• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 List of Figures
 Key symbols
 Abstract
 Introduction
 Data collection
 Wave transmission
 Structure induced currents
 Conclusions
 Appendix A. Significant wave height...
 Appendix B. Wave transmission theory...
 Appendix C. Laboratory bottom drogue...
 Reference
 Biographical sketch






Group Title: UFLCOEL-94022
Title: Wave transmission and current patterns associated with narrow-crested submerged breakwaters
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00085012/00001
 Material Information
Title: Wave transmission and current patterns associated with narrow-crested submerged breakwaters
Series Title: UFLCOEL-94022
Physical Description: xii, 118 leaves : ill. ; 28 cm.
Language: English
Creator: Browder, Albert E
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal & Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1994
 Subjects
Subject: Breakwaters -- Mathematical models   ( lcsh )
Shore protection -- Mathematical models   ( lcsh )
Artificial reefs -- Florida -- Palm Beach   ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF   ( lcsh )
Coastal and Oceanographic Engineering thesis, M.S   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by Albert E. Browder.
Thesis: Thesis (M.S. in Engineering)--University of Florida, 1994.
Bibliography: Includes bibliographical references (leaves 116-117).
 Record Information
Bibliographic ID: UF00085012
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 33143197

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
        Page i-a
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
        Page iv
    List of Figures
        Page v
        Page vi
        Page vii
    Key symbols
        Page viii
        Page ix
        Page x
    Abstract
        Page xi
        Page xii
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
    Data collection
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
    Wave transmission
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
    Structure induced currents
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
    Conclusions
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
    Appendix A. Significant wave height and period data from seadata gages
        Page 92
        Page 93
    Appendix B. Wave transmission theory derivation
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
    Appendix C. Laboratory bottom drogue trajectories/velocities
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
    Reference
        Page 116
        Page 117
    Biographical sketch
        Page 118
Full Text



UFL/COEL-94/022


WAVE TRANSMISSION AND CURRENT PATTERNS
ASSOCIATED WITH NARROW-CRESTED
SUBMERGED BREAKWATERS







by




Albert E. Browder






Thesis


1994















WAVE TRANSMISSION AND CURRENT PATTERNS
ASSOCIATED WITH NARROW-CRESTED SUBMERGED BREAKWATERS



















By

ALBERT E. BROWDER


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING

UNIVERSITY OF FLORIDA


1994










ACKNOWLEDGEMENTS

I want to express my sincere thanks to my committee chairman, Dr. Robert J. Thieke,

for his support and guidance, especially down the stretch. Considerable thanks go to Dr. Robert

G. Dean, not only for serving as a committee member, but for providing me with numerous

opportunities to 'get my feet wet,' for he knows I do not want to just stand around. I also thank

Dr. Dean for introducing me to the world of coastal politics. My thanks also go to Dr. Ashish

J. Mehta for serving on my thesis committee.

Vernon Sparkman, Jim Joiner, Sidney Schofield, Chuck Broward, Danny Brown, and

Sonya Brooks deserve my greatest thanks for their support in the Coastal and Oceanographic

Engineering Laboratory, making my lab study an unforgettable experience. I want to thank Vik

Adams and George Chappell for including me in their field excursions all over the state.

Thanks go to those people at the Town of Palm Beach, the Department of Environmental

Protection, and American Coastal Engineering, Inc. for their help and support of this project.

Many people in the Coastal Engineering office deserve a huge hand for making this work

so much fun. Many thanks go to Mike Dombrowski, my P.E.P. Reef partner in crime, for all

the field trips and headaches. Kenny, Mike, Paul, Eric, Chris and Monica, Mark, Sue, Darwin,

Tom, Santiago, Jie, and Wally made the days seem much shorter. Thanks go to Keeley for

taking responsibility. The real reason I can graduate is the support from Becky, Sandra, Lucy,

Helen, Cynthia, and Laura, because if you don't know the secretaries, you don't know anyone.

Market Street didn't hurt either. Thanks, Pam.

Finally, I want to thank my parents, Larry and Susan Browder, for everything, but most

importantly for the opportunity to take opportunity.

















TABLE OF CONTENTS


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


. . . . . . . . . 11


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

KEY TO SYMBOLS ........................................... viii


A BSTRA CT ................................................. xi

CHAPTER 1 INTRODUCTION .................................... 1
1.1 Objectives and Rationale ................................. 2
1.2 Report Organization .................. ................... 4
1.3 Literature Review ..... ...... ...... ..... ....... ..... . 5
1.3.1 Wave Transmission Studies ........................... 5
1.3.2 Structure Induced Current Patterns ...................... 13
1.4 Com m ents ........................................... 14


CHAPTER 2 DATA
2.1 Descriptio
Program.
2.1.1
2.1.2
2.1.3
2.1.4
2.1.5
2.1.6
2.1.7
2.1.8
2.2 Methodolo
2.2.1
2.2.2
2.2.3
2.2.4
2.3 Comments


COLLECTION ................
n of the Midtown Palm Beach Monitoring
. . . . . . . . . . . . . .
Site Description ................
Wave Data Analysis ..............
Background Wave Climate and Verification
Current Measurements ............
Volumetric Changes ..............
Unit Settlement .................
Scour Rod Measurements ..........
Present Status ..................
gy of Laboratory Study ...........
Experimental Equipment ...........
Test Plan ....................
Wave Height Measurements .........
Current Measurements ............
. . . . . . . . . . . . .


CHAPTER 3 WAVE TRANSMISSION .............
3.1 Field Measurements ...................
3.1.1 Transmission Coefficient Determination
3.1.2 Spectral Analysis ...............
3.1.3 Individual Wave Tracking .........


. . . . . . . . . 15

. . . . . . . . . 15
. . . . . . . . . 16
. . . . . . . . . 18
S. . . . . . . . 22
. . . . . . . . . 22
. . . . . . . . . 22
. . . . . . . . . 24
. . . . . . . . . 25
. . . . . . . . . 25
. . . . . . . . . 26
....... ......... 26
. . . . . . . . . 28
................ 31
. . . . . . . . . 32
. . . . . . . . . 3 3

. . . . . . . . . 35
. . . . . . . . . 35
. . . . . . . . . 36
. . . . . . . . . 4 0
. ... ......... 44









3.2 Laboratory Measurements ................. ................ 47
3.2.1 Cross-Shore Wave Height Decay ....................... 47
3.2.2 Laboratory Transmission Coefficients .................... 49
3.3 Analytical Model ............. .. ..... ........ ......... 52
3.3.1 Totally Submerged Barriers ......................... 52
3.3.2 Partially Submerged Barriers ........................ 54
3.4 Comments ................... ........................ 59

CHAPTER 4 STRUCTURE INDUCED CURRENTS ........................ 60
4.1 Motivation from Field Results ............ .. ... ..... ......... 60
4.2 Laboratory Investigations .................. ................ 65
4.2.1 The 'Pumping Current' ................ ............ 65
4.2.2 Other Current Effects ......... .................... 69
4.3 Analytical Approach .................................... 71
4.3.1 Explanation of the Problem .......................... 71
4.3.2 Mass Conservation Approach ........................ 74
4.3.3 Momentum Approach ................................... 76
4.4 Comments ............................................. 81

CHAPTER 5 CONCLUSIONS .................................... 83
5.1 Midtown Palm Beach Installation ............................. 83
5.2 Vero Beach Laboratory Study ............................... 85
5.3 Analytical Models ........................................ 87
5.4 Design Considerations ................................... 89

APPENDIX A SIGNIFICANT WAVE HEIGHT AND PERIOD DATA FROM
SEADATA WAVE GAGES ............................. 92

APPENDIX B WAVE TRANSMISSION THEORY DERIVATION .............. 94
B.1 Totally Submerged Barriers ................................ 94
B.2 Partially Submerged Barriers ............... ............... 98

APPENDIX C LABORATORY DROGUE TRAJECTORIES/VELOCITIES ........ 101

REFERENCES ................................................ 116

BIOGRAPHICAL SKETCH ........................................ 118















LIST OF FIGURES

1.1 Transmission Coefficient vs. Non-Dimensional Wavelength for Four Analytical
Approaches. Freeboard Ratio (f/h) = -0.25. ......................... 8

1.2 Transmission Coefficient vs. Relative Freeboard for Four Experimental
Studies (H /L = 0.02 to 0.04) ................................. 11

2.1 Location Map Relative to Port of Palm Beach Entrance ................. 17

2.2 Location of P.E.P. Reef ..................................... 17

2.3 Cross-Sectional View of P.E.P. Reef (Courtesy American Coastal
Engineering, Inc.) ......................................... 18

2.4 Survey Profile Plan ........................................ 23

2.5 W ave Basin Schematic ...................................... 27

2.6 Reef Unit Arrangements for Initial Tests ................. ......... 29

2.7 Reef Arrangements for Additional Model Testing ..................... 31

2.8 Cross-Shore Wave Height Profile Lines ........................... 32

3.1 Transmission Coefficient History, Midtown Palm Beach Installation.
1 January 1994 to 24 October 1994, CDN Gages ..................... 37

3.2 Wave Height Transmission Coefficients, Midtown Palm Beach Installation.
Seadata Gages, 21 September 1994 to 24 October 1994 ................. 38

3.3 Significant Wave Heights, Midtown Palm Beach Installation. Seadata Gages,
21 September 1994 to 24 October 1994 ........................... 40

3.4 Spectral Density of Offshore, Nearshore, and Shoaled Offshore Records.
CDN 26 November 1993, 6:00 PM .............................. 42

3.5 Spectral Density of Offshore, Nearshore, and Shoaled Offshore Records.
Seadata 5 October 1994, 4:00 AM .............................. 42

3.6 Spectral Density of Offshore, Nearshore, and Shoaled Offshore Records.
Seadata 17 October 1994, 8:00 AM ............................. 44

v








3.7 Surface Elevation Records for Offshore and Nearshore CDN Gages.
18 December 1993, 6:00 PM ................................ 45

3.8 Cumulative Frequency Distribution of Wave Heights for the Offshore,
Nearshore, and Shoaled Offshore Records. 18 December 1993, 6:00 PM ...... 46

3.9 Cross-Shore Wave Height Profiles for Initial Laboratory Tests. Freeboard
Ratio, f/h = 0.0 ................... .......... ............. 48

3.10 Wave Height Transmission Coefficients for Initial Laboratory Tests versus
Freeboard Ratio, f/h = 0.0 ................................... 49

3.11 Transmission Coefficients Versus Relative Freeboard, f/Hi ............... 51

3.12 Definition Sketch for Transmission Over a Submerged Barrier ............. 53

3.13 Analytical Approaches for Transmission Coefficient Compared to Laboratory
and Literature. Laboratory Scale Values, Hi = 0.012 ft ................. 57

4.1 Isolines of Elevation Change (ft), August 1993 to December 1993. Contours
in 1.0 foot intervals. .................. ..................... 61

4.2 Volumetric Changes for Latest Survey Period and Last Year (yds3). .......... 62

4.3 Bottom Drogue Trajectories, f/h = 0.0. .......................... 66

4.4 Schematic of Mass Transport Profile Under Wave Passing Over a Barrier ...... 72

4.5 Schematic of Wave Basin and Pumping Currents ...................... 73

4.6 Average Exit Velocity vs. Length of Structure. Continuous Structure,
f/h = 0.0. Figure Applicable for Model Conditions. .................... 75

4.7 Schematic of Lateral Inflow Model to Determine Water Surface Profile ....... 77

4.8 Ponding Level Calculated for Laboratory Scale, 100% Flow Divergence
H = 0.04cm (0.012 ft), T = 2 s. .............................. 79

4.9 Ponding Levels for P.E.P. Reef Prototype Scale. H = 3.28 ft, T = 6 s.
Velocities Shown Are Exit Plane Values (x = 2,000ft.) ................. 80

A. 1 Offshore Seadata Gage Significant Wave Height, Julian Date, 1994. ......... 93

A.2 Offshore Seadata Gage Modal Period, Julian Date, 1994. ................ 93

A.3 Nearshore Seadata Gage Significant Wave Height, Julian Date, 1994. ......... 93

A.4 Nearshore Seadata Gage Modal Period, Julian Date, 1994. ............... 93

vi








B.1

B.2

C.1


C.2

C.3

C.4


C.5

C.6

C.7


C.8

C.9

C.10

C.11

C.12

C.13

C.14


Definition Sketch of Bernoulli Principle Theory .............

Definition Sketch of Weir Flow Theory ..................

Control and Type A Case, f/h = 0.0. Wavemaker is to the right.
ft/s . . . . . . . . . . . . . . . . . . . .. .

B and C Cases, f/h = 0.0. Wavemaker is to the right. Units in ft/s

Type D Case, f/h = 0.0. Wavemaker is to the right. Units in ft/s

Control and Type A Case, f/h = -0.2. Wavemaker is to the right.
ft/s . . . . . . . . . . . . . . . . . . . ..

B and C Cases, f/h = -0.2. Wavemaker is to the right. Units in ft/s

Type D Case, f/h = -0.2. Wavemaker is to the right. Units in ft/s

Control and Type A Case, f/h = -0.4. Wavemaker is to the right.
fts . . . . . .. . . .. ... . . . . . . . . ....


B and C Cases, f/h = -0.4. Wavemaker is to the right. Units in ft/s .......

Type D Case, f/h = -0.4. Wavemaker is to the right. Units in ft/s ........

Type E Case, f/h = 0.0. Offset Distances = 2w and 4w. Units in ft/s ......

Type E Case, f/h = 0.0. Offset Distance = 6w. Units in ft/s ............

Type F Case, f/h = 0.0. Offset Distances = 2w and 4w. Units in ft/s ......

Type F Case, f/h = 0.0. Offset Distance = 6w. Units in ft/s ............

Type G Case, f/h = 0.0. Offset Distance = 4w. Units in ft/s ............


Units in






Units in






Units in


. 95

. 98


102

103

104


105

106

107


108

109

110

111

112

113

114

115















KEY TO SYMBOLS

A channel cross sectional area

Asw linearization constants

At structure cross sectional area

A, area of opening in barrier

B channel width

C wave celerity

Cf Chezy coefficient

C, wave group celerity

C1,2,3,4 coefficients, Ahrens (1987)

dso median stone diameter, Ahrens (1987)

d, total water depth, Ahrens (1987)

E wave energy per unit surface area

Ec specific energy, weir flow

f freeboard

f/h freeboard ratio, freeboard over water depth

f/Hi relative freeboard, freeboard over incident wave height

.7 wave energy flux

g acceleration due to gravity

h total water depth

hc critical depth over weir








hc height of structure, Ahrens (1987)

Hir,. wave height (incident, reflected, or transmitted)

H, significant wave height

H. offshore significant wave height, Ahrens (1987)

i subscript denoting incident (offshore condition)

k wave number, 27r/L

K,,t wave height coefficient, reflected or transmitted

L wavelength

Lp wavelength, Ahrens (1987)

M momentum function

N number of waves in record

P wetted perimeter

q flowrate

q, flowrate through barrier openings

q, flowrate over weir

r subscript denoting reflected wave

s spreading parameter

Sf channel friction slope

So channel bottom slope

t subscript denoting transmitted conditions

T wave period

u velocity

w structure cross-shore width

x distance along structure








z elevation above mean water level

ia coefficient, Goda (1969)

3 coefficient, Goda (1969)

7y specific weight of seawater

r Gamma function

A integration step

0 water surface profile

p density of seawater

a wave angular frequency, 2ir/T

TO channel bottom shear stress

4 wave direction















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering

WAVE TRANSMISSION AND CURRENT PATTERNS
ASSOCIATED WITH NARROW-CRESTED SUBMERGED BREAKWATERS

By

Albert E. Browder

December 1994

Chairperson: Dr. Robert J. Thieke
Major Department: Coastal and Oceanographic Engineering

This study presents design guidance as to the performance of narrow crested submerged

offshore breakwaters. Performance information is based on a field monitoring program currently

underway by the Coastal and Oceanographic Engineering Department of the University of Florida

(UFCOE) of the Palm Beach, FL, Prefabricated Erosion Prevention (P.E.P.) Reef Installation

and a laboratory investigation of the P.E.P. Reef recently carried out by UFCOE. Analytical

models developed for submerged barriers and a review of pertinent literature on the subject

provide additional insight.

