 1 1
-1-
hL -IIIH RESPECT TO IEAM SEA LEVEL)
I I I I I
0 50 100 150 200 .250 300

DISTANCE (M)





6
EXPTaE2 TINE. 00o RS ...... TI' E Io MAS

0 -



- 0
S-2 -

- -I -
cr
>- ---- LIE MAWTE LEVEL 11.10 II
U -6 -
-. ImIlH RESPECT TO IERM ISE LEVEL$
LU I I- I
0 50 100 I50 200 250 300

DISTANCE (H)


Figure 2.12: Experiments (a)El and (b)E2, Mean profiles at 00 and 18 hours.









and its position oscillated slightly before the profile attained equilibrium in about
12 hours. The MSL shoreline was unchanged (i.e., no horizontal or vertical retreat
or advancement). The net change in the measured profile was -4.1 m3/m (which
corresponds to 0.09 cm in model units).
Experiment E2
The initially linear-sloped beach was subjected to 2.6 m high monochromatic (8
seconds period) waves for 18 hours with the water level at +1.9 m with respect to
MSL which corresponded to the crest elevation of the barrier island. Thus, the onset
of wave action caused a setup of the water level and mild overtopping over the crest
of the barrier island (nominal overtopping of 0 m).
In the mean profile, there was mild washover of sand over the crest of the barrier
island in the range 0-90 m, see Figure 2.12. The amount of deposition increased
(reaching up to ~ 0.6 m) in the range 90-135 m. The region 150-190 m experienced
substantial erosion (up to about 1.4 m). The crest of the longshore bar extended from
190-200 m and this region exhibited accretion. This was followed by some erosion till
230 m and accretion offshore till 275 m. The MSL shoreline retreated ~ 9 m. The
net change in the measured profile was +7.4 m3/m (which corresponds to 0.15 cm in
model units).
Again, a prominent longshore bar developed within the first 2 hours. The position
of the bar fluctuated by about 9 m in the next 2 hours. After 6 hours, the position
of the bar appeared to approach quasi-equilibrium; however, even after 18 hours the
position was still varying slightly, although there was only minimal change in the
size and shape of the bar. In the final mean profile, the height of the longshore bar
was about 1.5 m. Except for a wider crest and washover of sand over the crest of
the barrier island, the patterns of deposition and erosion were similar to those in
Experiment El. Sediment transport was both onshore and offshore.
Experiment E3
The initially linear-sloped beach was subjected to 2.6 m high monochromatic (8
second period) waves for 18 hours with the water level at +3 m with respect to MSL.
This resulted in a 1.1 m nominal overtopping depth over the crest of the barrier island.







42
Figures 2.13, 2.14 and 2.15 are samples of typical data analysis carried out during
the experimental program and they document changes in profile B1 over the course
of the experiment. Profiles taken every 2 hours are superposed. The longshore bar
developed within the first two hours. The size of the bar grew with time and its
position oscillated slightly while the crest of the bar seemed to flatten. In the final
mean profile, the crest of the bar was at about 170 m while the trough was at 160 m.
In the mean profile, there was erosion (up to more than 0.3 m) in the range 0-60
m followed by accretion (up to 0.5 m) till 105 m (see Figure 2.16). The entire sloping
profile was eroding extensively (up to 1.2 m) except in the region of the prominent, 1.3
m high longshore bar. Figure 2.17 presents the variance calculated using 9 measured
profiles at 18 hours. The variance, a2, is defined as

a' = 7T- (2.18)

where z is the elevation and the overbars denote spatial averaging. It can be observed
that the profiles exhibited substantial variations around the position of the longshore
bar. Significant erosion extended up to about 210 m. The MSL shoreline retreated
about 18 m and it was noted that the elevation of the crest of the bar was above
that of the MSL. The net change in the measured profile was -57.3 m3/m (which
corresponds to 1.2 cm in model units). In contrast to Experiment E2, there was both
erosion as well as accretion over the crest of the barrier island, extensive erosion of
the sloping beach and no accretion far offshore. In fact, the transport was completely
onshore now.
Experiment E4
The experimental conditions were the same as for Experiment E3 except that the
storm surge level was raised to 3.5 m, i.e., the nominal overtopping level was increased
to 1.6 m.
A mild longshore bar developed within 2 hours. The position of the bar oscillated
till about 10 hours before flattening out to a more gradual shape.
The final mean profile indicated that there was deposition (up to 0.5 m) till 100
m, see Figure 2.16. The crest of the barrier island eroded in the range 100-120 m (with




















+*6
i -



0-
+2 -


-2-


-6 -
-6


-a


-8




*fi


1 I I I I I I
0 50 100 150 200 250 30
DISTANCE (H)


I I I I I I I
0 50 100 150 200 250 30(
DISTANCE (M)


DISTANCE (MI

Figure 2.13: Experiment E3, Profile Bl, 00-06 hours.


I


........... T-00 HR -----SEA WATER LEVEL MOO0 MI

T- T02 HR


----------- T-02 HR ----- SER WATER LEVEL MOO III,

T-04 HR n


........... T-011 HR -----SfA WATER LEVEL MOO MIn

T-0T6 HR


+4


+2 -

0-1


-6


+6

+2 -

0-

-2

-6



















+6

z
Z +2
,- 0
> -2
J ,------.---- T-06 HR ----- SEA WATER LEVEL (3.00 NJ
-_J -4 -
-6 T08 HR

-8 ----
S 50 100 150 200 250 300
DISTANCE (MH

+'6
S+4 -____ ______ _____
z
o
0-
> -2
U ---------- T-08 HR -----SEA WATER LEVEL (3.00 I ..--.
-_j -q
^ -6 -T -- -10 HR .....
-6
-8 I-I-I-I-I
0 50 100 150 200 250 300
DISTANCE (M

*6


Z +2

0 -
I-- 0--
cr
> -2
S ..........-------- T-10 HR ----- SEA HATER LEVEL 13.00 NM
-J -
-6 ---- T2 HR
-6
-8 I I-I-I--
I 50 100 I50 200 250 300
DISTANCE (M

Figure 2.14: Experiment E3, Profile Bl, 06-12 hours.


































DISTANCE (M)


DISTANCE (MI


........... T16 HR ----- SEA HATER LEVEL 13.00 HI

--T-18 HR

I I I I I

0 50 100 150 200 250 300
OISTANCEIM)

Figure 2.15: Experiment E3, Profile B1, 12-18 hours.


----------. T-12 HO ----- SEA HATER LEVEL (3.00 nH

--- TT-I H


6 -


*2 -

0-

-2 -

-6
-6-
-a -
















EXTE 1E 0EN TA: I A


DISTANCE (M)


I I I I I I
0 50 100 150 200 250

DISTANCE (H)




Figure 2.16: Experiments (a)E3 and (b)E4, Mean profiles at 00 and 18 hours.


-- SEA IaIER LEVEL 13.00 HI

IM11 RnESPECT 10 ERAN SEA LEVEL


EXPT:EI T-- INE. 00 NMS --""-- nlls to HIs
.o.- .._ oo oo--.-o - --o.. .


-.- -- SEA RATER LEVEL 13.SO NI
IMITH RESPECT 10 MERN SEA LEVEL)


EXPT:E3 -- IHnE 00 HRS


....---. TIEs s1 NAS


...... .








10.00


8.00

C)
6.00
(M



4.00
LLiJ
z
a:
CC 2.00



0.00 -M L
0.0 50.0 100.0 150.0 200.0 250.0 300.0
OISTIONCE (M)

Figure 2.17: Experiment E3, profile variance at 18 hours.


erosion levels reaching up to 0.3 m). Beyond this, the entire profile was eroding except

in the region 210-230 m which exhibited slight deposition. Extensive erosion (up to

1.1 m) occurred in the range 150-200 m. The entire sloping beach became undulatory.