Performance of a submerged barrier focuses on two major aspects. Wave attenuation is

the primary objective of a breakwater. Generally, submerged barriers are expected to provide

partial reduction of storm waves in order to provide some measure of shore protection. The

second consideration involves the alteration of the nearshore current pattern in the vicinity of the

reef. Any structure placed in the nearshore zone will change the existing current patterns, which

in turn will alter the sediment transport in that region.








Design guidance for submerged barriers is provided in terms of planform arrangement

of barriers and relative height of the structure. The relative height of the structure becomes the

primary variable in any submerged breakwater design since it directly affects the wave height

attenuation. The degree of wave height attenuation is also found to be related to the alteration

of the current system in the vicinity of the structure.

To provide a significant amount of wave height attenuation (at least 10%), it is

recommended that the height of the barrier be at least 80% of the mean water depth, including

any settlement of the barrier and any storm surge associated with the design wave height.

Alternatively, it is recommended that the amount of clearance over the structure crest should be

no more than 1.3 times the design incident wave height. The determination of the crest elevation

then dictates the degree of change in the associated current patterns. To offset any adverse

current generation in the lee of the structure, a problem documented herein through laboratory

results, it is recommended that a submerged shore-parallel breakwater be segmented and offset

along its length in order to relieve any adverse currents that may be created.

It is recognized that the performance of submerged breakwaters is extremely site specific.

Results from one installation should not be applied directly to another. This study is intended

to provide general design criteria and planform options.














CHAPTER 1

INTRODUCTION

In recent years there has been a desire to find a long lasting solution to beach erosion.

"Soft" solutions such as beach nourishment and beach dewatering have been shown to be effective

in certain applications. In many cases, however, these solutions either prove to be ineffective

or costly to maintain. Beach nourishment, for example, often requires additional placement of

material on the beach to maintain the success of the project. In light of these difficulties,

attention has turned to permanent "hard" structures placed in the coastal zone to prevent beach

erosion. One such structure is a submerged breakwater, which is the focus of this study. A

submerged breakwater is a rubble-mound or solid barrier whose crest is at or below the Mean

Water Level (MWL) and is usually placed parallel to shore. These breakwaters are used to

provide partial protection against incident wave attack, primarily against large storm waves.

Submerged breakwaters are an attractive alternative to large emergent structures. The

primary benefit is the financial savings of submerged barriers. Since the crest elevation is

considerably lower than that of an emergent barrier, the amount of material needed for

construction is obviously considerably less. Another benefit is the aesthetic value of a submerged

structure which does not obstruct an otherwise attractive ocean view. An additional benefit is that

the barrier often serves as an artificial reef, attracting its own biological community. The

immediate drawback to a submerged breakwater is the lower level of protection it affords against

wave attack. Another possible problem is the alteration of the natural current and sediment

transport systems. These aspects require attention when considering such a structure for use

along a given stretch of beach.








2

Most of the research concerning submerged breakwaters focuses on wave transmission

over such barriers. Laboratory studies are plentiful, dating back to the 1930s in some cases.

This material covers many wave conditions and barrier configurations, both experimentally and

analytically. Very little data exist from field measurements as most actual installations have

either not been monitored or have not been monitored for wave climate. Very little information

exists about the behavior of the current patterns in the vicinity of such barriers. Some numerical

analysis has been conducted, and a handful of laboratory experiments discuss this behavior, but

field data are nearly non-existent due to the intensive measurements required to adequately

address the problem.

The State of Florida passed legislation in 1989 to allow experimental projects to be

installed to try to solve the beach erosion problem. Since that time, two submerged breakwater

projects have been installed, one in Palm Beach fronting the DuPont property, and the second in

Midtown Palm Beach. The first installation was not extensively monitored and has since suffered

wave attack which has scattered the units in the project and rendered it ineffective. The second

installation is currently being monitored for its performance in the modification of both the

sediment transport patterns and the wave climate.

A third experimental project is currently under consideration in Vero Beach, Florida.

This project builds on the experiences of the previous two installations and has prompted

additional engineering study into the behavior of submerged barriers. The focus of the additional

work lies in physical and numerical modelling. For projects currently under consideration and

for future installations, a basis for design is needed. This study attempts to fill that need.



1.1 Objectives and Rationale

The purpose of this paper is to present results of recent investigations into the

performance of submerged breakwaters and to provide basic design information to those planning








3

to install such a structure. As in most coastal engineering endeavors, results can be very site

specific and many times predicting the outcome of a project can be difficult. It is necessary to

have a basic idea of how a submerged barrier will perform when installed, particularly in terms

of wave attenuation and potential side effects.

This paper presents information on wave height attenuation for submerged breakwaters,

specifically narrow crested barriers. These are structures whose crest width is much smaller than

the wavelengths of the waves approaching the barrier. Field measurements, laboratory studies,

analytical developments, and pertinent literature are presented in an attempt to define the wave

transmission behavior of a given submerged barrier arrangement. Design guidance is given in

general terms to establish the necessary height of a barrier to achieve a given level of wave

attenuation.

Guidance is also offered to the changes in the current and sediment transport systems that

may result from installing a submerged barrier. This focuses on relieving or preventing currents

that may induce erosion in the vicinity of the barrier. This erosion runs counter to the objectives

of installing a submerged breakwater and it is obviously desirable to minimize or prevent such

a problem. Recommendations for planform design based upon physical modelling and field

observations are given.

The rationale for this report stems from the three year monitoring program of the

Midtown Palm Beach Prefabricated Erosion Prevention (P.E.P.) Reef. This program, conducted

by the University of Florida Coastal and Oceanographic Engineering Department and sponsored

by the Florida Department of Environmental Protection and the Town of Palm Beach, FL,

involves monitoring of the wave climate, sediment erosion/accretion patterns, scour behavior,

sediment size analysis, and structure settlement of a 4,000 foot long pre-cast concrete submerged

breakwater. In order to determine the performance of this structure, information regarding the








4

expected behavior was needed. The literature review included in this report attempts to define

the expectations of structures like the P.E.P. Reef, specifically submerged, narrow crested,

impermeable breakwaters. Another rationale for this report is the consolidation of the material

gained during this monitoring program and a laboratory study conducted for the Vero Beach, FL,

P.E.P. Reef permit request. In the past, the coastal engineering field has suffered from a lack

of documentation regarding field projects. Monitoring of projects, such as beach nourishment

fills, provides valuable information that can be used to improve techniques to prevent beach

erosion.



1.2 Report Organization

This report is arranged as follows. A literature review of submerged breakwaters follows

this section and includes prominent works on wave transmission and associated current patterns.

Chapter 2 discusses the methodology and development of an extensive field monitoring program

as well as a physical model study conducted as part of a State of Florida permit request for

installation of a submerged barrier. Chapter 3 will present the wave transmission results from

the above investigations and comparison of these with a simple analytical development and

previously published works on the subject. Chapter 4 will discuss the limited amount of data on

current patterns from the field and lab work and presents an analytical approach for the prediction

of the flow behind such structures. Again comparison to existing literature will be made. Some

conclusions about the currents in the lee of such structures will be drawn from hydrographic

survey results taken during the monitoring program of the Midtown Palm Beach (P.E.P.) Reef

Installation. Chapter 5 will summarize the results and present design recommendations for

submerged breakwaters.








5

1.3 Literature Review

The dominant information related to submerged breakwaters concerns the wave

transmission characteristics of such structures. Of the many sources found regarding this topic,

most involve rubble mound structures, since these are practical to build and have been

constructed in several areas around the world. The first portion of this review attempts to define

the history of wave transmission studies and discuss some of the more relevant works that involve

submerged breakwaters. Where possible, an attempt is made to focus on the portions of these

works that involve narrow crested impermeable structures.

A considerably smaller body of knowledge exists regarding the current patterns around

offshore submerged breakwaters. The material found on this topic is presented herein, and will

be developed and compared to both laboratory and analytical data in Chapter 4.



1.3.1 Wave Transmission Studies

The use of artificial submerged breakwaters is not new to the coastal engineering field.

Hall (1939) mentions the installation of a 'low pre-cast concrete "artificial reef" parallel to shore

in shallow water' intended to increase sand accretion in the Hollywood, Florida, area. While no

details of that installation were given, laboratory experiments are described for triangular,

trapezoidal, and thin walled (narrow crested) breakwaters. The study measured the wave

transmission of monochromatic waves of varying heights in varying water depths over the

structures. Hall (1939) concluded that a submerged barrier parallel to shore will reduce the rate

of littoral drift in its lee. From this he concluded that the barrier would cause accretion on the

protected shoreline and provide 'a means of protecting a beach without disfiguring it.' The report

also noted that a vertical wall is the most effective shape in attenuating wave height and that for

storm wave protection, the structure height should be at least 0.8 times the average water depth.








6

Dean (1945) presented an analysis of the reflection of waves by a submerged plane

barrier. Using linear wave theory, reflection and transmission coefficients for deep water waves

were derived. This development did not consider any loss of energy through turbulence or wave

breaking over the barrier. Johnson et al. (1951) presented an energy flux approach to

determining transmission coefficients, Kt, defined as the ratio of transmitted to incident wave

height. By calculating the average energy flux above a submerged barrier crest (equation (1.1))


= f 2 cosh2k(h+z)
S = f pogonz dzdt (1.1)
TJ -t cosh (kh) sinh (kh)

and redistributing that portion of the energy flux over the entire water column on the lee side of

the barrier, a transmission coefficient is obtained (equation (1.2)). This equation is applied for

a given value of barrier submergence.



K = 1 sinh(2k(h-f)) + 2k(h-f) (1.2)
J \sinh(2kh) + 2kh

At this point it is useful to define the term freeboard ratio. This non-dimensional value,

f/h, is used to describe the distance from the mean water level (MWL) to the barrier crest divided

by the total water depth at the barrier toe. It is defined herein as a negative quantity in order to

distinguish submerged structures from emergent structures. Several other non-dimensional values

are also used to plot transmission coefficient variation. The freeboard, -f, is often divided by the

incident wave height, Hi, to create a relative freeboard value. This ratio is also negative, again

to reflect the fact that it describes a submerged barrier. This notation means that, for the same

water depth, a structure with a lower freeboard ratio (such as -0.6) lies further below the surface

than a structure with a larger freeboard ratio (such as -0.2).

Ogilvie (1960) provided an analytical treatment of wave transmission of shallow water

waves over thin walled barriers. His results were presented as a function of relative wave length








7

(water depth divided by wavelength). Mei and Black (1969) presented coefficients for a full

range of relative wave lengths from solutions of the Laplace equation for wave propagation over

submerged obstacles. Mei and Black provided coefficients for both thin walled barriers as well

as barriers of finite width. An interesting finding of this work involves the oscillating

transmission coefficient that results from varying the crest width. The relation between the

wavelength of the attenuated waves and the crest width affects the degree of attenuation

experienced. Massel (1983) verified this phenomenon, stating that the finite barrier width causes

higher harmonics to be generated in the space above the barrier and transmitted forward as free

waves. Harmonic generation also provides a means of distinguishing between barriers with finite

crest widths and those considered to be narrow crested. While this study focuses on narrow

crested structures where harmonic generation does not occur, this phenomenon is noteworthy in

the design considerations of submerged breakwaters.

Figure 1.1 presents a comparison of the analytical developments discussed above for a

freeboard ratio of -0.25. The plot presents transmission coefficient versus relative wave length.

Again, the transmission coefficient is defined as the ratio of the transmitted wave height to the

incident wave height. The plot shows the range of applicability of the various methods. Ogilvie

(1960) presented results for shallow water waves, therefore these results pertain to values less

than kh = 0.314. Similarly, Dean (1945) developed equations for deep water waves (kh >

3.14). The results indicate the effect of wavelength on wave transmission. The work of Mei and

Black (1969) provides a value for all kh, and shows that the maximum wave height reduction for

this freeboard ratio value is only approximately 8%.

As the length of the incident wave increases, the barrier effect diminishes as only a small

portion of the wave experiences the barrier at one time. An extreme example of this would the

astronomical tides. These waves obviously experience no effect of the barrier. As the wave

length decreases relative to the water depth, the wave motion does not extend deep enough to












1.0




0.9




0.8




0.7




0.6




0.5


- Dean(1945)
.----- Johnson et al. (1951)
-- O. gilvie(1960)
Mei & Black (1969)


5 6

Short Waves


Figure 1.1 Transmission Coefficient vs. Non-Dimensional Wavelength
Analytical Approaches. Freeboard Ratio (f/h) = -0.25.


for Four


experience the effects of the barrier and the waves pass over the barrier unaffected. Therefore,

only an intermediate range of wavelengths experiences an appreciable amount of wave height

attenuation. Fortunately, this range of wavelengths applies to typical wind wave climates

approaching most coastlines. An interesting note from Figure 1.1 is that although the energy flux

approach of Johnson et al. (1951) is given for all kh, laboratory experiments indicate that realistic

results are only obtained for deep water cases. This is observed for the full range off/h values.

Goda (1969) and Goda et al. (1967) conducted extensive laboratory measurements of

submerged breakwaters. He presented transmission coefficients as a function of the relative

freeboard and developed an empirical expression for Kt as well as best fit curves through the

individual data points. The tests included various crest widths, from 0.9 cm (0.03 ft, considered


0 1

Long Waves


' I I L 41CP
-- -~**~' - -- .


/~


I

I.


/--1


S/'
-
/:
/

^ ./' I ,


-


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








9

to be narrow crested) to 40 cm (1.31 ft) in width, and various incident wave heights, from 3 to

34 centimeters (0.10 to 1.12 ft). The tests also included a variation in water depth, creating a

range of freeboard ratios from -0.2 to 0.0 for the submerged barrier tests. Equation (1.3)

presents the empirical expression for Kt from these experiments. The values of the coefficients

a and # are proposed as 2.0 and 0.4 for the thin-walled barriers in the re-analysis (Goda et al.,

1969), respectively.


K H .5 [1sin f + p ] (1.3)
H 2 a HM

Dattatri et al. (1978) tested a range of shapes and depths of submergence to determine

transmission coefficients. This report concluded that the relative depth of submergence is the

most important parameter in the performance of submerged breakwaters. Quantitative data from

the thin-walled barrier tests were not presented for analysis.

As stated previously, many submerged breakwaters are rubble mound structures

composed of large stones. A large laboratory test was conducted by Seelig (1980) to study the

wave transmission characteristics of various breakwater designs. Most of the designs involved

rubble mound structures and all involved barriers of finite crest width. Ahrens (1987) conducted

over 200 laboratory tests of various submerged rubble mound configurations to determine

damage, stability, and wave attenuation characteristics of these barriers. From the wave

transmission data, the following expression for K, was developed, where C1 = 1.188, C2 =

0.261, C3 = 0.529, and C4 = 0.00551, At = cross sectional area, Lp = incident wavelength,

d5o = median stone diameter, and f/H, = freeboard ratio < 1.0.



1.0
Ke A f A3/2 (1.4)
1.0+ d) (d Hmo+ dso 2Lp)]
ds "Ip H,, d50 ^p








10

While equation (1.4) was developed for rubble mound barriers, the influence of the stone

size is small. This is seen since the coefficient relating to median stone diameter, C4, is two

orders of magnitude smaller than C3. It will be shown in the results section that equation (1.4)

yields results that compare well with solid, non-rubble barriers and that the stone size effect is

small.

Van Der Meer and d'Angremond (1992) reviewed several works on rubble mound

submerged breakwaters, including Ahrens (1987) and several experiments conducted at Delft

Hydraulics in the Netherlands. They also cite the relative freeboard of the barrier as the most

important design parameter of such structures. An interesting and counter-intuitive result from

their literature survey is the suggestion that the transmission coefficient is constant at 0.8 in the

lower range of relative freeboards tested (-2.0 < f/Hi < -1.0). As the relative freeboard

approaches -oo, it is expected that the transmission coefficient would approach 1.0 as the barrier

height shrinks to 0.0. Thus it is expected that there would be an asymptotic behavior of Kt as

the relative freeboard decreases.

Cornett et al. (1993) investigated the performance of reef-type breakwaters, both as stand-

alone shore protection structures and in tandem with larger emergent breakwaters. This work

investigated not only the transmission of a single representative wave, but also the transmission

of the full wave spectrum over a structure. This provides a more detailed look into the energy

transmission and dissipation over submerged barriers. Other methods of investigating wave

transmission characteristics are given. The surface elevation records of the offshore and onshore

sides of the reef area are plotted to show the reduction in wave height of individual waves. From

these types of records a cumulative distribution of wave heights can be computed. Comparison

of the offshore and onshore records is provided in this work to show how the higher waves in

a record experience more wave attenuation. This would indicate that submerged breakwaters








11

would have a greater effect on storm waves than on mild waves. However, this improvement

in wave attenuation during storms is often countered by an increased water level due to the

associated storm surge.

Figure 1.2 presents the results of several of the laboratory studies discussed above. The

transmission coefficient is plotted versus relative freeboard, consistent with most of the laboratory

works surveyed above. In each case the wave steepness and water depth to wavelength ratios are

1 .0 q I I o -- 1.- ..b 4.. .j. .. | I I I I I I I I I I I I I I I I I


0.8



0.6



0.4



0.2


A r\A


u.,


II


l. .. . .. ...


-- Goda(1967)exp
------ Goda (1969) eq. (1.3) -- --
---- Ahrens (1987) eq. (1.4)
S Van Der Meer
& d'Angremond (1992)
... Cornett et al. (1993)


submerged

si 1i 1111111Il


111111 I


-5 -4 -3 -2 -1 0 1 2
f/Hi
Transmission Coefficient vs. Relative Freeboard for Four Experimental
Studies (Hi/L = 0.02 to 0.04).


approximately equal. Goda et al. (1967, 1969) presented a curve plotted through experimental

points as well as an equation taken from the entire set of data from the experiments. Both

representations are shown, and they show some variation, differing by 30 percent atf/Hi = 0.0.

Equation (1.3) does include data from finite crest width structures, which serves to lower the

transmission coefficient in comparison with the narrow-crest only cases.


Figure 1.2





l| m








12

Van Der Meer and d'Angremond (1992) presented tests for both emergent and submerged

cases, but did not extend their tests to the submerged range where they reported a constant

transmission coefficient. They did, however, test emergent structures up to a range where the

reported transmission coefficient becomes constant at approximately 0.1. These findings are not

supported by other laboratory studies. Of primary interest here is the range of submerged

barriers where the transmission coefficient would be expected to asymptotically approach 1.0.

In this case, the wave height over the structure becomes very small or the height of the barrier

becomes very small. This would present little to no obstruction to an incident wave, hence

allowing it to pass unattenuated.

Figure 1.2 indicates that in most cases the effectiveness of submerged breakwaters in

attenuating wave heights diminishes with increasing freeboard. Below a value off/Hi = -1.5 the

incident wave height was reduced by less than ten percent in passing over the structure. In most

of the literature reviewed, the amount of freeboard over the barrier was cited as the most

important variable in the performance of a submerged breakwater. The variable most often used

in conjunction with the freeboard is the incident wave height. In Figure 1.2 the ratio of

freeboard to incident wave height is used to compare transmission coefficients from several

different laboratory studies over a 25 year span. Using two different ratios does lead to some

confusion, however. Comparison of the analytical results presented in Figure 1.1 to the

experimental results in Figure 1.2 becomes difficult in that the analytical approaches do not

consider the actual size of the incident wave relative to the freeboard. While the experimental

works present information in terms of wave heights and water depths, the analytical curves do

not include the effect of wave height ,which prevents any comparison between the two.








13

1.3.2 Current Patterns Associated with Submerged Breakwaters

The addition of a structure in the coastal zone obviously changes the current patterns in

that area. Knowledge of the changing patterns is important in terms of safety and shoreline

response. In some instances structures added to a coastal system can create rip currents which

are hazardous to swimmers. On another level, the purpose of adding a submerged breakwater

is to protect the area behind it and to promote the accretion of sand. The current patterns in the

vicinity of the barrier have a strong effect on the deposition of sand on the protected beach.

Longuet-Higgins (1967) described the rise in Mean Water Level (MWL) behind a

submerged breakwater or sand bar. He presented a simple calculation to determine the vertical

change in MWL based on the Bernoulli equation and requiring knowledge of the incident and

reflected wave amplitudes. The rise in MWL behind a breakwater has been labeled 'ponding,'

and while Longuet-Higgins provides a means of predicting the ponding level, he does not discuss

the consequences of this rise.

Seelig and Walton (1980) presented a method of estimating the flow through offshore

breakwater gaps. They reported that wave overtopping of breakwaters creates an offshore flow

through breakwater gaps and around the ends of such structures. The goal was to provide design

information for breakwaters in order to avoid high velocities through these gaps that could cause

erosion. Using the ponding level as a gradient to drive a flow, they presented a simple

continuity-energy calculation to predict the average flow through a given gap size. Seelig and

Walton expressed the need to limit offshore flows to below 0.5 ft/s to avoid eroding material

from the supposedly protected area behind a breakwater.

Lin (1986, 1988) investigated the performance of the P.E.P. Reef during the initial

development of the unit. His investigations included numerical simulations and a limited set of

field data from the DuPont site P.E.P. Reef I installation. Results from the field studies shed








14

little light on the change in velocity of the longshore current behind the Reef. Lin concludes that

the Reef converts some wave energy into current energy and thus creates a strong current along

the top of the Reef. He also concludes that the Reef does not alter the longshore current and that

the Reef is very effective in stopping offshore sediment loss during summer storms. In addition,

it is reported that the shoreline behind the Reef is very stable and insensitive to changes in

offshore wave conditions.



1.4 Comments

While information regarding the performance of submerged breakwaters is available to

design engineers, these data are not entirely consistent and cannot replace project specific wave

climate and sediment transport information. As stated previously, the need for comprehensive

monitoring of coastal engineering projects, especially experimental ones, is imperative. Often

political and environmental interests cloud the issue as to the actual performance of coastal

installations. It is important to evaluate data from such monitoring objectively and not apply data

from one site directly to another with an expectation of a complete predictive capability. This

report is intended to provide a basis for the performance of submerged narrow crested

breakwaters and should be treated as such.














CHAPTER 2

DATA COLLECTION

Data for this report were obtained from two sources. The first source is the three year

monitoring program of the Midtown Palm Beach Prefabricated Erosion Prevention (P.E.P.) Reef.

This program is being conducted by the Coastal & Oceanographic Engineering Department of the

University of Florida (UFCOE) and is currently in its second year of operation. The monitoring

program is quite extensive, including hydrographic surveys, continuous wave climate analysis,

scour analysis, and unit settlement surveys. Data from the surveys are available from July, 1992,

which is just prior to installation, and data from the wave climate analysis are available from

October, 1993, to the present.

The second source of information for this report is a laboratory study conducted by

UFCOE at the UFCOE Laboratory in Gainesville, FL, during the summer of 1994. The study

was sponsored by the Indian River County Board of Commissioners to provide physical model

guidance for a permit request to install a 4,000 foot long P.E.P. Reef in Vero Beach, FL.

This chapter details the methodology of both the monitoring program and the laboratory

study. This information is provided in order to present both the extents and the limitations of

the field measurements and the physical modelling.



2.1 Description of the Midtown Palm Beach Monitoring Program

In 1989, the State of Florida passed legislation to permit experimental projects to attempt

to solve Florida's beach erosion problems. One such experimental project is the P.E.P. Reef,








16

a pre-cast concrete structure placed parallel to shore in approximately ten feet of water depth at

the Midtown Section of the Town of Palm Beach, FL. The Reef is composed of interlocking

units, each twelve feet long. 330 units were placed approximately 250 feet from the shoreline,

forming a 4,000 foot long barrier broken only by a 220 foot gap to allow an AT&T cable

crossing, and a twelve foot gap to accommodate an emergency storm water outfall. Placement

of the units began in the summer of 1992. 57 units had been installed when Hurricane Andrew

struck South Florida in August, 1992. One additional unit was placed immediately after the

hurricane when it was noticed that a significant amount of settlement had occurred for the first

57 units. Installation was suspended until the following summer. The remaining 273 units were

placed during the period of May to August, 1993.

As part of the project, a program to monitor the performance of the Reef was

implemented. This program is sponsored by the Florida Department of Environmental Protection

(D.E.P.) and the Town of Palm Beach, FL. The program began in the summer of 1993 with the

installation of scour rods and wave gages and a complete hydrographic survey conducted

immediately after installation was complete. Survey data taken in July, 1992, serve as a baseline

for the monitoring program surveys.



2.1.1 Site Description

The Midtown Palm Beach P.E.P. Reef Installation is located off the Town Of Palm

Beach, FL, approximately 4.5 miles south of the Port of Palm Beach Entrance as shown in

Figure 2.1. Figure 2.2 indicates the location of the Reef relative to DEP monument R-95. The

Reef lies in roughly 10 feet of water and is approximately 250 feet from the shoreline. The tidal

range in this area averages 2.80 feet with a spring tide range of 3.03 feet. The Reef units

themselves are six feet high, twelve feet long longshoree direction), and fifteen feet wide. A

cross sectional view of the unit is shown in Figure 2.3.












Net Longshore
ediment Transport





Port of
Palm Beach
/, Entrance


SGAP (216 Fl) FOR AT&T CABLES


PEP REEF4216 FTLONG,
'(INCLUDING GAP) INWATER DEPTH
oF9.5 FTNGVD


DIRECTONAL WAVE GAGES


0 5000
SCALE(FT)


P
"r



0
0


oReef 4176f

Reef 4176ft


0 5 Miles
I I I I I


Location Map Relative to Port of Palm Beach Entrance.


R105


Figure 2.2 Location of P.E.P. Reef


Figure 2.1














'' 8

-rI I


Figure 2.3 Cross-Sectional View of P.E.P. Reef (Courtesy American Coastal
Engineering, Inc.).



2.1.2 Wave Data Analysis

One of the expectations of a submerged breakwater is that it will provide protection

against wave attack by reflecting or dissipating wave energy. To monitor the effectiveness of the

Reef in attenuating wave heights, two wave gages were installed, one on either side of the Reef.

These gages, as indicated in Figure 2.2 lie fifty feet on either side of the Reef along the same

perpendicular to the shoreline. The gages lie in different water depths; the offshore gage lies in

13.5 feet of water while the nearshore gage lies in roughly 6.5 feet of water. The gages have

been in concurrent operation since the middle of October, 1993.

The gages measure both pressure and two-directional currents in order to produce wave

height and direction and current magnitude and direction data. The gages are cylindrical


Seaward -


note: unit sections 12 feet long








19

packages with the pressure sensors and electromagnetic current meters located at the top of the

package. These packages are secured to pipes jetted into the seafloor. The offshore gage is

attached to a jetted-in tripod for protection. The nearshore gage is attached to a single jetted pipe

near the seafloor to prevent the sensors from lying too close to the water surface. The packages

are installed and their orientations measured to obtain the correct directional information.

The data collected from the sensors is transferred to temporary memory storage inside

the package. Data is stored there until it is downloaded by telephone to the UFCOE Laboratory

for analysis. The packages are hard wired by buried cable to shore where a shore station/modem

package connects to a telephone line for modem communications. The cable connection also

supplies power to the wave gages. The packages do contain batteries and a hard disk drive for

backup use should the cable be damaged or the power supply lost from shore. These batteries

can power the package for several weeks, long enough to allow a field crew time to visit the site

and make necessary repairs.

Both wave gages collect data on an hourly basis. The collection scheme for the gages

includes sampling the pressure and two directional current components at a frequency of one hertz

for 17.1 minutes (1,024 seconds). Every hour the average pressure and current are recorded.

Every sixth hour the entire 1,024 second record is stored. The hourly averages are used to

determine tidal records and current variations with the tidal cycle, if any. The full pressure and

current records are used to calculate wave heights, directions, and spectral information.

Using information from the gages, performance information can be obtained regarding

the wave attenuation characteristics of the reef. When the package is 'called' via modem, the

internal clock in the package is set to the clock time of the laboratory computer. This ensures

the data from both gages is truly concurrent. Wave records from both gages can be compared,

both in the time and frequency domains, to calculate transmission coefficients.








20

Data from the gages are analyzed in a format consistent with the Florida Coastal Data

Network, operated for many years by UFCOE. This format provides significant wave height,

modal period, modal wave direction, current magnitude, and current direction data for each six-

hour record. The 1,024 second record is divided into 128 second blocks that overlap by fifty

percent. A Fast Fourier Transform (FFT) is performed on each block, and the results of each

block are averaged to create an energy spectrum. The significant wave height is computed from

the energy spectrum as shown in equation (2.1).



H, = '4 fE(ada (2.1)




The modal period is taken as the period associated with the peak of the energy spectrum. The

modal wave direction is determined by a directional spectra model which uses a symmetric

cosine-power function (Cartwright 1963). Equation (2.2) presents the directional spectrum,

E(a,O), in terms of the one dimensional spectrum, E(a), and the Gamma function.



E(O,) = E(a) 22s-1 r2 (s+l) COS2s ( (2.2)
n I r(2s+1) 2

s is the spreading parameter, calculated from the co-spectra of the pressure/current data. Coastal

and Oceanographic Engineering (1993) provides a detailed explanation of the directional spectrum

analysis. The peak of the function in equation (2.2) is taken as the predominant direction of wave

travel.

To compare the two records to determine transmission coefficients in a consistent manner,

the offshore record must be modified to include the shoaling effect which naturally results from

the gages lying in different water depths. To accomplish the comparison, the offshore significant

wave height of each record is shoaled using linear wave theory and the modal period to the








21

corresponding depth at the nearshore gage. Linear wave theory computes shoaled wave heights

according to equation (2.3):



shoa shoaled = ofh Cgf (2.3)
g Sf shore shoaled

Where C, is the group speed of the wave. Once the shoaled incident wave height is determined,

the transmission coefficient, K,, can be calculated as shown in equation (2.4):



Kt = H- 8Hbo(2 (2.4)
So.ffshore shoaled

This provides a fair evaluation of the wave attenuation provided by the Reef by comparing the

wave height at the nearshore gage to the wave height that would have occurred at the same point

in the absence of the Reef.