The elevation of the crest of the primary bar coincided with that of the initial beach at

that position. The final position of the crest of the primary bar was 150 m-(which was

landward of the MSL shoreline) and the final height was about 0.6 m. A secondary

bar was discernible landward of the slope break of the initial profile with its trough

at ~ 115 m and its crest at 120 m. The MSL shoreline retreated about 15 m. The

net change in the measured profile was -39.6 m3/m (which corresponds to 0.9 cm in

model units).

The patterns of erosion and deposition were very similar to those of Experiment

E3 except that the longshore bar was smaller, subdued and diffuse.

Experiment E5

This experiment simulated a storm of 18 hours duration with a peak surge of 3.45

m. Waves were allowed to mold the initially linear-sloped beach to near-equilibrium

by impinging upon the beach for 6 hours at MSL conditions prior to the advent of







48
the storm. The rates of rise and fall of the surge were the same. The hydrograph
used in this simulation was presented in Figure 2.6
The near-equilibrium profile (at 6 hours) prior to the storm exhibited a prominent
longshore bar which persisted when the water level was raised to 0.15 m (6-8 hours).
However, the bar disappeared when the water level was raised further (to 0.89 m) in
the next stage of the storm (8-10 hours). No prominent longshore bar was evident as
the water level was raised to 3.45 m above MSL and then lowered back to 0.89 m over
the next 12 hours. A prominent longshore bar again developed when the storm surge
subsided to 0.15 m and back to MSL conditions. Figure 2.18 shows the evolution of
the bed in terms of the mean profile at different times.
Comparison is made here of the mean profiles at 06 hours (just prior to the
storm) and at 24 hours (just after the surge had subsided). There was washover of
sand over the crest of the barrier island with the amount of deposition increasing
up to 0.6 m towards the ocean-side of the barrier island, see Figure 2.19. The
region 120-140 m exhibited slight erosion which was followed by mild deposition till
152 m feet. There was substantial erosion (up to 0.6 m) in the range 160-205 m and
accretion (up to 0.3 m) further offshore except for mild erosion in the range 220-235
m. A prominent, 1.2 m high longshore bar was evident with its crest at about 223
m. Another small, very mild-sloped, broad-crested bar formed in the region 140-152
m. The MSL shoreline retreated about 6 m. During the process of rising water levels
with accompanying overtopping of the crest of the barrier island, the entire sloping
portion of the beach eroded and transport was entirely onshore. The longshore bar
flattened out. Sand was deposited on the crest of the barrier island with the amount
of deposition decreasing away from the slope break. Some sand was also lost in the
bay. As the water level subsided, some of the sand was returned back to the longshore
bar which had reformed with the cessation of overtopping. The longshore bar was in
the same position as before the advent of the storm surge but was of milder relief.
The profile landward of the bar experienced erosion, and overwash processes resulted
in loss of sediment to the budget of the near-offshore region. The net change in the
measured profile was +5.5 m3/m (which corresponds to 0.12 cm in model units).














-I


.11

+2
-2

0
-2
-4
-6
-8



46
+t
*2
0
-2
-(
-6
-8



+6
.4
+2

0
-2
-I
-6
-8


I I I I I
0 50 100 ISO 200 250 3

DISTANCE (M)

Figure 2.18: Experiment E5, (a)Mean profiles at 00 and 06 hours, (b)Mean profiles

at 06 and 16 hours, (a)Mean profiles at 16 and 24 hours.


--------- T=00 HR ----- SEA HATER LEVEL (0.00 0I .0.

S------ T=06 HR ----- SEA WATER LEVEL (0.00 Hl


I I I I I
0 50 100 150 200 250 30'

DISTANCE (MI







--
----........... T=06 ----- SEA HATER LEVEL (0.00 nM

- ---- 16= I H ----- SEA HATER LEVEL 13.qO HI


0 so50 100 150 200 250 3C

DISTANCE (M


I
-

-


-


6


........... T=16 HR -----SER WATER LEVEL (3.40M -- --- ---

T-24 11R -- EA WATER LEVEL (0.50 MI




























6
EXPI. S TINE. 08 MRS ........ 21 HMRS








6 _- "- SE VL 1.00 Ml
2





IU .g------------------- ---------------^~--~-~-~-~-~-~---------------------------------------------
Z -2
cr
. -6 -- SEA MATER LEVEL 10.00 NO
tINI n RESrECT TO IEnEN SEA LEVEL$
S-8I I I I I
0 50 100 150 200 250 300

DISTANCE (M)


Figure 2.19: Experiment E5, Mean profiles at 06 and 24 hours.









Thus, the profile subsequent to the storm was quite similar to that prior to the
storm especially in terms of the longshore bar position, size and shape. The storm
caused washover of sand over the crest of the barrier island.
Experiment E6
The experimental conditions were the same as El (water level at MSL, no storm
surge, no overtopping) except that a narrow-banded spectrum of irregular waves of
2.1 m significant wave height and carrier period of 7.6 seconds was allowed to impinge
upon the barrier island.
Swash excursions caused deposition landward of the shoreline in the range 125-165
m with maximum deposition reaching up to 0.6 m, see Figure 2.20. Seaward of the
shoreline, the region 165-210 m exhibited erosion and this was followed by deposition
still offshore. The crest of the 0.6 m high longshore bar was at about 230 m. The
formation of the bar was not immediate (as was the case in Experiment El), it took
about 12 hours to develop. There was no change of the MSL shoreline.
The patterns of deposition and erosion were similar to Experiment El except
that the changes were smaller, the longshore bar was much less prominent (and the
inflexion of the bed profile was only on the landward side of the bar) and a greater
portion of the beach face was affected by swash mechanisms. There was onshore
transport seaward of the longshore bar. The net change in the measured profile was
+10.7 m3/m (which corresponds to 0.24 cm in model units).
Experiment E7
The experimental conditions were the same as E2 (1.9 m surge, water level equal
to the crest of the barrier island) except that irregular waves were used with a carrier
period of 8 seconds. Thus, the onset of wave action caused mild overtopping over the
crest of the barrier island (nominal overtopping depth of 0 m over the crest of the
barrier island).
Washover occurred over the crest of the barrier island, with the deposition in-
creasing from the bay-side towards the ocean-side (see Figure 2.20). Accretion was
more than 0.3 m in the region 60-105 m. Substantial erosion (up to 1 m) occurred
from the MSL shoreline (which was nominally at 122 m) till about 210 m. There












6
EXPT:E6 l--- lE 00 HRS ----- tIlE. tI ItS

2
0
Z -2


s-- -6
-J
> -6 -'-.-. SEn iE" ltlE LVEL 10.00 Ni
..1
,1 INIH ESIPECi I HIMAN SEAl LEVEL
-8I I I I
0 50 100 150 200 250 300
DISTANCE (M)




6
EXPT:E7 I---- 00 HIIS ---- IlTiE II IMS
q--
2 -.-- ------ -------------------- .. ---------- 0

- a a t
S -2 -..


U. -6
{u -------- T- ------- I -------- I -------- I --------------------
IT imm FiR~sm MEERC I S N0 N LEVEL(

0 50 100 150 200 250 300
DISTANCE ([H


Figure 2.20: Experiments (a)E6 and (b)E7, Mean profiles at 00 and 18 hours.







53
was deposition of about 0.6 m at around 210 m and this was followed by decreasing
amounts of accretion still further offshore. A small, low-relief bar was discernible with
its crest at about 220 m. The formation of the bar was not immediate and took about
16 hours to develop. The MSL retreated about 9 m. The net change in the measured
profile was +7.32 m3/m (which corresponds to 0.1 cm in model units).
Again, the patterns of erosion and deposition were similar to those of Experiment
E2 except that the changes were more subdued and the longshore bar was low and
much less prominent (with the inflexion in the bed profile occurring on the landward
side of the bar only).
Experiment E8
The experimental conditions were the same as E3 except that a narrow- banded
spectrum of irregular waves was used with a carrier period of 8 seconds. Thus, the
surge level was 3.0 m resulting in a 1.1 m nominal overtopping depth over the crest
of the barrier island.
The crest of the barrier island exhibited mild uniform accretion (about 0.15 m) all
over, see Figure 2.21. There was substantial erosion (up to 0.8 m) from 120 m to about
190 m, followed by decreasing amounts of deposition in the offshore. No longshore
bar was evident. The MSL shoreline retreated about 8 m. The net change in the
measured profile was +8.9 m3/m (which corresponds to 0.18 cm in model units).
Patterns of deposition over the crest of the barrier island were similar to Ex-
periment E3. However, unlike Experiment E3 where the entire sloping part of the
profile was eroding, there was deposition offshore of about 180 m in this experiment.
Also, Experiment E3 had a prominent longshore bar while no longshore bar formed
here and changes in the beach profile were much subdued as compared to those in
Experiment E3.
Experiment E9
The experimental conditions were the same as E4 except that a narrow- banded
spectrum of irregular waves was generated with a carrier period of 8 seconds. The
surge level was 3.5 m above MSL resulting in a 1.6 m nominal overtopping depth over
the crest of the barrier island.
















6


6 ---------------------------------------------------------------------------



Z -2 I
00 ... .... ... .0
EXPT:E9 ..I.HEl .0 ........ ...IH.. II S
CD -.....

-4
-. ------ 3EA MAIER LEVEL 53.00 I'
J -6 -
I, mH REIrECI 10 HEAN SEA LEvI LS
J IIII\
0 50 100 150 200 250 300

DISTANCE (M)





6
6--------------------- -------------------------------------------------------------------------
EXPTE9 I--- I IME 00 RS IE End (b MeS



2 ----- ...-..
0

ED -2


-J
S- ----- SEA WATER IEVEL 1.50G N O

Lai- -0 6 IITH RESPECT TO MLAN SEA LEVEL) -
II

0 50 100 150 200 250 300

DISTANCE (H)






Figure 2.21: Experiments (a)E8 and (b)E9, Mean profiles at 00 and 18 hours.







55
Overtopping caused washover of sand up to ~ 0.5 m over the crest of the barrier
island till 115 m, with the deposition again increasing from the bay-side to the ocean-
side, see Figure 2.21. This was followed by substantial erosion (up to 0.8 m) in the
range 120-200 m and mild, decreasing amounts of deposition still further offshore. No
longshore bar was evident. The MSL shoreline retreat was 21 m. The net change
in the measured profile was -4.4 m3/m (which corresponds to 0.09 cm in model units).
Patterns of deposition over the crest of the barrier island were similar to those
of Experiment E4. However, the bed profile of Experiment E9 was devoid of the
presence of a longshore bar and the profile exhibited mild accretion beyond about
200 m unlike Experiment E4. Changes in Experiment E4 were much more prominent
when compared to those in Experiment E9.
2.3.5 Discussion of Results

The results of a series of nine wave tank tests to investigate the evolution of beach
and barrier island profiles under the action of various wave and tide conditions are de-
scribed. The range of tests included steady and time-varying normal and storm water
levels and regular and irregular waves. Overtopping of the barrier island occurred for
the elevated water levels. Sand with a mean size of approximately 0.2 millimeters was
used in all tests. The crest of the model barrier island was 7.5 m wide and a nominal
model to prototype scale of 1:16 was considered. The beach for all tests was initially
planar with a slope of 1:19. For each test, documentation included the incident waves
and beach profiles at intervals of 0.5 hours. More details of the data are provided in
Srinivas, Dean and Parchure (1992).
The first series of four experiments maintained the wave characteristics reasonably
constant while increasing the water level from test to test. Water levels tested were, in
prototype units, 0 m, 1.9 m (the same as the barrier island crest), 3 m, and 3.4 m. For
Experiment 1 with the normal water level (0 m), a prominent bar formed and a fairly
substantial triangular berm was established immediately landward of the waterline.
The profile evolution for the remaining tests may be interpreted in light of the forces
which caused profile evolution in the first test (Experiment El). For the second test







56
(E2) with the water level at the barrier island crest, a bar of approximately the same
height but of much greater width formed. Since overtopping of the barrier island
could occur, the sediment that had formed a triangular berm in the first experiment
was deposited over the seaward portions of the barrier island. In Experiment E3 with
a water level of 3 m, the bar was similar to that in Experiment E2; however, sand
was transported over the barrier island resulting in substantial losses of sediment to
the beach system. Experiment E4, the final test with a steady water level and regular
waves, extended the trend established in the preceding two tests with the exception
that the offshore bar was considerably more subtle. In all cases, the longshore bars
were break-point bars (confirmed visually).
Experiment E5 was conducted with regular waves and a time-varying water level
which simulated the rising and falling hydrograph associated with a storm. There were
similarities and differences between this and previous experiments which contribute
to understanding the causes of bar formation. During periods of slow changes in
water level, a prominent bar formed on both rising and falling water levels. However,
during those portions of the hydrograph when the water level was either rising or
falling fairly rapidly, the bar became much more subdued to nonexistent, apparently
because the processes of bar formation were not able to keep pace with the changing
water level. There was substantial loss of sediment over the barrier island but of
course less than for the case of an elevated water level over the entire testing period.
Experiments E6 through E9 replicated approximately the conditions of Experi-
ments El through E4 with the exception that the waves were irregular. The following
discussion focuses on the similarities and differences between the tests with regular
and irregular waves. The processes at the landward end and over the barrier island
were substantially the same for regular and irregular waves. Without overtopping
(Experiment E6), the berm formed was less distinct than with regular waves. For the
remaining experiments in which overtopping occurred, sand was carried over the bar-
rier island where some was deposited and a portion transported beyond the island.
The major difference occurred in the characteristics and degree of bar formation.
With irregular waves, the bar was less prominent and less distinct for the case of







57
no overtopping as compared to the regular wave case. In those cases in which over-
topping occurred, the bar feature was more subtle with the mean water level at the
barrier island crest elevation and was not present at all during Experiments E8 and
E9 with water elevations of 3 m and 3.4 m, respectively.
The experiments with overtopping show accretion over the crest region. This sand
is lost to the subaqueous sediment budget with the return of normal conditions after
the storm and if equilibrium beach concepts are assumed, this loss has to be made up
with additional erosion occurring elsewhere. The situation then becomes complicated
as a result of this interaction and longshore processes need to be taken into account.
Dissipation of wave energy acts as an effective sediment- mobilizing agent and in
conjunction with other (non wave-driven) currents, which are apt to' be present in
nature, has a greater transport potential. Under these conditions, overtopping can
result in a serious erosive impact to the barrier island system. This hypothesis was
tested and validated by conducting additional tests (unpublished data and Pirrello
1992) combining the actions of waves and currents. The data presented here provide a
basis for the development and calibration of a numerical model to simulate overwash
of barrier islands during storms. In addition to these data, the principal results from
these experiments include further evidence of the mechanisms of bar formation. It
appears that contrary to other proposed causes, offshore bars are simply break-point
bars and that the return flow of mass transport, sometimes termed "undertow" and
the relative constancy of wave breaking location play important roles in bar formation,
at least for the conditions tested here in the laboratory. The aspect of identification
of causes of bar formation/generation is investigated next.
2.4 Bar Formation Mechanisms