Additional analyses are performed on the wave records to determine Kt values for

individual waves. By performing an FFT on the full 1,024 second record, adapting the Fourier

coefficients to the surface conditions, and then performing an inverse FFT on the new

coefficients, the surface elevation record is found. This record can be examined for individual

waves, or it can be processed by a zero-upcrossing routine to obtain the distribution of wave

heights. The actual elevation record can be used to directly compare wave heights and to verify

the clock times of the wave gages. The distribution of wave heights from each record can be

compared to determine the dependency of transmission coefficient on wave height. This is

accomplished by first shoaling the offshore record appropriately (as previously described), then

calculating the cumulative distribution of wave heights for both records. Differences in the

distributions indicate which waves are affected more by the presence of the Reef.








22

2.1.3 Background Wave Climate and Verification

Additional wave gages were installed in September, 1994, to provide further information

about the wave climate near the Reef. These gages were first installed next to the FCDN gages

to provide a check of the wave data already collected. The gages were then moved to a nearby

location south of the Reef to provide background wave climate information, specifically the

amount of natural wave height reduction occurring in that vicinity as a result of wave breaking.



2.1.4 Current Measurements

The electromagnetic current sensor on each wave gage provides the current magnitude

and direction information for each hourly record. This provides a general description of the

overall currents in the vicinity of the Reef. It does not, however, provide significant information

about the spatial variation of current patterns around the Reef. The two gages provide point

measurements roughly 3 feet from the seafloor at the gage locations.



2.1.5 Volumetric Changes

A large portion of the monitoring program focuses on the hydrographic surveying. The

surveying provides erosion/accretion data as well as changes in the position of the Mean High

Water (MWL) level. Figure 2.4 depicts the profiles along which the surveys are conducted every

three months. 75 profile lines are surveyed by land surveying methods, wading/swimming

surveys with a rod and level, and boat fathometer measurements. These three techniques are

overlapped to provide repeatability in the data. The quarterly surveys extend offshore to 1,200

feet. An annual survey extends offshore to 3,500 feet. The profile lines shown in Figure 2.4

that extend from DEP monuments are surveyed to 6,500 feet offshore. The surveying is

conducted by an outside firm, Sea Systems, Inc., of Pompano Beach, FL, and the data from their

surveys are compiled and sent to UFCOE on computer disk and in printed form.






















S- 0 'E NOTES:
-0N 80*E All Profile Unes at 90 Azimuth Except, as Noted,
8 -75' for 12 of the 15 Lines From DNR Monuments
S- BREAKWATER Total of 75 Unes. (DEP Monuments Only Surveyed
-.,N 80E Annually, Others Quarterly).
20'"N 80E
4-1so.N800E
-...-N750E

1 -,-". 1 Dwnotes 6 Spaces at 75 ft
Between Profile Lnes

---- ---'- 2- N 900E
S- -.N 800E Most Southerly Line Except
for Those at DNR Monuments


0 5000 t
am --mmc---m


Figure 2.4 Survey Profile Plan.








24

The data are analyzed to produce volumetric change information for each intersurvey

period as well as a cumulative volumetric change based on the July, 1992, baseline survey. The

volumetric changes are calculated using a trapezoidal rule method. This method calculates the

volumetric change along a profile line in terms of volume per unit distance. The volumetric

change is then computed by multiplying by the distance halfway to the next survey lines. For

instance, if the survey lines were 200 feet apart, the volume per unit distance value would be

multiplied by 200 feet (100 feet north + 100 feet south).

The volumetric change along a given profile line is divided into eight cells each roughly

sixty feet in length. These cells are used to create seafloor elevation change contour plots. These

cells vary in length depending on the exact distance of the Reef from the shoreline. Four cells

make up the distance from the Reef to the shoreline, and four more cells extend roughly the same

distance offshore from the Reef. This provides approximately 500 points to create reasonably

smooth contour plots.

Additional information from the surveys includes the change in Mean High Water

shoreline position. This information is determined from the individual profile lines and the

MHW mark on each. Tidal information taken from Lake Worth Pier, a few miles south of the

Reef, places the MHW mark at +1.87 feet relative to the National Geodetic Vertical Datum

(NGVD). Observation of the individual two dimensional profile changes provides additional

insight into the sedimentation patterns in the area.



2.1.6 Unit Settlement

During the surveys, the top elevation of each individual unit is measured. These data

have been collected since installation of the Reef began, and they document the settlement of the

units. Following Hurricane Andrew, it was noticed that the units settled a great deal, and the








25

settlement became an important issue in the performance of the installation. Settlement of the

units is an important consideration since it strongly affects the amount of wave transmission over

the Reef. Too much settlement can render a submerged breakwater ineffective.



2.1.7 Scour Rod Measurements

Twenty-eight scour rods were installed around the Reef to determine if the Reef causes

problematic scour around its periphery. The scour rods are two inch diameter copper pipes eight

feet long jetted into the sand approximately six feet. The pipes have large disks that move freely

up and down the length of the pipes. These disks are set on the sand surface and follow the

surface during periods of erosion due to scour. The disks are then measured relative to the pipe

cap and the scour depth determined. The disks often sink to a given level then are covered over

with sand during recovery periods. In these cases the scour depths are measured and the disks

are reset to the current sand level.

Twenty-two pipes are located near the edges of the Reef. Eighteen of these are at the

ends of the Reef or at the AT&T gap to measure scour. Four pipes are located at the centerline

of the structure, and six pipes are located well north and south of the Reef for control purposes.



2.1.8 Present Status

The monitoring program is entering its second year. Update reports for the performance

are presented every six months (Dean et al., 1994b; Browder et al., 1994). These include the

compilation of the wave data for the period, the analysis of the survey data for the surveys

conducted during that time, and updated conclusions as to the performance of the Reef. The

wave data obtained since October are verified and augmented by additional wave gages installed

in September, 1994, to verify the data and provide background transmission data.








26

2.2 Methodology of Laboratory Study

A physical model study of the hydrodynamic performance of the P.E.P. Reef was

conducted in the summer of 1994 at the UFCOE Laboratory in Gainesville, FL. As mentioned

previously, the study was sponsored by the Board of County Commissioners of Indian River

County, FL. The purpose of the study was to provide design guidance to the county to assist in

the permitting of an experimental P.E.P. Reef in Vero Beach, FL. This laboratory study

provides design information regarding the relative height of the barrier and the planform

arrangement of Reef units relative to the shoreline. The study was conducted on a 1:16 scale,

which results in time and velocity scales based on Froude modelling of 1:4.



2.2.1 Experimental Equipment

The tests were conducted in the three-dimensional wave basin at the UFCOE Laboratory.

A schematic of the basin is shown in Figure 2.5. This basin consists of a multi-paddle wave

maker, a sloping offshore section leading up to a concrete horizontal bed fronting an area where

a fixed or movable bed beach may be installed. For this study, concrete block walls were

installed to create a 47 foot long beach. Gravel was used to make an immovable bed beach of

1:8 slope. This slope was chosen to recreate the beach-face slope at the site. The horizontal bed

area was painted with a one foot square grid to facilitate velocity measurements.

Forty-eight individual 1:16 scale model Reef units were fabricated from dimensions (see

Figure 2.3) provided by American Coastal Engineering, Inc. These models were concrete units

cast in fiberglass molds constructed at the UFCOE Laboratory. The model units are 4.5 inches

high by 9.0 inches longshoree length) by 11.25 inches (cross-shore width). Blocks inserted

during fabrication provided the vents in the units. The units were placed in various planform

arrangements roughly 15.6 feet (250 feet prototype) from the still water shoreline in the model.














/ P.E.P. Reef Model


1:8 Gravel Gridded
Beach Test Area


Paddle
Wavemaker


Figure 2.5 Wave Basin Schematic


Regular waves with 2 second periods and 4 cm wave heights (0.012 ft) were generated

in the basin by the multi-paddle wavemaker. The paddle wavemaker, made of nine inch wide

paddles, is capable of generating waves at various angles and heights by setting the individual

phases and amplitudes of each paddle. For this test, however, all 63 paddles were set to the same

phase and amplitude to create a near-uniform wave height across the basin approaching normal

to the gravel beach. The wave height was chosen to provide a compromise between the average

wave height conditions at the site and the need to limit basin effects in the model study. Large

wave heights put too much energy into the model and make the basin effects dominant over the

desired experimental effects. The two second period in the model translates to an eight second

period in prototype, which is typical of swell periods at Vero Beach, FL.








28

Wave heights were measured with a standard capacitance type wire wave gage. A wire

partially immersed in the water functions as the capacitor in a tuned circuit. The amount of water

covering the wire changes the capacitance in the circuit and changes the output frequency from

the wave gage. A signal conditioner receives the signal from the wave gage and translates that

signal from a frequency to a voltage signal, which is then sent to a strip chart recorder. The

estimated error in the wave height measurements from such an arrangement is estimated to be

approximately 10% of the measured wave heights.

Currents were measured in the experiments using drogues. These drogues consisted of

table tennis balls injected with water to make them slightly negatively buoyant and sealed. This

resulted in a bottom drogue that would experience only minor friction against the concrete bed.

The moving drogues were videotaped on the horizontal concrete bed, which was painted with

a one-foot square grid to provide distance measurements. The videotape was post processed to

obtain current patterns and magnitudes for each test.





2.2.2 Test Plan

The test plan consisted of twenty initial tests using four planform arrangements and a

control run at four different depths. The control run for each depth consisted of the same

measurement pattern performed in the basin with no Reef units present. This was done to

establish background wave height profiles and current patterns. The four different water depths

were chosen to be 12, 15, 20, and 30 cm (0.037, 0.046, 0.061, and 0.091 ft). These depths

provide freeboard ratios, f/h, of 0.0, -0.2, -0.4, and -0.6, respectively. The planform

arrangements are shown in Figure 2.6. Each arrangement is labelled with a letter, and future

references to a particular arrangement will use these letters. The Type A case consists of 45 Reef









A) 45 Continuous Units
S1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I


B) Three 11 Unit Segments


~F 1
11111 I II 1 11111 I ll

--F -F F-


C) 45 Staggered Units


D) Five 5 Unit Segments
Hi I N I I l i I I I i I I i I I I


thw i


I I I I I I I I


HHi


I i. f


Si


Reef Unit Arrangements for Initial Tests


m
0 L I I I I


r I I i I Ii


F~FFFff~~


Ir


IIIIIIII!


I^^^^^^^ L I


FI~K#Jill


l i. .


I I I I I


I 1 1 1 1r m


i i i


i II


' ' '


I


Figure 2.6








30

units placed in a continuous line 33.75 feet long. This represents a prototype length of 540 feet,

and is the longest continuous arrangement tested in the 47 foot long basin. The Type B case has

three 11 unit segments separated by 10 unit wide gaps. This represents 132 foot long prototype

segments separated by 120 foot long gaps. The Type C case uses 45 units staggered in five unit

segments. The stagger distance used in the initial tests was 1.875 feet, equivalent to two cross-

shore unit widths. The 45 units are equivalent to 540 feet of actual Reef length, and each

segment would be 60 feet long. The Type D case derives from the Type C case only in this

instance the offshore segments have been removed to create 60 foot long (prototype) gaps along

the total 540 feet of Reef units.

Following the initial tests, the results were analyzed and additional tests were conducted

to further explore the most promising arrangement seen in the initial tests. Figure 2.7 depicts

the three additional arrangements tested in the basin. These cases were derived from the Type

C case seen previously, and were only tested at f/h = 0.0 (crest at SWL). The type E case

consists of 45 units divided into five nine-unit segments. These segments represent 108 foot long

segments in prototype. The offset distance was varied from twice the cross-shore unit width, 2w,

to six times the cross-shore width, 6w (30 to 90 feet in prototype). The Type F case shortened

the offshore segments to seven units, creating a small gap along the shoreline between segments.

The offshore segments represented 84 foot long sections in prototype. Again the cross-shore

offset distance was varied as before. The Type G case was conducted based on the results of the

Type F case and consisted of segments and gaps that were twice as long as the Type F case, 216

foot prototype onshore segments, and 132 foot offshore segments separated by two unit length

longshore gaps.










E) 9 Unit Segments


SI w

2w to 6w




F) 9 & 7 Unit Segments


I I I


11 Unit Segments


2w to6w
:I I I ] :


El"'


III


I II I I I I I
+f+ i ~~~I IIIIIIT


I I I


miII i I I I _1


i it . . 1I.. .I .I.I. 1 1 1 1 1 1 1 -


I i i -


,*W
Vt Y


Figure 2.7


Reef Arrangements for Additional Model Testing.


2.2.3 Wave Height Measurements

For each test (27 total) wave heights were measured at 70 different locations. These

measurements fell along five profile lines defined by the grid on the horizontal bed. Figure 2.8

indicates the profile lines relative to the basin centerline. Wave heights were recorded at each

intersection point on the grid to measure the wave height decay along each profile line. The four


E E 11 11


G) 18


I1 L


i7


Iccilll


aaa~a


1 1 1 1 1
N J 1 1


1--rT


1 I I I








32

points on the landward and seaward extents of each measurement line on the grid were averaged

together, respectively, for all five lines to determine overall incident and transmitted wave heights

for each experiment. This provided twenty measurements in the average for both the incident

(seaward) and transmitted (landward) wave heights. The measurements on the offshore side were

extended past the grid in cases where the offshore segments fell too close to the edge of the grid.

Some of the cases contained profile lines that fell along breakwater gaps. These data were

included to indicate sections of shoreline that would be unprotected from wave attack. Results

from the wave height measurements were compared in terms of wave height decay profiles and

transmission coefficients. These coefficients are presented as functions of both the freeboard

ratio, f/h, and the relative freeboard, f/Hi.


-12 ft. -6 ft. O ft. 6 ft. 12 ft.




Figure 2.8 Cross-Shore Wave Height Profile Lines.



2.2.4 Current Measurements

For each test (including control tests), dye and drogues were used to determine the

current patterns both qualitatively and quantitatively. In each test, approximately 30 drogues

were tracked on the floor, moving over the painted grid on the bottom of the horizontal bed. The
" " ."" ^ " "" ""
:m!1m l lIiziiz~ii~ m m~z
:izz m m zz:zzzzzzi Ii I IIzzz
izzzzziiizzziz~miiiiu~I ti^^^ mm
- - - -l - l ^ ^ ^ ^ ^ -i ^:^ I [ [I^^ ^ ^




















were tracked on the floor, moving over the painted grid on the bottom of the horizontal bed. The








33

drogues were tracked with videotape. The videotape was then analyzed to plot the trajectory of

each drogue and calculate average velocities of the drogues.

The drogues were placed in both longshore patterns and cross-shore patterns to obtain

adequate coverage of the area around the Reef. Of particular interest was the area between the

end of the Reef and the sidewalls of the basin. A higher concentration of drogues was placed in

and near the gaps to determine the magnitude and direction of flow in those areas. Average

bottom velocities were determined and compared for each test to study the effects of the Reef.

These values were compared to the control cases where no Reef was placed in the basin.



2.3 Comments

Field monitoring and laboratory studies have been conducted to gather information on the

performance of the P.E.P. Reef submerged breakwater system. This system is classified as a

narrow crested submerged breakwater (justification of this is discussed later). It is useful to

discuss some of the limitations of the monitoring and of physical modelling.

The field monitoring provides the best information on submerged breakwaters, i.e. actual

prototype data. Some limitations of the program, however, must be recognized. Surveys are

conducted on a quarterly basis, and are subject to the seasonal variations and timing of episodic

events. A survey may fall during a relative calm time in which the protected beach has

experienced accretion of sediment, or it may fall after a particularly damaging storm, where the

beach may have lost a considerable amount of material. Thus it is important to look at the

performance of a project over a sufficiently long time so as to distinguish the overall trend from

episodic events. In addition, current measurements from the monitoring program are taken at

only two points along a 4,000 foot long structure. Therefore no current pattern information can

be gained from the current meters. It would be very useful to have field measurements of the








34

current patterns, and aerial dye studies have been conducted, but obtaining quantitative current

data would be far too measurement intensive and costly to be effectively realized.