2.4.1 Background

The initial step in the formulation of a rational, physics-based cross-shore sedi-
ment transport model is the correct identification and quantification of the dominant
forcing functions. In terms of sediment transport, the most active region of any bed
profile is the surf zone where wave breaking results in dissipation of organized wave







58

energy and the transfer of wave momentum to the water column. As mentioned earlier
(Section 2.3), the final bed profiles of the conducted experiments with barrier islands
were characterized by a distinctive, single longshore bar, as is the case with many
natural coastlines. A good sediment transport model should have the capability of
generating bars wherefore the proper physical mechanisms) for bar formation needs
to be identified. A bar is characterized as a local region of a bed profile (excluding the
swash zone) exhibiting a surplus of sediment; that is, it is a subaqueous accretionary
feature where sediment has deposited. However, the need to establish bar cross-shore
parameters (extent, position, volume of sand stored) requires the definition of a refer-
ence profile to define "surplus sediment" such that, for example, the volume of sand
stored in a bar may be quantitatively evaluated and compared with other investiga-
tions consistently. An unambiguous definition of a reference profile is difficult and not
really necessary for the present purposes, as long as a more pragmatic definition is
consistent and essential characteristics of the system can be quantified. For example,
this reference can be a "fitted" equilibrium beach profile following Dean (1977) or it
can be the initial profile of an experiment.
The concept of an equilibrium beach profile is inherent in studies of beach pro-
file evolution where it is assumed that the beach will remain unchanged after being
exposed to constant forcing for a long time. The concept of an equilibrium beach
profile is a useful idealization which is difficult to achieve in practice because of vari-
ations in water temperature, wave heights and periods, tides, etc. It is also noted
that the definitions of Bruun (1954) and Dean (1977) predict only monotonic profiles
for equilibrium beaches. An equilibrium beach profile can be fit (using, for example,
least- squares technique) to form the reference profile by assuming uniform wave en-
ergy dissipation per unit volume, that is, a depth oc (distance)2/3 relationship (Dean
1977).
For the present series of experiments, the most practical definition for the refer-
ence profile was the initial bed profile in all experiments as it was readily available.
Figure 2.22 illustrates the definition of a longshore bar and some of its parameters
including the cross shore location in terms of distance to the bar center of mass,






















X=
Xd.


Final Profile


Bar Centroid


Initial Profile


Longshore Bar


Figure 2.22: Definition sketch of a longshore bar in a beach profile.







60

Xcm, distance to the bar crest, xc and depth at the bar crest, dc. For the present
experiments, the initial still water shoreline has been chosen as the local origin for
describing the position of the longshore bar. In many cases, a trough exists on the
seaward side of the bar crest. In nature, subaqueous beaches can be quite complicated
with multiple bars, and rhythmic and complicated three-dimensional topography.
There is a noticeable lack of consensus in the literature about definitive bar gen-
erating mechanismss. The existence of bars is due to the convergence of sediment
transport. The shear stress near/at the bottom for the case of progressive waves (to
second order) is in the direction of wave propagation (onshore transport* consider-
ing normally incident waves). The presence of a single longshore bar then indicates
an area of convergence of sediment transport with seaward directed (offshore) trans-
port being required landward of the bar crest. Based on a volumetric conservation
requirement, for a 2-D situation,
Ahh aq (2.19)
at ax
where h is the local depth and q is the sediment transport in direction x, whereby a
negative gradient of sediment transport is necessary for sand accumulation.
2.4.2 A Brief Literature Review

The ubiquity and importance of longshore bars has long been recognized and they
have been studied for about a century. The earliest investigators include Lehmann
(1884), Otto (1911) and Hartnack (1924). Hartnack (1924) noted the importance of
breaking waves in bar formation in the Baltic Sea and that the spacing between long-
shore bars increased with increasing water depth. Other early investigators include
Evans (1940) and Keulegen (1945).
Bar formation criteria
A number of generally heuristic relationships for offshore transport and bar for-
mation are available in the literature in terms of various non-dimensional parameters
including combinations of the deep water wave height (Ho) and wavelength (Lo), sed-
iment fall velocity (w,), wave period (T), initial beach slope (tan#/), median sand
diameter dmed, etc. Earlier criteria involved wave steepness only (Waters 1939, Scott










Table 2.4: Bar formation criteria
Researchers) Formation criteria
Waters (1939) Ho/Lo > 0.025
Sunamura and Horikawa (1975) Ho/Lo > C(tan P)-027(dmedD/Lo)0
Wright and Short (1984) Hb/wT > 1 6
Kriebel et al. (1987) Ho/Lo > A rw,/gT
Larson and Kraus, SBEACH (1989) Ho/Lo < 0.0007(Ho/w,T)3
Dalrymple (1992) gH > 9000 10400


1954), but later criteria have generally inculcated sediment characteristics (fall veloc-
ity or sand diameter). Some of these criteria are listed in Table 2.4.
Considering primarily suspended transport, one of the most rational criteria was
suggested by Dean (1973). If a sediment particle is entrained to an elevation (zi)
proportional to the wave height (H) during the passage of the wave crest (when the
magnitude of velocity is a maximum), the fall time is

t = PH (2.20)
W,
where w, is the sediment fall velocity and P is a proportionality factor (free parame-
ter). Thus, with instantaneous suspension at the wave crest phase position, we have
the condition

tF < T/2, onshore transport

> T/2, offshore transport (2.21)

As explained earlier, offshore transport is necessary for a bar to develop, whence
/H T
>P (2.22)
w, 2
and dividing both sides by Lo, we have

Ho/Lo > r (2.23)
0 gT
where the wave height and wavelength are in terms of deep water conditions. Com-
paring various data sets, Dean (1973) found good agreement for this functional depen-
dence with a value of 1/f of approximately 1.7 (for a lab scale). Kriebel et al. (1987)









extended this to include prototype scales and the new value of 1// was between 4 to
5. It is noted that this criterion is applicable for first and higher order wave effects
and the effects of bottom slope are not included.
Kraus and Larson (1988) and Larson and Kraus (1989) examined in detail data
from large-scale wave tank tests (for monochromatic waves breaking on sandy beaches)
of Saville (1957) and Kajima et al. (1982) and formulated two criteria, depending on
the variables used as

Ho = 115(r,1.5 (2.24)
Lo gT
o= 0.0007D3. (2.25)
L0
where Do = H is the Dean number in deep water, for separating storm (barred) and
normal profiles. Dalrymple (1992) re- evaluated these criteria and developed a single
new criterion in terms of a profile parameter, P, given as

P = gHO ~ 9,000 10,400 (2.26)
W3T
Bar formation mechanisms
In general, bar formation has been attributed to the convergence of sediment
transport due to either wave breaking induced mechanisms) or long (infragravity
IG) waves (including leaky and trapped modes). The dissipation of wave energy
due to wave breaking is the source of turbulent kinetic energy (tke). This promotes
sediment entrainment into the water column, and cross-shore mechanisms due to the
transfer of wave momentum and resultant torque on the water column can result in
a bar. The energy of short waves is depth-limited in the surf zone (due to breaking);
however, due to their low steepness, the energy of IG waves is not necessarily depth
dependent in the inner surf zone. Energy spectra in the inner surf zone exhibit
pronounced levels at infragravity scales which are at least of the same magnitude
as that of the primary incident frequencies. This is the reason why IG waves are
often called "surf beat". These low steepness, incident IG waves can be efficiently
reflected from the beach. Now, a standing long wave has mass transport towards
the antinodes in the upper part and towards the nodes in the lower part of the







63
bottom boundary layer (Longuet-Higgins 1953) whence, depending upon the elevation
of sediment entrainment, there can be accumulation under the nodes or the antinodes
of the wave envelope. If bedload is dominant, bars can form under the nodes, while
bars can form under the antinodes of a standing wave envelope if suspended transport
dominates. Trapped long waves or edge waves can be another source of IG energy
and different modes may produce complex topographies.
Bars have been related to the reflection of the incident short wave field (Carter,
Liu and Mei 1973). Lau and Travis (1973) extended the idea by including a planar
slope, however the spacing was still in terms of the short- wave envelope- which is
physically unrealistic for bars in nature. Short (1975) and Bowen (1980) related
bars to free, reflecting long waves and the resultant spacing was qualitatively more
accurate.
Symonds, Huntley and Bowen (1982) demonstrated how an oscillating break point
due to a non-rionochromatic incident wave field can generate free long waves in both
directions (onshore and offshore). The resulting standing wave envelope in the surf
zone can result in sediment convergence. The oscillating break-point mechanism has
also been analyzed by Schaffer and Svendsen (1988).
Edge wave (trapped IG waves) modes have been investigated by Bowen and Inman
(1971) and Guza and Inman (1975) and can cause barred topography. Holman and
Bowen (1982) used the edge wave hypothesis to show that rhythmic and complicated
three-dimensional topography can develop due to the interactions of different modes.
Hansen and Svendsen (1974) showed that the presence of free and forced harmon-
ics of a dominant fundamental primary wave results in the alternate reinforcement
and cancellation of the wave envelope as the celebrities of the harmonics are differ-
ent. This effect is possible in wavemaker-type laboratory experiments. Contrary to
field evidence, this mechanism predicts decreasing bar spacing with increasing water
depths.
Mei (1985) described the short wave interaction with a periodic bar field while
Boczar-Karakiewicz and Davidson-Arnott (1987) describe the interaction between the
first and second harmonics of a wave train and its effect on bar formation.







64
The presence of a surf zone is not necessary for the above mechanisms (except
for Symonds et al. 1982 and Schaffer and Svendsen 1988). Models for bar formation
including surf zone processes take into account some/all of the following effects

Undertow (due to momentum flux transfer)

Asymmetric flow (due to wave non-linearities)

Turbulence (due to wave breaking)

Infragravity waves (forced waves due to wave groups can be free after breaking
of the primary waves)

Dyhr-Nielson and Sorensen (1970) first associated surf zone return flow, gener-
ally termed "undertow", with bar formation. As a result of wave breaking, there is
a transfer of wave momentum to the water column and an augmented mass flux in
the region above the wave trough. Continuity requires a strong return flow in the
lower part of the water column (below the wave trough). Dally (1980) was the first
to develop a quantitative description for undertow with monochromatic waves and
also pointed out the necessity for including wave-breaking induced turbulence to ac-
count for the increase in suspended load. Stive and Battjes (1984) and Stive (1986)
extended the undertow formulation to include random waves. Stive (1986) indicated
the importance of including wave asymmetry. Roelvink and Stive (1989) developed
a numerical model inculcating undertow, wave asymmetry, turbulence and long wave
effects and concluded that including all effects gave the best results. Even though
there have been impressive advances in understanding and analytically/numerically
modeling the essential physics of cross shore flows in terms of integral (time and some-
times depth integrated) wave properties (e.g., the radiation stress), the solution of
the governing second-order equation for undertow requires two boundary conditions
whose proper choice is not very obvious (Svendsen and Hansen 1988). This facet is
elaborated later during the discussion of cross-shore flows (Chapter 3).
It is realized that any, some or all of these causative processes may be dominant
depending upon the specific physical model (including field situations) parameters.









Field observations
In terms of field observations, precise positioning of the nodes and antinodes of
an IG wave envelope has never been actually documented. Munk (1949) and Tucker
(1950) first documented augmented IG energy levels in the nearshore. Dolan (1983)
analyzed bar spacings in Chesapeake Bay, Lake Michigan, Cape Cod Bay and the
Alaskan coast. He found little support for the IG wave hypothesis and concluded
that wave breaking was the more successful hypothesis (using Dally's (1980) breaking
wave model).
Extensive beach profile surveys and long term remote sensing by Howd and Birke-
meier (1987a, 1987b) and Lippman and Holman (1990) at Field Research Facility
(FRF), DUCK, North Carolina revealed that normal rhythmic topography becomes
barred and two dimensional during storms. It is instructive to compare the findings
of Sallenger and Howd (1989) and Trowbridge and Young (1989) regarding the long-
shore bar during different times. Sallenger and Howd (1989) documented results for
two storms (October 1982 and September 1985) at FRF, DUCK, NC. During the
October 1982 storm, significant wave heights were ~ 1.8 m and storm periods were
6-8 seconds. The winds shifted and energetic swell of 16-18 seconds existed the last
day (10/12/82). A mild longshore bar became more developed and moved seaward
with time (see Figure 2.23) during the course of the storm.
For analysis, they defined the surf zone energy saturation in terms of a parameter

7rms = Hrms/h (2.27)

where Hrms is the RMS wave height, h is the water depth and 7rms is a function of
the beach slope (tan 3). Two points can be raised against this method of analysis.
By their definition of 7rms, H/h is constant in the inner surf zone regardless of
offshore wave characteristics, which is open to question. Furthermore, beach slope is
an ambiguous parameter for non-planar beaches and is difficult to specify precisely
and consistently. Also, their measurement packages were seaward of the bar crest
and in water depths greater than 3 m whereas the depth at the crest of the bar
was 1 m. By this method, the bar position was definitely landward of the outer








66







2-

0- -- 10/07/82
S- 10/10/82
.------ 10112/82
> -2-

.4-

00 200 300 400
DISTANCE OFFSHORE (m)



Figure 2.23: Formation and movement of a longshore bar during the 10/82 storm at
FRF, DUCK, NC (from Sallenger and Howd 1989).


limit of the inner surf zone. The second (September 1985) storm resulted in deep-

water significant wave heights over 1.5 m. Wave periods were always less than 10

seconds due to strong winds. A prominent bar quickly developed and moved seaward

(Figure 2.24). They did not discount the break-point hypothesis as a bar- generating

mechanism during this storm. In the field with a random wave climate it is very

important, albeit quite difficult, to precisely quantify energy saturation and specify

profile equilibrium. It is felt that a wave model like Dally (1980, 1987a) with energy

flux considerations is more rational for defining energy saturation. For this reason,

the wave height computations in the cross-shore model presented later use the Dally

(1980) model which is discussed in the Appendix.

Trowbridge and Young (1989) presented an attractive model for onshore sediment

transport under random, weakly non-linear and relatively long waves for sheet flow

conditions and turbulent bottom boundary layers. The model was tested and success-

fully reproduced the onshore movement of a longshore bar, and the motion of depth

contours near the bar crest, reported in field data sets at FRF, DUCK, NC (Howd

and Birkemeier 1986) during the period February 1982 October 1982 when wave

conditions were comparatively mild.