As in any physical model study, limitations and basin effects must be discussed. In this

model, only shore normal waves were tested. This is obviously not the case in nature, but these

waves were used to provide basic performance information. Attempts were made to minimize

basin effects, primarily by reducing the wave height used so as not to 'drown out' the effects of

the Reef itself. Control tests were conducted to document the basin effects, and these effects

were considered in the conclusions.

Finally, it is again stressed that coastal engineering projects are extremely site specific,

and nothing can replace actual field data from the site of interest. The field and laboratory work

presented herein are given as a basis for initiating a submerged breakwater project, and should

not be blindly applied to a project at another site.















CHAPTER 3

WAVE TRANSMISSION

The first objective of any breakwater is to do just that, 'break' the water, i.e., reduce the

height of the incoming waves to protect the area behind the structure. The transmission of waves

past a submerged breakwater is the focus of this chapter. The amount of wave height attenuation

provided by a submerged barrier is the primary variable used to describe the success or failure

of such structures.

Performance of a breakwater for wave height reduction is provided here in terms of a

transmission coefficient, Kt, which describes the ratio of the transmitted wave height to the

incident wave height. In cases of sloping bottoms, the incident wave height is corrected for

shoaling effects before comparison, as described in Chapter 2. Transmission measurements have

been taken for the Midtown Palm Beach P.E.P. Reef installation and the Vero Beach P.E.P. Reef

laboratory study and are discussed in this chapter. In addition, a simple analytical approach to

determining K, is presented and compared to both the field and laboratory results as well as

previously discussed literature. From this work, performance criteria and design

recommendations can be made in terms of freeboard ratio, f/h, and relative freeboard, f/Hi.



3.1 Field Measurements

Wave data have been collected continuously from the Midtown Palm Beach P.E.P. Reef

installation since mid-October, 1993. As discussed in Chapter 2, the data are analyzed for

significant wave height, modal period, direction, and energy spectrum. Comparison of values








36

from both gages produces transmission coefficients based on significant wave heights.

Compilation of the wave data can be found in Dean et al. (1994b) and Browder et al. (1994).

The focus of the field data concerning transmission coefficients will be the one month

period from 21 September 1994 to 24 October 1994. During this time two additional Seadata

wave gages were installed at the site to verify the data from the existing CDN gages and provide

background wave climate information. These two gages were installed adjacent to the CDN

gages for two weeks during this period to provide concurrent data, then they were moved to a

location 500 feet south of the Reef (at the same cross-shore distances) where the background

measurements were taken for the remaining two weeks. The data from the Seadata instruments

(significant wave heights and modal periods) are compiled in Appendix A.



3.1.1 Transmission Coefficient Determination

Wave height reduction is customarily measured in terms of a non-dimensional

transmission coefficient, K,. Chapter 2 outlined the procedure for determining the transmission

coefficients from significant wave heights, which actually provides an indicator of the amount of

energy transmitted over the structure. Figure 3.1 shows a plot of the transmission coefficient

versus time for the Midtown Palm Beach P.E.P. Reef installation. The plot indicates a fairly

consistent range of K, from January, 1994, to roughly the end of June, 1994, between 65% to

85%. Starting at the end of June, the values began to drift, reaching an average value of 1.0 by

October, 1994. This behavior suggests that one of the CDN gages has lost its calibration. Both

gages have been in place continuously since October, 1993, which is a long time for an

instrument in the ocean to survive. It is believed that the rubber portions of the pressure sensor

have degraded over time, resulting in small changes in the measured wave heights. These small

changes have a large effect on K,, especially for smaller wave heights.










1.2


** *i





*: *o$ *

0.6 -


0 .4. .. . .... . .
0 50 100 150 200 250 300
Julian Date, 1994

Figure 3.1 Transmission Coefficient History, Midtown Palm Beach Installation.
1 January 1994 to 24 October 1994, CDN Gages.



An attempt was made to correct the coefficients through the tide ranges measured at each

gage. Since the approach used to obtain K, is a linear one, the ratio of the tide ranges can be

used to correct the transmission coefficients directly. The ratio of tide ranges measured,

however, was very nearly one over the range of suspected poor values. This would not account

for the larger drift seen in the values. The apparent problems are high frequency dynamic

problems (roughly 0.1 hertz) while the calibration method using the tide ranges is a low

frequency (0.00005 hertz) static calibration. The use of the static calibration does not correct the

dynamic problems seen in the CDN gages over the last three months. As a result, the

comparison of the Seadata to CDN transmission coefficients will be studied between times of

similar wave conditions with the CDN data taken from the previous winter season.

Figure 3.2 shows the transmission coefficients calculated from the Seadata gages during

the month long test period. The first two weeks of the period indicate the time when the gages

were installed within the confines of the P.E.P. Reef. Here the average values of K, range from












1 .2 . I .i






0.4

0.2 A Seadata Reef
V Seadata Control
0.0 i I
260 265 270 275 280 285 290 295 300
date


Figure 3.2 Wave Height Transmission Coefficients, Midtown Palm Beach Installation.
Seadata Gages, 21 September 1994 to 24 October 1994.



roughly 0.70 to 0.90, similar to the results seen in the CDN gages during the first six months of

1994. This provided a level of confidence in the quality of the data from both the Seadata

packages and the CDN data from the first half of the year. The second half of the test period

indicated in Figure 3.2 shows the background (control) transmission coefficients measured south

of the Reef. Here the average values are slightly higher, ranging from 0.79 to 0.97. The lower

values seen in the graph from day 282 to day 288 have been excluded from the averages, since

these data are obviously anomalous and are believed to be caused by biological growth on the

nearshore Seadata gage. The sudden jump in Kt at day 288 indicates that the growth or blockage

on the pressure port was removed either by a large wave event or another biologic entity. It is

noted here that this data set is quite small and that additional measurements will be conducted in

the future once the mechanical difficulties in the CDN gages are resolved. While it is unfortunate

that the equipment problems occurred during the Seadata test period, such is the nature of ocean

field measurements, and to have two gages operate successfully together for nearly nine months

is indeed fortunate.








39

The preliminary results of the Seadata test period indicate that between 5 and 20% of the

wave height reduction seen in the Palm Beach data previously published can be attributed to the

natural reduction of wave heights caused by energy losses between the gages. In that regard, for

the cases where larger reduction in wave heights are reported, more of the reduction is likely due

to wave breaking. For example, in the instances where the CDN gages reported a 35% reduction

in wave height, it is likely that as much as 15% of this reduction is attributable to causes other

than the Reef. This is due to the fact that the larger reduction of wave heights occurs during

larger wave events such as storms. It is also during this time that more natural energy losses

would occur between the two gages. As a result, the Reef itself is most likely contributing

roughly 10 to 20% of the wave height reduction previously reported to be 15 to 35%. This

degree of wave height reduction is more comparable to previously published works (see Chapter

1) for a structure whose crest elevation is relatively low in the water column. The Midtown Palm

Beach installation has an average freeboard ratio of -0.56 relative to the NGVD water depth. At

normal high tide the ratio decreases to an average of -0.62, and at low tide the ratio increases to

-0.51. Most data for these ratios predict the transmission coefficient to be 90% or more.

To try to compare coefficients more closely, storm data are examined from both gages.

Figure 3.3 shows the significant wave height history for the one month Seadata test period. Of

particular interest is the six day period beginning 15 October 1994 (Julian Date 288). During this

time a large storm passed through the area, generating significant wave heights of up to 4.92 feet.

During this time the average significant wave height was recorded to be 3.12 feet. The

corresponding average transmission coefficient was 0.91. This storm was compared to an eight

day period beginning 15 February 1994 (Julian Date 46). The February storm produced similar

significant wave heights (up to 4.60 feet) and posted an average significant wave height of 3.12

ft as well (the data were searched specifically to find a storm with the same average wave height).












5 I I Seadata Offshore
4 Seadata Offshore




+
4 + Seadata Onshore





1 1


260 265 270 275 280 285 290 295 300
Julian Date

Figure 3.3 Significant Wave Heights, Midtown Palm Beach Installation. Seadata Gages,
21 September 1994 to 24 October 1994.



The average K, calculated during the February storm was 0.77. Considering the similarity in the

two storm events, it is presumed the Reef was responsible for a 14% reduction in the wave

heights approaching the beach, while other natural causes were responsible for the other 9%

reduction in wave height measured during that time.

While the data set described above is quite short, it does address the question of

background wave height reduction in the vicinity of the Midtown Palm Beach P.E.P. Reef. This

comparison raises a good point that will be discussed further in Chapter 4. A submerged

breakwater or any hard structure does not act alone to defend upland development, rather, it

works in combination with the natural beach to cause waves to dissipate their energy, either by

breaking or reflection, before they impact the beachface and upland areas.



3.1.2 Spectral Analysis

Other features of the transmission of waves over a submerged breakwater have been

investigated during this study. One is the spectral transformation of the irregular wave climate








41

passing over the structure. The CDN and Seadata gages both provide time series of pressure that

can be translated into spectral density information. Chapter 2 outlined this process, where the

pressure records are passed through a Fast Fourier Transform routine and their spectral

components transferred to the surface level. This results in a spectral density plot that describes

which frequencies contain the most energy and how much energy is transmitted past the structure.

Plots such as these also provide information about the generation of higher harmonic components

of the incident waves. These harmonics would appear as peaks in the spectral density plot at

multiples of the incident frequency. As discussed in Chapter 1, the generation of higher

harmonics is characteristic of broad-crested structures, where the high frequency components are

generated in the space above the crest and transmitted as free waves (Massel, 1983). This

criterion is used to further classify the structure as narrow or broad crested.

Figure 3.4 shows the spectral density for a wave record recorded 26 November 1993.

The figure indicates a very narrow frequency wave climate consisting of swell of ten second

period. The significant wave height measured from the spectrum for this record was 4.26 feet

at the offshore gage. The transmission coefficient for this record was calculated at 0.72. A field

crew visit to the site during this particular storm visually verified the period and wave heights

coming from the consistent offshore swell. The storm conditions here persisted for several days,

causing noticeable erosion and two to three foot scarps to be cut in the beach in some locations.

No other frequency components are noticed in the figure, indicating the absence of either local

wind generated waves (typically 0.25 to 0.33 hertz components) or higher harmonic generation.

Figure 3.5 depicts the wave spectral density recorded 5 October 1994. This record was

obtained from the Seadata test period data when the gages were in place within the confines of

the P.E.P. Reef. The shape of the spectrum looks quite similar to Figure 3.4, indicating long

period swell conditions with an offshore significant wave height of 2.96 feet and a transmission






















101-


0L
0.


0


0.3
f(Hz)


Figure 3.4 Spectral Density of Offshore,
CDN 26 November 1993, 6:00


0L-
0.0


0.4


0.5


Nearshore, and Shoaled Offshore Records.
PM.


0.1 0.2 0.3 0.4
f(Hz)


0.5


Figure 3.5 Spectral Density of Offshore, Nearshore, and Shoaled
Seadata 5 October 1994, 4:00 AM.


Offshore Records.


I'
'1
I 1
I I
S offshore
....... nearshore
---- shoaled offshore
I I


I I
\


I .' -




I. *l


'''''


' ` ' '








43

coefficient of 0.72. In this instance the significant wave height would come close to what would

be observed in the field during that time. The significant wave height is based on the integral

of the spectral density curve, equation (2.1). This approach takes the energy from the spectrum

and represents it as a single wave height. This method would return wave heights that were

similar to what would be observed by eye if the spectrum is narrow banded, as in Figure 3.4 and

Figure 3.5. When the spectrum is not narrow banded, as in Figure 3.6, an observer is not likely

to recognize the reported significant wave height as being the typical wave height.

Figure 3.6 describes the spectrum of a record taken during the October storm described

previously. The gages from which this record was taken were located south of the P.E.P. Reef

in the control location. The sea state depicted in Figure 3.6 is fairly irregular, consisting of long

period swell and shorter period, local storm wind waves. Weather reports from this time listed

sustained onshore winds of at least 20 knots for several days. In instances such as this, the

significant wave height (4.17 feet, offshore) provides more of a measure of the wave energy

rather than a description of a representative wave height. The plot also indicates the effect of

period on transmission; as described in Figure 1.1, only a middle range of frequencies indicates

any noticeable attenuation. The short and long waves are not significantly affected.

Figure 3.6 also indicates a smaller degree of wave attenuation than the previous two

spectra, yielding a K, of 0.93. Two different effects contribute to this. The first is the absence

of the P.E.P. Reef which would contribute to the wave height attenuation. The second reason

is the amount of erosion that occurred in the immediate area of the inshore wave gage. The

nearshore gage was installed 2.20 feet above the seafloor. When the gages were pulled out two

weeks later (one week after the storm), the divers measured that the seafloor had eroded by 2.10

feet around the gage. Strangely enough, the offshore gage seafloor elevation remained relatively

constant. The increased depth at the nearshore site results in a smaller shoaled wave height used

in the Kt calculation, driving the value closer to 1.0.










20 I I




15 offshore
....... nearshore
--- shoaled offshore


10










0.0 0.1 0.2 0.3 0.4 0.5
f(Hz)

Figure 3.6 Spectral Density of Offshore, Nearshore, and Shoaled Offshore Records.
Seadata 17 October 1994, 8:00 AM.



3.1.3 Individual Wave Tracking

In addition to examining significant wave heights and average values for transmission

coefficients, individual waves can be 'tracked' to see how they are attenuated as they pass over

a submerged breakwater. The wave records from the Midtown Palm Beach installation can be

analyzed to provide the water surface elevation records as a function of time. By performing a

Fast Fourier Transform (FFT) on the pressure record, the Fourier coefficients in the frequency

domain are obtained. The record is a pressure signal, thus the values must be transferred to

surface elevation values through the respective pressure response function at each frequency

component. The result is a frequency domain description of the surface. To obtain the true

surface displacement, an inverse FFT is performed to obtain the time series. If both the offshore

and the nearshore gage are treated this way, individual wave records are obtained that travel over








45

the structure from one gage to the other. In this way each wave height can be examined and a

transmission coefficient for a single wave can be calculated.

Figure 3.7 shows a portion of the surface record from 18 December 1993. Here the two

records are matched by moving the offshore record ahead in time to account for wave travel time

between the gages. In the plot the first large peak indicates how the height for that wave has

been noticeably reduced. Thirteen such high waves were measured in this record, shoaled

appropriately to the nearshore gage depth, and their transmission coefficients calculated. The

average Kt for these waves was 0.76 while the value for the entire record was 0.78. Another

feature of the plot is the area around the 516 second mark where the surface fluctuations are quite

small. This matching area indicates that the gages are sampling the wave climate at the same

time, which is obviously valuable for concurrent comparisons between the gages.






2










4-4

-2 offshore + 8 s
....... nearshore

-3 I I. . .
480 496 512 528 544
t(s)


Figure 3.7 Surface Elevation Records for Offshore and Nearshore CDN Gages.
18 December 1993, 6:00 PM.








46

As mentioned previously, submerged breakwaters have a more pronounced effect on

waves of larger heights. This can be demonstrated from surface elevation records such as in

Figure 3.7. If a zero-upcrossing routine is used to identify the individual waves in a record and

their periods, then a distribution of wave heights can be calculated. Figure 3.8 indicates the

cumulative frequency distribution of wave heights for the record taken 18 December 1993. The

plot shows the nearshore, offshore, and shoaled offshore records. The shoaled record represents

what the distribution would look like in the absence of the breakwater. In this example the

distributions do not differ noticeably until the wave height exceeds two feet. At this point the

breakwater begins to affect the waves more, reducing their heights by a larger percentage. For

example, at a cumulative frequency of 0.5 the corresponding K, value is 0.93. At a cumulative

frequency of 0.9, Kt = 0.81. Thus the higher waves in the record are affected more by the

presence of the breakwater than the smaller waves are.