STATION LOCATIONS
a 0 .......... 09/09/85
09/11/85
---- 09/12/85
4- 09/13/85

2-

a-2

-4I

DITAMCE OFFSHORE W()



Figure 2.24: Formation and movement of the longshore bar during 9/85 storm at
FRF, DUCK, NC (from Sallenger and Howd 1989).


For the October 82 storm, it is possible that a storm of greater duration might

have moved the longshore bar farther offshore and more proximate to the exterior

edge of the surf zone. Thus, the position of the longshore bars in the field can be

considered to be responding to changes in wave height. Higher waves during storms

result in seaward movement of the exterior edge of the surf zone and the longshore

bar, when compared to normal/summer conditions. When this is followed by milder

wave activity during summer, the exterior edge of the surf zone is shifted landward

and so is the position of the longshore bar.

2.4.3 General Characteristics of Present Laboratory Experiments

A series of nine experiments was formulated to investigate bar formation mech-

anisms with emphasis on infragravity (IG) wave and break-point hypotheses. The

experiments, which were conducted in the air-sea tank at COEL, tested the effects of

wave action only, effects of tides were not represented. IG waves were generated as a

result of the interaction of the primary wave field whose spectral characteristics were

monochromatic (single discrete frequency), bichromatic (two discrete frequencies) or

multifrequency (discrete and continuous frequencies over a narrow band). Of course,

there were no IG waves for cases with monochromatic primary waves. The primary











Table 2.5: General features of bar formation investigation experiments.
Condition Characteristic
Initial bottom slope 1:19.5
Mean sand diameter 0.2 mm
Offshore depth, h0 0.46 m
Carrier Period, T,,e. 2 sec
Breaking wave height, Hb 0.14,0.20 cm
Breakpoint steepness, 0.057
Deepwater steepness, 0- 0.043
Deepwater fall velocity parameter, 2.7
Breakpoint fall velocity parameter, 3.4


waves were fully documented. The spectral characteristics of IG waves were either
monochromatic or multifrequency, and the IG waves were also fully documented.
Eight experiments commenced from an initially planar slope (~ 1 : 19.4) while one
experiment had an initially barred profile. Table 2.5 details the general features and
nominal values of some non- dimensional parameters of the experiments, while Fig-
ure 2.25 illustrates the general morphological configuration of the experiments and
the typical positioning of beach features in the air-sea tank.
Similitude considerations and model characteristics were discussed in Sections 2.1
and 2.2. The essential aspects of the same are reiterated here briefly. The (mean)
diameter of sand in the air-sea tank was 0.2 mm. The prototype sand diameter
was chosen as 0.4 mm. Using Froude number and fall velocity parameter scaling, the
model to prototype geometric scale ratio was 1:16, while the time scale was 1:4. Using
storm-like prototype conditions (Chapter 2), the offshore maximum wave height was
fixed at 2.3 m with mean period around 8 seconds for all experiments, which, in
model units, correspond to a wave height of 0.16 m and a time period of 2 seconds.
Hereafter, all dimensions in the text are in model units unless otherwise noted.
The displacement of the free surface was measured along the wave tank using
standard resistance-type wave gages. Infragravity wave characteristics were measured
at various points along the profile using a manometer and stilling well arrangement




























In _


E
c3
MI


\o
r -


j


It)


I


L
C1

L
E


(IcJL puti









that acted as an analog low-pass filter.
All wave gages were connected to an IBM-compatible 386 PC using the software
GLOBLAB for signal acquisition, display and analysis. Signal acquisition was via
the GLOBLAB A/D module (Data Translation 2801 board) and analysis was in both
time and frequency domains, as necessary. The primary and IG waves were sampled
at 10 Hz and the sampling duration was at least 102.3 seconds. This results in a
spectral resolution of 0.0098 Hz and a Nyquist frequency of 5 Hz.
All experiments were carried out for at least 4.5 hours by which time a state of
quasi-equilibrium existed for the bed profiles. Three parallel, cross-shore profiles (Bl,
B2 and B3) were measured at one hour intervals and the measuring interval between
successive points was 0.15-0.30 m. B3 was the tank centerline profile while Bl and B2
were 0.21 m on either side. The standard deviation of the three profiles was calculated
and indicated generally strong two-dimensionality. Thus, the mean bed profile was
used in all calculations (unless otherwise noted).
The carrier/average frequency was maintained at 0.5 Hz and the maximum wave
height was approximately 0.16 m at the toe of the beach for all cases. In cases with
bichromatic waves, the input signal to the wavemaker consisted of equal energies at
the two primary frequencies only. However, energy spectra of measured total waves
along the air-sea tank showed energies at interaction frequencies which is a result
of non-linear wave-wave interaction. Analysis of wave data from various stations
along the flume indicated generally moderate harmonic generation seaward of the
surf zone. However, levels of energy at infragravity frequencies well inside the surf
zone was comparable to or more than that at the primary frequencies. In the field,
two obvious mechanisms for long waves are present. One is wave non- linearities
causing the (second-order) "beat" (IG) envelope associated with a narrow-banded
spectrum, and the other is the oscillating break-point associated with the narrow
-banded spectrum primary waves. Desired long wave generation using wavemakers
is quite complicated. A bichromatic signal to the wavemaker results in a second-
order forced progressive, long wave at the difference frequency. As shown by Madsen
(1971), if the second-order boundary condition for the paddle motion is not specified,








71
a spurious free long wave, also of second-order (Flick and Guza 1980), is generated
which is initially 1800 out of phase with the forced long wave. Ottensen Hansen
et al. (1980) showed how to account for this boundary condition in the signal to
the wavemaker. After several wave periods, continuous reflection along the shoaling
beach and at the shoreline generates a quasi- steady standing wave pattern. It is also
quite possible to have substantial to complete reflection of IG waves at the wavemaker
paddle. Neither of these spurious effects was eliminated from the tests. Instead, the
long wave envelope was always measured (at 1 hour intervals) at points spaced 0.3
m apart and only measured values are used throughout the text, unless otherwise
stated. This eliminates the need to account for any extraneous effects in terms of
estimation of the amplitude of the long wave envelope.
2.4.4 Correlation of Bar Characteristics and Infragravity Waves

This part of the study was basically an extension of that conducted by Dally
(1987b) in which the incident primary wave spectra were biharmonic. However, por-
tions of the method of analysis differ. The two pronounced and discrete primary peaks
in the spectrum of the drive signal result in an infragravity (IG) wave correspond-
ing to the difference frequency of the primary waves. Reflection of the infragravity
component from the wavemaker, an artificiality due to the wave tank, modifies its
amplitude (depending on the phase of the reflected wave).
The rationale for the present analysis was that infragravity waves can be effi-
ciently reflected and form a standing wave system, whence the position of the bar
may be correlated to the nodes/antinodes of the wave envelope. The investigations
of Suhayda (1974), Short (1975), Bowen (1980), Katoh (1984) and Sallenger, Hol-
man and Birkemeier (1985) tend to support such hypotheses. With the objective of
investigating these hypotheses, four experiments were conducted in this part of the
investigation in which the frequency of the monochromatic IG wave was varied to
assess its impact on bar formation, while the carrier frequency was maintained at 0.5
Hz. The carrier frequency is defined as the average of the primary frequencies. The
maximum wave height at the toe of the beach (x = 18 m) was 0.16 m in all cases.