1.0



0.8 .*'y

o /
0.6



0.4 -

7 .- offshore
S....... nearshore
/ ---- shoaled offshore
0.2 -,;



0.0
0 1 2 3 4 5 6
H (ft)

Figure 3.8 Cumulative Frequency Distribution of Wave Heights for the Offshore,
Nearshore, and Shoaled Offshore Records. 18 December 1993, 6:00 PM.








47

3.2 Laboratory Measurements

As part of the Vero Beach P.E.P. Reef physical model tests, the wave height transmission

coefficients were calculated for each test. The procedure for the tests is outlined in Chapter 2.

Wave heights were measured at fourteen points along five cross-shore profile lines (Figure 2.8).

The seaward-most and landward-most four data points along each line were averaged together,

respectively, to determine average offshore and onshore wave heights. Four points were taken

on each offshore line to attempt to compensate for reflection effects on the seaward side.



3.2.1 Cross-Shore Wave Height Decay

As waves approach and pass over a submerged breakwater, their heights are reduced by

the reflection and dissipation of the incident wave energy. The amount of wave energy remaining

on the transmitted side reforms the wave and continues to propagate toward the beach. In the

case of a sloping beach, the transmitted wave height will grow due to shoaling until it breaks on

the beachface or seawall. The function of a submerged breakwater is to increase the decay of

the wave height before it strikes the beach so that a smaller, less damaging wave breaks on the

beach or seawall. Figure 3.9 shows the cross-shore average wave height decay profiles taken for

the initial four arrangements and a control test conducted at a freeboard ratio, f/h, of 0.0. The

plot shows the reduction in wave height as the incident wave passes over the structure. The

laboratory study was conducted on a smooth horizontal bed so no significant increase or decrease

in the wave height due to shoaling after passing the structure is expected. The solid line indicates

the control wave height, which is fairly consistent from the offshore location to the beach toe.

In each test case, the seaward side indicates the reflection pattern caused by the structure.

In comparison to the no-structure control test, the Type A and Type C cases result in the greatest

reduction in wave height at the 0 foot gridline, located at the toe of the gravel beach in the wave










0.20



0.16



S0.12
*-r-


S0.08



0.04



An n


0 1 2 3 4 5 6 7 8 9 10 11 12 13
Offshore Distance (ft./grid)

Figure 3.9 Cross-Shore Wave Height Profiles for Initial Laboratory Tests. Freeboard
Ratio, f/h = 0.0.



basin. These cases have a continuous longshore stretch of units, with no longshore gaps where

waves will pass unaffected. The cases that have gaps along the shoreline (B and D) indicate

slightly higher wave heights at the beach toe. This is because the gaps allow waves to approach

the beach unattenuated. These profile lines serve to raise the average landward side wave height

at each cross-shore distance for these cases, resulting in higher transmission coefficients overall.

At lower freeboard ratios, the wave attenuation decreases in similar fashion. At a freeboard ratio

of -0.6, the greatest water depth tested, none of the arrangements indicated significant wave

attenuation. This behavior was consistent with all aspects of the laboratory tests. At higher

freeboard ratios (0.0 and -0.2) the structure induced effects (wave transmission, currents, etc.)

were readily apparent. As the freeboard increased, the structure effects diminished until they

were indistinguishable from the control cases.


i I I I I I





-^
: i ". : :.
. ....... .. ! ..... i .... ..... .





.- Control




A
S45 Continuous (A)
---- 3 Segment (B)
---- 45 Staggered C) ...... ....
--- 5 UnitTaps (D) eef :.. 1
Line:










3.2.2 Laboratory Transmission Coefficients

Taking the landward and seaward data points described above and averaging them across

the basin, a transmission coefficient was calculated for each test. In the laboratory test, no

shoaling corrections were made to the offshore values since the tests were conducted on a

horizontal bottom where no shoaling should occur. Figure 3.10 depicts the K, values determined

for the initial twenty tests. The values are plotted as a function of freeboard ratio, f/h. For each

arrangement, the transmission coefficient increases as the freeboard ratio decreases (right to left).

At a freeboard ratio of -0.6, all four cases produced coefficients of roughly 1.0, indicating no

reduction of wave height at all. Recall that the Midtown Palm Beach installation has an average

freeboard ratio of -0.56, indicating that it should produce little wave attenuation according to

these results. This apparent contradiction was one reason for conducting the extra wave gage

testing described in Section 3.1.


-0.6


-0.4
f/h


-0.2


Figure 3.10


Wave Height Transmission Coefficients for Initial
Freeboard Ratio, f/h.


Laboratory Tests versus


O
. . . . . . . . . . . . - - - - -



-- -- - -- -- -- -- - -- - -- - - - -- - - -- 0 .



A 45 Continuous (A) A
O 3 Segments (B)
O 45 Staggered (C) .


35 Unit Gaps (D)
- Ahrens (1987) eq. (1.4)
, I 1 I ,


. I I II I I I I


1 1 1 I








50

The arrangement that produced the most wave height attenuation was the continuous 45

unit case, Type A. This arrangement produced a 25% reduction in wave height at a freeboard

ratio of 0.0. The next best case was the Type C, 45 unit staggered arrangement, which

performed nearly as well as the Type A case at all depths. The Type B and Type D cases

provided considerably less wave height reduction, again due to the fact that these cases have gaps

along their lengths that allow waves to pass to the beach unattenuated. At greater depths all the

arrangements perform similarly, producing transmission coefficients within 10% of each other.

For such a structure to be effective in reducing wave heights, it is generally accepted that a

transmission coefficient of 90% or less is required. Otherwise no noticeable protection for the

beach will be realized. Figure 3.10 also includes the empirical equation developed by Ahrens

(1987). Equation (1.4) is plotted here using the laboratory scale values. Good agreement is seen

with laboratory data, particularly for the continuous structure case. The percent difference

between Ahrens' work and the Type A case is less than ten percent at f/h = 0.0, decreasing to

less than 1% at a -0.6 freeboard ratio. Ahrens' work was conducted with rubble mound

structures, which are porous. It will be shown later that the porosity of a rubble mound structure

and the holes in the P.E.P. Reef model units behave quite similarly in affecting the transmission

of wave heights.

Figure 3.10 describes the influence of water depth and freeboard on Kt. Intuitively, as

the clearance over a submerged breakwater increases (decreasing freeboard ratio), the incident

waves are less affected. Figure 3.10 does not, however, describe the relationship between the

wave height and the freeboard. Both relationships are important in the performance of a

submerged breakwater and demand design consideration, but the two are obviously related by the

freeboard. The freeboard is the single most important variable in the design of such structures,

as it directly affects the wave transmission and the generation of structure induced currents.









51

The effect of wave height and freeboard on the transmission coefficient are indicated in

Figure 3.11. This is the same data of the previous figure plotted versus the relative freeboard,

f/Hi. Here only the Type A case is compared against Ahrens' (1987) work. The other cases

compare similarly to this plot as in the previous plot. With a fixed incident wave height in the

laboratory, the water depth is varied to create a range of freeboards over the structure. As the

freeboard increases in magnitude, the relative freeboard becomes more and more negative and

the waves pass over the barrier more easily. The data indicate that below a relative freeboard

of roughly -1.3, the wave heights are reduced by less than 10%, indicating the structure is fairly

ineffective. The results of both Figure 3.10 and Figure 3.11 indicate that in order to significantly

reduce the incident wave height, the barrier must occupy at least 80% of the mean water column,

a result which mirrors the conclusion drawn by Hall in 1939.


-4 -3 -2
f/Hi


-1 0


Figure 3.11 Transmission Coefficients Versus Relative Freeboard, f/Hi.


1.0




0.9




0.8




0.7




0.6


A I











A 45 Continuous (A)
---Ahrens (1987) eq. (1.4)

,isillI~Iri


5


-


S








52

3.3 Analytical Model

In the study of submerged breakwaters for design purposes, it is useful to have some

simple means of predicting the transmission associated with a certain design. Several previously

published works have attempted to predict values for K,, with varying degrees of success. Many

methods present transmission coefficients in terms of the wave number, k, and the water depth,

with no inclusion of wave height. Other methods have resulted in empirical expressions from

laboratory data, which produce good results for the range of conditions tested. Presented herein

is a simple analytical approach to predicting the transmission coefficient for narrow crested

submerged breakwaters. The approach includes the influence of freeboard, total water depth, and

wave height. This approach, like most others, has its limitations and drawbacks, which are

discussed herein. The development includes barriers that are completely submerged and partially

submerged, including any openings in the barrier, up to the point where the time varying water

surface on the seaward side does not reach the crest elevation of the barrier. The basis for the

analyses is discussed in this chapter, while the entire derivations are found in Appendix B.



3.3.1 Totally Submerged Barriers

The first portion of the solution applies to structures whose crest elevation never exceeds

the trough elevation of the waves on the seaward side. A schematic of the problem is shown in

Figure 3.12. The offshore water surface of the barrier is composed of the incident and reflected

wave patterns. The two offshore components, as well as the transmitted wave, are all assumed

to be in phase. The water surface profiles of each component are described by the following:



1ir, = Cicos(t) (3.1)
,r c 2








53

where r = water surface profile, H = wave height, a = wave angular frequency, and i,r, and

t denote incident, reflected, and transmitted, respectively. Each term is spatially averaged so that

the kx term that would occur in the cosine argument equals zero.




Hi Hr Ht
SMWL

f flow (q)


h

barrier
SSeaward





Figure 3.12 Definition Sketch for Transmission Over a Submerged Barrier



If the difference in elevation of the water surfaces on either side of the barrier is taken

as the driving head for a flow over the barrier, equation (3.2) defines the velocity, u. This

velocity is linearized with the coefficient, A,.


U = #2g(l+1-Tt) = A,(11+T1,-TI)


(3.2)


The linearization constant can be determined in many ways. Here it is found by equating the

maximum velocities of the two velocity descriptions. Equation (3.3) shows the result of the

linearization constant:


(3.3)


As
H.
S(1+K-K








54

where Kr,t represents the reflection and transmission coefficients, respectively. The linearized

velocity expression is then integrated over the freeboard above the barrier to obtain the flowrate.

Also included in the flow is the contribution of the flow through any holes in the barrier. The

P.E.P. Reef units have three large holes across the length of each unit. The flow through these

holes is included in the same fashion as the flow over the barrier. The area of the holes, A, per

unit structure length, replaces the area over the barrier in that calculation. The total flow is then

equated to the flow on the transmitted side, assuming shallow water conditions. Since the

transmission coefficient is the variable of interest, the reflection coefficient is removed from the

equation by invoking the conservation of mass over the barrier:


Ui+Ur = U 1-Kr = Kc (3.4)

Equating the two flowrates and solving for K, results in the implicit equation, (3.5).


1
SH h (3.5)
1+ H 2 (1-Ke)
4(A -f) H.




3.3.2 Partially Submerged Barriers

When the water reaches an elevation where the incident/reflected wave trough is at or

below the structure crest, the barrier becomes only partially submerged, and the above approach

is not valid. In this section partially submerged barriers will be addressed. The approach taken

here will be that of intermittent critical flow over a sharp-crested weir. The flow associated with

any holes in the barrier will be incorporated in this development as well.

Consider the specific energy in the critical flow of water over a sharp-crested weir as

shown in equation (3.6). The derivative of the specific energy, set equal to zero, determines the

value at which the flow becomes critical, that is, no information downstream of the barrier is











dE 2
dE- 1- 0 (3.6)
dhc ghc3

transmitted upstream to affect the flow. Here, hc is the critical depth of water over the crest from

the crest elevation to the water surface. The energy in the flow is generated by the head of water

created as the wave form approaches the barrier. This head is the difference in the surface

elevation and the structure crest. It is recognized that during certain portions of the wave cycle

there will be no flow over the barrier, only through the holes, if any. The portion of the flow

over the barrier is then written as equation (3.7) when 7i+ r.-f > 0, q, = 0 otherwise.



Q = vi[ (1i+r-f)] = Aw(z+r -f) (3.7)


The linearization constant is determined here by matching the maximum flow of the two,

resulting in equation (3.8).


2 = Vg 2 (3.8)
A = yg(- [ (1+K) cos(ut)-2 i (3.8)
3 2 H.

The flow over the barrier can be represented by a Fourier series with components at an infinite

number of frequencies. Here the primary frequency component is found and assumed to be much

larger than any secondary harmonic components. The limits of integration for the calculation of

the first Fourier coefficient are determined from the geometry of the problem. These limits are

taken to be the times during the wave cycle when the water surface elevation on the incident side

is above the crest elevation of the barrier. The first Fourier component of the flow then becomes

equation (3.9). Again, the details of this development are contained in Appendix B.


it (Hl1+Kr)COS_( 2f
q = A [ (1+K) cos-2( )] (3.9)
x 2 2 Hi (1+Kr)








56

This intermittent portion of the flow is then added to the flow through any holes in the barrier.

The flow through any holes is calculated in the same manner as the flow over a totally submerged

barrier, via a Bernoulli-type argument. The linearization constant for the hole flow, As, is of the

same form as equation (3.3). The area of the holes is included in the development as the height

of the holes per unit width of barridr. For the case of the P.E.P. Reef, the three holes represent

46% of the longshore length of the barrier. In addition, a flow contraction coefficient for the

holes of 0.6 is included. Therefore, the effective area of the holes, A,, is the height of the holes

multiplied by the longshore percentage and the contraction coefficient. The flow through the

holes is then given by equation (3.10).


qv = A, A(i+r-le) ) (3.10)

Combining the two flows, equating the sum to the flow on the transmitted side, and solving for

K, results in another implicit equation for the transmission coefficient, shown in equation (3.11).

K 2 ={ Hi 2 2f 1
Kt = {2( ) [ (2-Kt) cos (a t) ] 2
it 2h 3 Hi
1 (2-K) cos-
2 Hi (2-Kt)
+ 2 2 A (1-K)
N hH (1-K.)

The second term on the right hand side indicates the contribution from the flow through any holes

in the barrier.

The two equations for K, are solved iteratively over an appropriate range of relative

freeboards for the laboratory scale values discussed in section 3.2. Figure 3.13 plots the results

of the two analytical expressions as well as the laboratory results and the published works of

Goda (1969) and Ahrens (1987). The ranges of relative freeboards are extended slightly past

their realistic ranges in order to show how the two methods overlap. As the plot indicates, the











1.0



0.8 -~~ --- -- -- ---- - - ----~-~' ~
i



0 .6 . . . . . . . . . . . . . .. . .. ... . ... --- . .-.. . . . . .. .




A 45 Continuous (A)
-- Ahrens (1987) eq. (1.4)
-**-.. Goda(1969) exp \
0.2 *--- Goda (1969) eq. (1.3) .
--- equation (3.5)
equation (3.11)

0.0 I I I I I I
-5 -4 -3 -2 -1 0 1
f/Hi
Figure 3.13 Analytical Approaches for Transmission Coefficient compared to Laboratory
and Literature. Laboratory Scale Values, Hi = 0.012 ft.



two methods do not smoothly intersect. This discontinuity is a result of the fact that the two

mechanisms of the flow actually occur together beginning at some point near f/H, = -0.5. At

this point the flow over the barrier begins to be intermittent, but still strongly resembles the

submerged barrier approach of equation (3.5). As the barrier becomes less and less submerged

the flow begins to more closely resemble the weir flow approach. The actual mechanics of how

this transition occurs are not fully understood at this time. The two equations are plotted here

to indicate the behavior of each. The weir flow approach is terminated in the figure at the point

where the incident/reflected water surface drops to the top of the holes in the laboratory study.

At that point the structure begins to more resemble an emergent structure, which is not the focus

of this study. Note that beyond this point, flow over the top of the barrier is now accomplished

by run-up and overtopping, neither of which resemble weir flow.








58

The analytical expressions show good agreement with the present laboratory study and

the experimental work of Ahrens (1987) at lower relative freeboards. As the barrier crest

approaches the Mean Water Level (MWL) the agreement worsens. At a relative freeboard of

-0.35 (where the two methods intersect) the predicted Kt differs from the measured value in the

laboratory by 41%. In addition, the holes in the model units contribute about 38% of the wave

transmission. The calculated value of Kt at that relative freeboard is 0.48. Without the flow

through the holes, the calculated value would be roughly 0.30.

The differences between the analytical data and the laboratory data can be seen in the

assumptions used in the development. The flow over the barrier is modelled as a steady flow,

when in fact the flow of a wave over an obstacle is quite unsteady. This means that acceleration

effects are neglected. It is recognized that the flow of a wave over such a barrier would have

considerable acceleration components, particularly as the barrier occupies more of the water

column. These acceleration components would serve to increase the flow over the structure, thus

increasing the transmission coefficient. This is seen in the plot where the discrepancy widens as

the barrier crest approaches the MWL. Also the approach has been linearized to facilitate

calculation of the transmission coefficient. Although there are many ways to linearize the

equations, all techniques are still approximations to the exact solution.

The agreement of the laboratory work with that of Ahrens (1987) is explained by the fact

that Ahrens' work was conducted using porous rubble mound structures. The holes in the P.E.P.

Reef model units represent porosity, which increases the level of wave transmission. The results

of Goda (1969) were obtained in the laboratory with impermeable structures with no holes in

them. Consequently the transmission coefficients are lower. The analytical approaches presented

herein would be expected to predict higher transmission, but without the acceleration effects the

predictions are too optimistic. These values could be taken as a lower limit for design purposes,








59

but the results from experimental and field work would likely provide a better estimate for the

wave height reduction at a given relative freeboard.



3.4 Comments

Wave height attenuation over submerged narrow-crested breakwaters has been

investigated in several manners in the field, in the laboratory, and analytically. The interest in

studying this phenomenon is obviously to determine the degree of protection against storm wave

attack provided by a given barrier at a given depth of submergence. It is apparent that the

freeboard, f, is the most important variable in the design of a submerged breakwater. The greater

the freeboard, the less attenuation afforded by the barrier.

From a wave height reduction standpoint, the freeboard should be kept as small as

possible in order to reduce the wave heights significantly. However, the freeboard affects much

more than just the wave attenuation. Chapter 4 discusses the effects of structure induced currents

in the nearshore zone, and it will be shown the amount of freeboard can contribute to undesired

current effects. It is desirable to have at least a 10% reduction in the heights of large waves for

a submerged barrier to be judged effective, and to achieve this the freeboard must be limited to

a certain value. But both issues must be addressed simultaneously and a compromise reached.

Considering only wave height attenuation, however, it is noted that the barrier should occupy at

least 80% of the mean water column in order to be effective. Alternatively, the ratio of

freeboard to incident wave height should be -1.3 or greater in order to have a substantial effect

on wave height reduction.














CHAPTER 4

STRUCTURE INDUCED CURRENTS

The second focus of this paper is the effect of a submerged barrier on the nearshore

current patterns. Obviously the presence of any structure in the surfzone will alter the existing

current patterns, diverting the flow around the barrier. Of primary concern is the possible

generation of currents strong enough to transport sediment away from the project area. This

concern is the focus of this chapter.



4.1 Motivation from Field Results

The motivation for this concern stems from the initial performance of the Midtown Palm

Beach P.E.P. Reef installation. During the first three months after the installation of the full

Reef, the area directly in the lee of the Reef lost a substantial amount of material, 35,000 cubic

yards (yds3), while the 2,000 foot long stretches of beach to the north and south of the Reef

gained 3,600 yds3 and 13,200 yds3 of material, respectively (Dean et al., 1994b). The movement

of such substantial amounts of sand clearly suggests that the current patterns in the area had been

modified from the natural condition.

Figure 4.1 shows the changes in seafloor elevation in the vicinity of the Reef during the

four month period from August to December, 1993. The solid contours indicate areas of

accretion and the dashed lines indicate erosion. The plot clearly shows the losses experienced

in the lee of the Reef during this period. In the lee the seafloor dropped an average of 1.0 feet,

while the region landward and south of the Reef gained 0.75 feet in elevation overall. The figure













250
200
150






-50


-200

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
North Distance from monument 92F (ft)




Figure 4.1 Isolines of Elevation Change (ft), August 1993 to December 1993. Contours
in 1.0 foot intervals.



suggests that material has been removed from the lee of the Reef and deposited to the north and

south of the Reef, predominantly to the south, which is the prevailing direction of longshore

sediment transport in the area.

Dean et al. (1994b) presented a hypothesis for the sedimentation patterns observed above.

The mechanism proposed derives from the fact that waves passing over the Reef transport mass

(water and possibly suspended sediment) shoreward over the Reef. Wave mass transport is a well

understood and documented phenomenon. This transport of mass is normally balanced by an

offshore return flow in the bottom portion of the water column. Dean et al. proposed that this

seaward return flow was reduced by the presence of the barrier parallel to shore. This

interruption causes at least a portion of the return flow to be diverted alongshore, where it is

superimposed upon any existing longshore current. This diverted flow impedes the longshore








62

flow in the updrift direction and augments the longshore flow in the downdrift direction. The

addition of this diverted flow may have increased the level of suspended sediment transport,

carrying water and sediment to the ends of the Reef where the restriction to the natural flow was

removed and the currents were reduced, thus causing the deposition of sediment, particularly in

the direction of the natural longshore current.

Further monitoring results from the Midtown Palm Beach Installation are consistent with

this conclusion. Figures 4.2a and 4.2b show the volume changes in six regions around the Reef

(Browder, 1994). Figure 4.2a shows the volume changes in the vicinity of the Reef for the most

recent survey period (as of this writing), March 1994 to July 1994. This period indicates that

the only region to lose material is the area in the lee of the Reef, while the remaining five regions

have posted modest gains. These depositional patterns are indicative of the current patterns

described above. The mechanism discussed is referred to herein as a 'pumping current.'



March 1994 to July 1994 August 1993 to July 1994
94A T- 94A

+2,000 +5,500 2000' -5,500 +1,800 2000'

9 5 E ........... 9 5 E .................................. ...................
*Reef IReef

t t
5 -4,400 +5,600 4000' 6 -37,000 +3,800 4000'
0 o
Z

9 9B. ....................... 99B .

+4,300 +2,300 2000' +17,100 -5,100 2000'

101A 101A
-- 240'+/---- 240'+/-- o 240'+/---- 240' +/---

(a) (b)


Volumetric Changes for Latest Survey Period and Last Year (yds3).


Figure 4.2








63

Figure 4.2b indicates the cumulative changes in the vicinity of the Reef for the two year

period from August, 1993, to July, 1994. The August, 1993, hydrographic survey was taken

immediately after the placement of the entire 330 P.E.P. Reef units and is considered by the

monitoring program to be the post-installation baseline survey for the performance of the project.

The plot indicates substantial losses in the lee of the Reef, resulting in a drop of the seafloor by

1.0 feet during this time. The region landward and south of the Reef has accumulated 17,100

yds3 of material during this time. This behavior would support the mechanism of the pumping

current superimposed on the southerly directed longshore current.

The net longshore sediment transport in the Palm Beach area is to the south, driven

mainly by the northeaster storms experienced during the winter months. It is during these times

that the longshore current is strong and southerly directed, and it is also during these times that

the most sediment is suspended in the water column. It is recognized here that much of the

volume changes observed to the north of the Reef are influenced by other structures in the

nearshore zone, and the losses seen in that region in Figure 4.2b may not be directly attributable

to the presence of the Reef. The magnitudes of the changes seen leeward of and south and

landward of the Reef, however, indicate that these are attributable, to some degree, to the Reef.

Definitive field measurements of the current patterns are not available due to the

measurement intensive nature of the problem. The wave gages in place at the site provide only

point measurements of the currents on either side of the Reef. These gages primarily provide an

indication of the longshore current. Current data have been compiled for both gages since

October, 1993. The data suggest that the longshore current is actually slightly higher during the

summer months, ranging between 0.3 to 0.6 ft/s and directed most often to the north. During

the winter the magnitude of the current is typically decreased to approximately 0.3 ft/s and

directed frequently to the south due to northeast storm conditions.








64

It appears that there exists a natural northerly current at the P.E.P. Reef location in

Midtown Palm Beach. This current is associated with the Gulf Stream, which flows closest to

the Florida Coast along the Palm Beach County shoreline. During the summer months when the

mild wave climate does not generate a substantial longshore current, this current predominates.

However, during the winter northeast storms, the longshore currents generated by wave action

overcome the northerly currents. The result is a net southerly directed longshore current of lesser

magnitude. Again it is noted that the times of highest suspended sediment concentration are

during the strong winter storms, which results in the net southerly longshore transport.

Limited dye and drogue studies conducted at the Palm Beach site have not documented

the presence of an increased current in the lee of the Reef. It is suggested that the pumping

currents hypothesized herein exist as secondary flows, flows whose magnitudes are substantially

smaller than the longshore current. Secondary currents have been documented, particularly in

flows around bends, such as river flows. There the result of the secondary flow is to accumulate

material on the inside of the river bend, which results in meanders and ultimately in the formation

of ox-bow lakes when the bend in the river becomes too severe. The presence of a secondary

flow in the lee of a submerged barrier manifests itself in an increase in the magnitude of the

velocity of the longshore current in the direction of flow, and a decrease in the magnitude of the

longshore flow where the flow is directed updrift. The increased velocity of the current can act

to increase the amount of sediment transport over that of the natural longshore current.

Again, no direct field measurements support the existence of the pumping mechanism.

Depositional features observed during the monitoring program of the Midtown Palm Beach

installation suggest that such a mechanism exists, although perhaps as a secondary, or minor,

current, prompting research into the problem.








65

4.2 Laboratory Investigations

One of the objectives of the laboratory study described in Chapter 2 was to verify the

existence of the pumping current proposed from the field work. The laboratory study was

conducted primarily to document the flow patterns around various planform arrangements for the

Vero Beach, FL, P.E.P. Reef design, including any pumping currents that could lead to erosion

problems. This section details the results of the laboratory experiments and the verification of

the presence of a pumping current. It is noted that the pumping current, while of considerable

interest, was not the only focus of the lab study regarding currents. The study was conducted

to document the entire current field around the model structure, including the possible occurrence

of rip currents.

As described in Chapter 2, bottom-moving drogues were used on a gridded floor in the

wave basin to trace their trajectories and calculate average velocities along their paths. Drogues

were placed both in the 'nearfield region,' six inches or less from the Reef model units, and

further away in the 'farfield region,' extending all the way to the beach toe in the wave basin.



4.2.1 The 'Pumping Current'

The laboratory study demonstrated the presence of an alongshore flow directed to both

ends of each Reef arrangement tested. Since the waves used in the study were all normally

incident on the beach, this current is appropriately considered to be a pumping current. Both dye

streaks and drogues were used to document this phenomenon. Figure 4.3 shows the trajectories

of the bottom drogues for a test in which a continuous Reef (Type A case) 33.75 feet long was

placed in a water depth of 12 cm (0.037 ft), creating a freeboard ratio of 0.0 (crest at Still Water

Level, SWL). The drogues placed in the lee of the Reef were all carried to the ends and

offshore. The laboratory study used sidewalls that directed the flow offshore; in the field the























Figure 4.3 Bottom Drogue Trajectories, f/h = 0.0.



flow would either be relieved offshore or diffused alongshore. Appendix C contains diagrams

of the flow patterns for the 0.0, -0.2, -0.4 freeboard ratio cases.

The magnitudes of the currents were measured along the exit plane of the Reef. This exit

plane is defined as the vertical area between the Reef and the shoreline. For a freeboard ratio

of 0.0, currents of up to 0.52 ft/s (prototype) were measured passing this exit plane. This

exceeds the limit of induced velocities suggested by Seelig and Walton (1980). The control case

corresponding to this test indicated prototype velocities of less than 0.04 ft/s and directed

onshore. With the normally incident waves, the patterns were nearly symmetric about the Reef

centerline, further validating the presence of the pumping current.

While Figure 4.3 depicts the flow patterns for a structure whose crest is located at the

SWL, other tests, both at smaller freeboard ratios and different platform arrangements (see

Figures 2.6 and 2.7), also demonstrated this behavior. For the Type A case at a freeboard ratio

of -0.2, the velocities along the exit plane were measured at 0.36 ft/s prototype and directed out

through the ends. Again the patterns were symmetric. For the -0.4 freeboard ratio case, the

velocities along the exit plane were 0.20 ft/s outward at one end, but were smaller and directed

onshore at the other end, indicating that the basin effects were beginning to dominate over the








67

Reef effects as the water depth increased. At a freeboard ratio of -0.6, the deepest case tested,

the velocities were indistinguishable from the control cases.

Changes in the planform arrangements affected the magnitudes of the currents around the

ends of the Reef. In the Type B Case where three separate segments were used, at f/h = 0.0

pumping patterns were observed around each segment. The velocities around each segment were

slightly reduced, averaging approximately 0.4 ft/s prototype at each exit plane, with slightly

higher velocities noticed at the ends of the entire test where the flow area was restricted near the

side-walls.

The Type C case provided little improvement over the continuous Reef case, with exit

plane bottom velocities measuring up to 0.52 ft/s at f/h = 0.0. The Type D case offered some

reduction of the pumping currents, indicating velocities of up to 0.40 ft/s. The Type B and Type

D cases provided gaps parallel to the shoreline which provided some offshore relief of the mass

transport accumulating in the lee of the structure. The difficulty with this type of arrangement

is that it leaves stretches of the shoreline unprotected from incident wave attack, which can lead

to an irregular shoreline.

The last three cases tested, Types E, F, and G, were performed as compromise

arrangements between the need for wave attenuation and the desire to limit the magnitude of the

pumping currents induced. The Type E case further investigated the offset case, Type C, to

determine if a different cross-shore separation distance would promote offshore flow between the

segments, thus reducing the pumping currents. All three types tested after the initial tests were

tested at a freeboard ratio of 0.0 in order to clearly demonstrate the Reef effects. Increasing the

separation distance to approximately 60 feet in prototype appeared to slightly reduce the induced

pumping currents, to roughly 0.4 ft/s prototype at the exit plane. Increasing the separation

distance to 90 feet appeared to provide no additional benefit.








68

The Type F case was investigated to further promote offshore flow. This was done by

shortening the lengths of the offshore segments. As a result small gaps in the Reef were created

parallel to shore, but the lengths (12 ft prototype) were not long enough to leave the shoreline

exposed to unattenuated waves due to a mechanism termed herein as bridging (to be discussed).

The results of this test reduced the pumping currents slightly in comparison to the continuous

Reef case, from roughly 0.52 ft/s to just under 0.4 ft/s in the most extreme cases.

The Type G case was an extension of the Type F case. The Type F case presented some

improvements in design including protection of the entire shoreline in the lee of the Reef from

wave attack. The Type G case was conducted to determine if longer individual segments would

increase the currents over that of the Type F case. It will be shown later that the magnitude of

the pumping current is approximately proportional to the length of the barrier segment.