Table 2.6: Characteristics of experiments with biharmonic waves
Case Primary Difference Nodal Antinodal Bar
Frequency Frequency Position Position Position
(Hz) (Hz) (m) (m) (m)
_f f2
1 0.53 0.47 0.06 14.3 15.3 14.8
2 0.54 0.46 0.08 13.5 15.0 14.9
3 0.55 0.45 0.10 12.5 15.0 14.8
4 0.57 0.45 0.12 11.6 13.1 14.5


The test conditions are documented in Table 2.6.
Spectral characteristics
The signal from the wave gages, after calibration, was transformed into the fre-
quency domain with a Fast Fourier Transform (no windowing was used). The re-
sultant signal was interpreted in terms of energy density as a function of frequency.
An example set of measurements for Case 1 is presented to display evolution along
the initially planar beach. Figure 2.26 documents the incident measured total and
long waves and associated energy spectra. This data set was measured at the toe of
the beach at 18 m. Most of the energy is contained in the two primary frequencies
(fi = 0.53 and f2 = 0.47 Hz). Lower energy levels are discernible at frequencies f-,
fi + f- and 2f2, where
f- = f f2. (2.28)

It is also seen that the stilling well acts to damp the amplitude of the IG wave in the
tank. Figure 2.27 is for x = 15.5 m which is seaward of the surf zone. It is seen that
E(fl) has sharply diminished and energies at f+, f- f+ + f-, f+ f- are visible,
where
f+ = fl + f2, (2.29)

while that at the IG frequency is almost unchanged. Thus, it is seen that the higher
primary frequency (fi) component decays even in the shoaling region. Figure 2.28
is for x = 15 m which is just inside the surf zone while Figure 2.29 is for x = 14 m
(well inside the surf zone) and energy at f = f2 is still dominant. Some energy is now
apparent at f = 2f_ (Figure 2.29). The landwardmost measurement point was at x














Li 3

-'




U




3


ENERGY SPECTRUM : TOTAL WAVE S M iI 1 i
ENERGY SPECTRUM : TOTAL WAVE SYSTEM .I


5o o. .l g.13 o 31 1 1. s Oi *. .1s o 1.n of 55 t o 0 o01s 0 o o 9 1
ENERGY SPECTRUM : INFRAGRAVITY WAVES '2


Figure 2.26: Case 1. x = 18m (toe of beach). (a)Measured total wave system
(b)Measured long wave (c)Energy spectrum of the total wave system (d)Energy spec-
trum of long waves.









= 11 m, and the data for the same are presented in Figure 2.30 where it is seen that
the magnitudes of wave energies are relatively small and the majority of wave energy
is at frequency f = f-.
Two general features were observed in the four experiments. The first, not totally
surprising, feature is the dominance of IG energy only in the region close to the
waterline; the other was the rapid decay of the higher primary frequency component
(E(fi) in the sloping portion of the beach (Cases 1-3) and in the horizontal portion
of the tank (Case 4).
Bed profile evolution
Figure 2.31 documents the evolution of the bed profile for Case 1. The presented
profiles were measured after successive one-hour intervals (except one profile at 0.5
hour). The longshore bar formed quickly within the first half-hour with xc=14.2
m and the height of the bar was 0.08 m. The position of the crest of the bar was,
quite well established by 1.5 hours. The crest of the bar had moved slightly offshore
to xc=14.8 m in the final profile and the height of the bar was about 0.11 m. As
mentioned above, IG energy was dominant in the region flanked by ~ x = 8.5 m and
x = 12 m. This region exhibited onshore transport and a substantial, triangular berm
was deposited above the still water level. Figure 2.32 presents the measured sediment
transport rates at different times for Case 1. The rates were computed by spatially
integrating the sediment conservation equation

dq dh (2.30)
dx dt

where q is the sediment transport rate, x is the cross-shore direction, h is the local
depth and t is time. It is seen that changes in the bed profile were greatest in
the beginning of an experiment (as evidenced by the transport curve for the time
interval 0-0.5 hours in the figure). Substantial transport occurred at the position of
the longshore bar. Transport was minimal during the last hour (3.5-4.5 hours) of the
experiment. The overall sediment transport rate, between 00 and 4.5 hours, is also
shown in the figure.
































-0


T o01 01 etS e Rm oR ei o0A W oA V s
TIME SERIES : INFRAGRAVITY WAVES


2n @
I *


500 a.a *.IS SO SIt Si Sfl *0 At ii ItS S.C 5CC *7


EAYSCUT- hIV S A A AA A
0 0 t O I 0g 01. 0 O. I I a a. a IC S tO S. I
ENERGY SPECTRUM : TOTAL WAVE SYSTEM .5


0 ocn oc o0at c 02o oS *M O *C 0. e S tC 000 ? 0 n ** o S 0. *o
ENERGY SPECTRUM : INFRAGRAVITY WAVES s(

Figure 2.27: Case 1. x = 15.5 m (just seaward of the surf zone). (a)Measured total
wave system(b)Measured long wave (c)Energy spectrum of the total wave system

(d)Energy spectrum of long waves.


I 1.00 1.1 *. In s .j .. 0..S '.S i.s$ .c t *..


I5S go d" o9 061 6.






































TIME SERIES : INFRAGRAVITY WAVES


A .. ^ ^ ^ A A_ eg ^t as w a I J gA g + .l e______
IH1I
ENERGY SPECTRUM : TOTAL WAVE SYSTEM *1










3. .r -- *j. ** *u ** *u ** n ft a *j .-


e *,1 .
ENERGY SPECTRUM : INFRAGRAVITY WAVES


C...'
91


Figure 2.28: Case 1. x = 15 m. (just inside the surf zone) (a)Measured total wave

system(b)Measured long wave (c)Energy spectrum of the total wave system (d)Energy

spectrum of long waves.


-I ~-















E


3
5
-2
5,


E

a
u


0 oM a 5 0l5 02 0 e2 3 0 O 03O 0s o 65s 0 6 6a oS 0 s O asW e s0 0 Os I 1.9 1.1 I .is I.n s1. 1 1 .4 t j is i.s e4 L .,F
TIME SERIES : INFRAGRAVITY WAVES n2









A A A A A A A
0 0 0o @ 0 .1 as 45 I IJ .4 1 .0 .7 Is 1.9 1
ENERGY SPECTRUM : TOTAL WAVE SYSTEM *,


,3






S' 0 os a L 01. o0s 3 oN o.4 B4 o4 4M LB MU 4- -- -0 4
01 01 Us1 a31 0.4 0)6 Oan as aft 6. an J t O M *


ENERGY SPECTRUM : INFRAGRAVITY WAVES


(H.]
.2


Figure 2.29: Case 1. x = 14 m (well inside the surf zone).(a)Measured total wave

system(b)Measured long wave (c)Energy spectrum of the total wave system (d)Energy

spectrum of long waves.
































II -.-. A A,* t^ . .* I
o 0 o 0 o 0 0 o 00 .1 o J 0. I .I t I 1 1..4 1. 1
[(H.
ENERGY SPECTRUM :TOTAL WAVE SYSTEM '







ENERGY SPECTRUM : INFRACRAVITY WAVES 0,

Figure 2.30: Case 1. x = 11.6 m nearshoree). (a)Measured total wave system
(b)Measured long wave (c)Energy spectrum of the total wave system (d)Energy spec-
trum of long waves.












20.0-


0. 0-


0.@-


-20.0-


-40.0-


Caso 1
T=00,0.5,1.5,2.5,3.5,4.5 hours.


-60. 0


-w
8


1 I
10


Figure 2.


I I I I I I
12 14 16 18
DISTANCE ( M)
31: Case 1 Evolution of the bed' profile 0-1.5 hours.


I


'








so80












15-
5 CASE 1
w 12-
{/ e-0.5 HOURS
N 9- -3.5-4.5 HOURS
9 ---- 0-4.5 HOURS

to 6


, 3- -'"




o -6-
S-3-

0 6
z -9-

-12-

-15- I I I I I I
8 10 12 14 16 18 20
DISTANCE ALONG FLUME (M)


Figure 2.32: Case 1: Sediment transport rates at different times for Case 1.









Documentation of IG wave
The positions of the long-wave nodes and antinodes were fixed by the long wave
period and bottom profile. In addition to measuring and documenting the long-wave
structure via the stilling well arrangement, they were also evaluated by considering a
numerical solution of the free long wave equation. The linearized long wave equations
(continuity and momentum) can be cross- differentiated resulting in

a2 (h ) (2.31)

where 77 is the free surface displacement, h is the water depth and g is the acceleration
due to gravity.
Assuming a harmonic form

qr(x,t) = i(x)e-i't (2.32)

where a is the wave angular frequency, we have

ar2q + g z (h ) = 0 (2.33)

where the circumflexes have been dropped. For the special case of a planar beach
with
h = mx (2.34)

where m is the beach slope, we get

2r] 1 a77 1 02
+ + -2-+ = 0 (2.35)
8x2 x dx x gm

which is a Bessel equation with solution

7 ~- Jo( x) (2.36)

where Jo is the zeroth order Bessel function of the first kind, and

,C = 42. (2.37)
gm

Recourse must be taken to numerical methods to solve the equation for cases with
non planar bathymetry.







82
The long wave equation (2.33) was non-dimensionalized with

77

h' h-
ho

x = (2.38)
L

where r70 is the shoreline amplitude, ho is the depth at the toe of the beach and L
is the distance of the toe of the beach from the shoreline, and the primes indicate
non-dimensional quantities. Dropping the primes, we get

8277 8h 877
= + [h + h ] = 0 (2.39)
oz2 aX Tx

where
gho (2.40).
L2a2
with the boundary conditions

7 = 1 (at x=0),

h =0 (at x=0). (2.41)

Equation (2.39) was represented in finite-difference form and numerically evalu-
ated for the wave envelope. In this form, we have (with i=1 at x=0)

771=1 h = 0 (2.42)

whence
2 = 1- (2.43)
h2-)
Also,
yh;l 7(hie + hi+l) Th.+l
vi-l1[(A x) + r7i[1 (Ah )2 ]+ i+1[(i, = 0 (2.44)
qi 1[(AX)2I (AX)2 (aX)+

The solution was tested and compared favorably with the analytical solution for
planar beaches, Equation (2.36). Figure 2.33 presents an example of the numerical
and analytical solutions for the wave conditions of Case 3 on a planar beach of 1:19
slope.








1 00-


0.80-


z
00.60-








0.20



0.00
0.O00


N\


10


15


DI STANCE
Figure 2.33: Numerical (line) and analytical (symbols) solutions for a long wave \ it il
a frequency of 0.10 liz on a planar (1:19) beach.









Results
Figures 2.34, 2.35, 2.36 and 2.37 document the measured and predicted long wave
envelopes for the four cases, together with the initial and final (after 4.5 hours) bed
profiles. A least-squares procedure was used to scale the measured to the predicted
amplitudes. As the IG wave frequency was increased (from Case 1 to Case 4), the first
node was shifted closer to the shoreline. The antinode at the shoreline was generally
not very well predicted as measurements were not possible immediately around the
MSL position; however, there seems to be reasonable agreement in the prediction of
the next node and anti-node in all cases. It is noted that measurements close to the
shoreline were hindered by the fact that the shallow water depths made it difficult
to keep the pressure-sensing end of the stilling well system under water at all times.
This sometimes resulted in the intake of air bubbles in the tubing of the stilling well
system and possible concomitant error. It is interesting to note that the results of-
a numerical model developed by Kirby et al. (1981) for trapped long waves over an
arbitrary profile exhibited the feature of trapping antinodes over multiple bar systems.
For the present experiments, it was noted that the bar did not trap the antinode of
the IG wave in position.
Figure 2.38 shows the change in bar position with change in the measured position
of the nearest node and antinode of the IG wave envelope. Changes are plotted relative
to the next lower IG wave frequency. If the hypotheses involving bar formation at
nodal or antinodal positions is valid, the change in bar position should coincide with
change in nodal/antinodal position. This is the line of equivalence in the figure.
The nearly unchanging position of the bar does not support the hypothesis that bar
formation is due to the position of the IG wave envelope. The position of the exterior
edge of the surf zone was the same for all cases as the maximum wave height was
the same in all the experiments. This leads to the conclusion that the break-point
hypothesis is more relevant. It is also relevant to note that the scales of the standing
wave features are much broader than those of the bar.








LJ .1
w.
n

0.
LI0.



z
>
L0.


z
00.


0.


0-


85


CASE 1
MEASURED (eol Ld) AD PREDICTED dottedd)
LONG WAVE


8-1


6-


4-


2-
T


20.0


0.0-





-20.0-
8 8-


10


1 I I 1
12 14 16


CASE 1
T = 00 and 4.5 hours.


-40.0





-60.0


-.4.


' 10
10


Figure 2.34: Case 1 (a) Measured
Final (4.5 hours) bed profiles.


' I 1 I
12 14


' Ik


'
18


DISTANCE (M)

and predicted IG wave envelope, (b) Initial and


S I
18


V


U







CASE 2
MEASURED ( ol td) AND PREDICTED (doLt d)
LCOG WAVE


U





L2
C
u


-40.0-


0.8-


0.6-


K0.4-
3
50.2-


0.0
8
20.0





0.0-





-20.0-


12
12


14


' It


CASE 2
MEAN PROFILES AT 00.


' I


> 18


4.5 HOURS.


-I


I 1
8 10


I I I I
12 14
DISTANCE (M)


Figure 2.35: Case 2 (a) Measured and predicted IG wave envelope, (b) Initial and
Final (4.5 hours) bed profiles.


w 1.0-
a(
0
I


10
10


-60.0


S I
16


1 I
18


1 I II








U 1 .0-
0-
w0.8-

Z
0.6-





60.2-
_z


0.0
20. to


I I1


0.0-




-20.0-
- 20 .08


CASE 3
MEASURED (eol td) AND PREDICTED (do LLed)
LONG WAVE


14


1 I
16


-40.0-


-1- I I


12 14
DISTANCE


1 I
16
( M)


Figure 2.36: Case 3 (a) Measured and predicted IG wave envelope, (b) Initial and
Final (4.5 hours) bed profiles.


16


-60.0


S I
10


I
18


1' 0
10


1 I
12







CASE 4
MEASURED (soI td) AND PREDICTED (dotted)
LONG WAVE


-.1 I. \_ -


10


1 I
12


14


CASE 4
T = 00


AND 4.5 hours.


0.0-


-20.0-


-40.0-


1
12
D


I
14
I STANCE


Figure 2.37: Case 4 (a) Measured and predicted IG wave envelope, (b) Initial and
Final (4.5 hours) bed profiles.


1.0


w
CL
00.
LJ
z



Z
0.


0
z
0
1 -


8-


6-

4-


1 91


8
0-


20.


16


18


-60.0


-r


16
16


( M)


18


I I




10


























LEGEND
-1.0
SChange in Change in
Long Wave Position
c* Period (sec) Node Antinode
Z Z' 8.3 to 10 A A
-i 10to 12.5 0 0
0 -0.5 12.5 to 16.7 0 3

0 /


-0.5 // 0.5 1.0 1.5 2.0


CHANGE IN POSITION OF NODE OR ANTINODE (m)


Figure 2.38: Change in bar position with changes in position of nodes and antinodes.




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