Lengthening of the segments reduces the cost and time required for installation. Longer segments

of units would require fewer end tie-downs and less time to install. This test produced currents

of the same magnitude as the previous case, reaching a maximum of just under 0.4 ft/s prototype.

Table 4.1 summarizes the exit plane velocities measured for the seven arrangements at

a freeboard ratio off/h = 0.0. It was observed in all tests that reducing the freeboard ratio (from

0.0 to -0.2 to -0.4, etc.) produced similar patterns of lesser magnitudes. This trend continues

until the effect of the structure becomes indistinguishable above the control behavior of the basin.

Table 4.1 indicates that in all cases the current patterns flowing from the middle of the lee of the

structure to the ends are of similar magnitude, and that certain arrangements provide small

reductions in the pumping currents. The cases where significant gaps are left in the planform

(Types B and D) allow for some offshore flow along the line of the structure, but again they

leave stretches of the shoreline unprotected from wave attack. In these cases, pumping currents

of slightly smaller magnitude were observed as well.








69

Table 4.1 Exit Plane Velocities for Seven Test Arrangements. f/h = 0.0, Types are
Illustrated in Figures 2.6 and 2.7.


Case Arrangement Prototype Exit Plane Velocity, ft/s

A 45 Continuous Units 0.52

B Three 11 Unit Segments 0.40

C 45 Staggered Segments 0.52

D Five 5 Unit Segments 0.40

E 9 Unit Segments 0.40
F 9 & 7 Unit Segments 0.40

G 18 & 11 Unit Segments 0.40


In all cases where the wave heights were reduced by the structure to a noticeable degree

(transmission coefficient, Kt of 0.9 or lower) the pumping current was observed. In these cases,

the barrier appears to block a sufficient percentage of the return flow and divert it alongshore,

creating the pumping currents. No one test arrangement appeared to be a clear solution to the

problem but each represented some degree of compromise between the wave attenuation and the

generation of structure induced longshore currents, which are inextricably linked.



4.2.2 Other Current Effects

The laboratory study also indicated other current patterns and effects of interest. In

particular are two items: 1) The presence of a 'bridging effect' between barrier segments, and

2) The lack of a strong near-bottom return flow in the lee of the barrier. These two aspects are

important in both the actual and perceived performance of a submerged breakwater.

The bridging effect mentioned previously appears to be a combined wave diffraction

effect from both segments on either side of a gap as the waves pass through the gap. The result








70

of this bridging mechanism is to provide some degree of wave attenuation in gaps between

segments and to create flow channels between segments. In cases where the barrier segments

were sufficiently close together, no significant offshore flow between segments was observed and

no reduction of wave attenuation was measured. The presence of the bridging mechanism

prompted the investigation into lengthening the cross-shore separation distances enough to just

overcome the bridging and provide some offshore relief of the pumping currents along the line

of the barrier. This bridging mechanism may prove to be beneficial in reducing the likelihood

of rip-current generation by such a structure, which is a concern along any recreational beach.

However, this bridging mechanism has been observed in the laboratory only, and does not negate

the need for concern about rip-currents in the field.

The second interesting observation regarding the current patterns was the lack of a near-

bottom return flow in any of the laboratory tests. In both the field and the laboratory, upwelling

of currents is observed over the line of the structure, particularly during the passing of wave

troughs. This upwelling has been attributed to the diversion of the seaward return flow up along

the landward face of the structure. The upward flow is then credited with blocking any seaward

transport of sediment from the lee of the structure. In two dimensional laboratory studies of

submerged barriers, the longshore flow component is obviously not present, and the return flow

must be forced back offshore over the barrier. The three dimensional tests conducted as part of

the Vero Beach study do indicate this upwelling, however, the belief that the upwelling would

prevent a substantial offshore loss of sediment is not supported by the lab findings. In very few

instances was a bottom flow observed to be moving offshore in the lee of the Reef. This would

suggest that the upwelling patterns seen in the field are localized effects generated by the transfer

of momentum of waves passing over the barrier. The momentum transfer to the water column

generates an eddy just landward of the barrier, and it is this eddy that appears as the upwelling








71

of water and sediment. This indicates that sediment suspended over the barrier comes primarily

from the nearfield region close to the barrier. Further away from the structure in the lee of the

structure, most bottom flows (those that would carry the most sediment) were directed onshore

or alongshore with the pumping current. Neither of these would carry sediment into the

upwelling region.




4.3 Analytical Approach

Having verified the existence of a pumping mechanism in the laboratory, it is desirable

to attempt to develop some analytical basis for both the existence and the prediction of such

currents. This section explains the basis for the generation of these currents and presents simple

analytical approaches for predicting the magnitude of such flows.




4.3.1 Explanation of the Problem

The pumping current discussed previously has been observed in a laboratory setting and

is proposed as the mechanism responsible for some part of the deposition patterns measured at

the Midtown Palm Beach P.E.P. Reef Installation. A physical explanation of the generation of

these currents is as follows. As waves propagate toward a beach, they transport a net mass of

fluid in the direction of wave propagation. In an Eulerian perspective, this net mass transport

exists in the upper portions of the wave water column between the trough and crest elevations

of the wave. Obviously, this net mass transport in the upper portions of the water column must

be balanced somewhere by an equal mass transport directed offshore, otherwise the water level

on the beach would rise continually which is an unrealistic situation. In the absence of strong

three-dimensional effects, this offshore directed flow is termed the return flow and is usually








72

observed in the lower part of the water column. Figure 4.4 shows a two dimensional description

of the balance of mass transport under a wave. The return flow is depicted here as a uniform

flow over the water column from the trough level to the bottom (in the absence of any barrier).

From this representation it is apparent that the presence of the barrier disrupts the natural return

flow. As a result, the flow must either be returned seaward over the top of the barrier (as in two

dimensional wave tanks) or a portion of the flow must be diverted in the alongshore direction (as

in the three dimensional wave basin experiments).

The presence of the barrier results in a transfer of momentum from the passing wave to

the water in the lee of the barrier. This momentum transfer results, in a two-dimensional sense,

in an increase in the mean water level on the lee side of the structure. This increase, termed

'ponding,' was investigated by Longuet-Higgins (1967) for waves passing over infinitely long

barriers and sand bars. Longuet-Higgins did not discuss the subsequent effects of an increased




Wave Travel



M L
V MWL ,," ",,,


Mass
Transport
Profile
h (in absence
of barrier)

barrier -----1
Seaward
777 //////77//////// ///////"/7////////////////////////////////;


Schematic of Mass Transport Profile Under Wave Passing Over a Barrier.


Figure 4.4








73
water surface elevation; the development was a two dimensional representation only. In three

dimensions, however, the effect of a ponding level in the lee of a finite-length structure is to

drive flows in the direction of the longshore water surface elevation gradient. This ponding level,

or superelevation of the water level, would be highest at the longshore centerline of the structure

and approximately zero at the ends of structure, and is consistent with the pumping currents

discussed above.

A simple representation of the three dimensional problem is shown in Figure 4.5. The

figure shows a schematic of the wave basin used in the experiments previously described. The

arrows in the figure indicate the transport over the structure along its length, and the relief of the

'ponded water' around the ends of the structure. In the laboratory, sidewalls on the basin forced

all the relief flow to eventually be directed offshore. In the prototype, this pumping current can

either be directed offshore or continue alongshore after reaching the ends of the structure (with

a subsequent reduction in magnitude, analogous to an expanding jet discharge).



P.E.P. Reef Model
/


Figure 4.5 Schematic of Wave Basin and Pumping Currents.


1:8 Gravel
Beach


Paddle
Wavemaker










4.3.2 Mass Conservation Approach

The simplest approach to predicting the magnitude of the velocity is to assume that some

percentage of the mass transported over the structure is diverted alongshore and must be balanced

by an equal transport of mass across the exit plane, the vertical area between the structure and

the shoreline. The linear wave theory mass transport is given by equation (4.1),




E pgH2 0 (4.1)
C 8 k

where E = energy per unit surface area of the wave, C = wave celerity, H = incident wave

height, a = angular frequency = 21r/T, and k = wave number = 2ir/L. If this transport, given

here per unit length of wave crest, is converted to a uniform volumetric flow rate along the

length of the structure and the area of the exit plane is known, the average exit velocity can be

computed by conservation of mass. Figure 4.6 plots the average velocity along the line of the

model reef tested in the laboratory. The family of curves shown indicates the percentage of the

transport over the structure that is diverted alongshore (the remaining fraction of the total

shoreward transport is assumed to 'escape' seaward over the structure). This plot represents the

continuous Reef case (Type A) withf/h = 0.0. At this level, the simple representation of Figure

4.4 would suggest that 100% of the transport is diverted alongshore. While the actual details of

diversion of the return flow are not fully understood, the measured bottom velocities taken during

the test indicate a higher velocity along the bottom than the average predicted by this method.

While the measured bottom velocity was 0.13 ft/s (model scale) through the exit plane, the

average velocity calculated for 100% diversion was 0.08 ft/s.

A portion of this discrepancy may be attributed to the 'channel' in the lee of the structure

in which the pumping currents flow. In the laboratory, 86% of the channel area is above a








75

0.15
Type A Case, f/h = 0.0




S0 1 0 .- ........ .. .... . ... ... .. .. . ...... .. ....
7. Diverted

S.0 1007%


0 .0 5 ........ ................ ........M C... -- ...

-.407.

.- ...*... 207.
^ .- ^.-' , ,.. ,' '''" '"


0.00
0 4 8 12 16 20
Distance from Structure Centerline (ft)

Figure 4.6 Average Exit Velocity vs. Length of Structure. Continuous Structure, f/h =
0.0. Figure Applicable for Model Conditions.


smooth concrete bottom, while the remaining area is over the rough gravel beach. If the total

flow were accordingly confined within 86% of the exit plane area, the average velocity in this

case would be 0.09 ft/s, which is still lower than the measured velocity. Another possible

explanation of this difference is that this method assumes the flow to be distributed uniformly

over the entire exit plane, while the actual velocity distribution is most likely non-uniform, and

may well have a local maximum shifted toward the structure.

Seelig and Walton (1980) presented a simple method for the calculation of the average

velocity through the exit plane of a submerged barrier based on the ponding level. This method

simply used a Bernoulli equation statement relating the difference in head between the lee of the

breakwater and the seaward side to the velocity generated. The length of the structure was not








76

considered in the development. Using this method for the laboratory situation above, Seelig and

Walton predict an average exit velocity of 0.16 ft/s, twice that predicted by the simple mass

conservation method. Seelig and Walton also emphasize that the value calculated is an average

velocity and that local velocities around the structure could be higher.



4.3.3 Momentum Conservation Approach

Using a momentum balance approach, the velocity profile along the line of the structure

and the water surface elevation, or ponding level, can be determined. Longuet- Higgins (1967)

presented a momentum approach to the determination of the ponding level that relied on

knowledge of the transmitted and reflected wave heights. This two dimensional model represents

a limit of the increase in water surface elevation since it does not include any three dimensional

effects, such as the driving of currents due to the elevation change. Using the laboratory scales

discussed above, and assuming conservation of energy, shown in equation (4.2)


1 = Kr2 + Kt2 (4.2)


Longuet-Higgins' approach results in a ponding level of nearly 40% of the incident wave height

(4 cm (0.012 ft)). The value of Kt was taken from the laboratory measurements for the

calculation. If this ponding level is used in a simple channel flow manner to compute an average

velocity at the exit plane of the structure, the resulting velocity is over 2.0 ft/s, clearly an

unrealistic value for the model. This suggests that the maximum ponding level predicted by

Longuet-Higgins is never attained for the finite length structure of the laboratory experiments.

To approach the problem in a simple three-dimensional manner, the structure is modelled

as an open channel loaded with a uniform lateral inflow. The lateral inflow is taken to be some

percentage of the wave mass transport over the structure, which is assumed to be invariant along

the line of the breakwater. Solutions for such flows exist in open-channel flow texts, such as








77

Henderson (1966). Figure 4.7 shows a simple schematic of the approach to the problem; the

perspective in the schematic is an elevation view looking seaward from the shoreline. The lateral

inflow is taken to be the wave volumetric transport and is uniform over the length of the

structure. The approach uses a local control volume (the dashed box in Figure 4.7) to consider

the local change in momentum, M, across the control volume.




Wave Transport Lateral Inflow




iV dy/dx

MWL

I flow Q Q + dQ



!Sf
I -, I
11111/11111/11/11/i/11/711111/1//I o= o

I I


Figure 4.7 Schematic of Lateral Inflow Model to Determine Water Surface Profile.



If the balance of momentum is written and the bed resistance and slope are considered,

the following equation (4.3) results:



yAM + yAbAz = -TPAx (4.3)

where the first term on the left hand side denotes the local change in momentum, the second term

includes the bottom slope (0 in this case), and the right hand term includes the bottom friction

effects. If this equation is written in differential form and the derivative taken with respect to x,










the following, equation (4.4), results:


S2q2
So Sf 2q
dh gAx (4 4)
dx q2B(
1-
gA3

where dh/dx = local water surface gradient, So = bottom slope (taken to be 0 in this analysis),

Sf = friction slope, q = volumetric flow rate, A = cross-sectional area, and B = width of

channel (distance from structure to shoreline). The friction slope, Sf, is taken to be


u2p
S, (4.5)
C2A

where u = average velocity at cross section, P = wetted perimeter of channel, and C = the

Chezy coefficient (calculated as the hydraulic radius divided by the Manning coefficient to the

1/6 power).

Using this method, the profile of the water surface can be calculated, similar to backwater

curve calculations, starting from a known elevation and moving the control volume stepwise 'up

the channel' to the structure centerline. In this case the known elevation is taken to be the

elevation of the water surface at the end of the structure, where the elevation must return to the

ambient level. Figure 4.8 shows the alongshore profile of the water surface elevation in the lee

of the structure tests in the laboratory. The profile indicates a minuscule centerline water surface

elevation of only 0.0002 ft, but this elevation difference taken over a length of 16.9 feet produces

an average exit velocity of 0.07 ft/s (for 100% divergence of the return flow). If this elevation

head is used in a simple Manning's equation manner as a check (with a linear water surface slope

from centerline to end), the average velocity calculated at the exit plane is 0.08 ft/s, which is in

line with previous calculations and the measured results for bottom velocities.











ftx 104
2.0



< 1.0 -1.5-----------------

0



<0.0
0 4 8 12 16 20
Distance from centerline (ft)

Figure 4.8 Water Surface Elevation Profile Calculated for Laboratory Scale, 100% Flow
Divergence. H = 0.04 cm (0.012 ft), T = 2 s.



The proportions of the graph present the appearance of a substantial discontinuity in the

water surface at the end of the structure, however this difficulty is attributed to the lack of an exit

loss in the development. Similar to a jet discharge, the flow at the end of the structure will have

an exit loss that will extend the superelevation of the water surface beyond the end of the

structure and will remove the discontinuity. The water surface slope at the centerline of the

structure is zero, reflecting the stagnation point along the breakwater where the flow must be

diverted to one direction or the other, since in the absence of other effects the flow must be

symmetric.

Figure 4.9 shows the water surface elevation profiles calculated for the P.E.P. Reef

prototype. Using a wave height of 3.28 ft. (1 .0 m) and 6 second period, the elevation profile

along 2,000 feet of Reef is determined for various percentages of diverted return flow. The

centerline elevations range from 0.30 ft. for the 100% diverted case to 0.01 ft. when only 20%

of the return flow is directed alongshore. Again the profiles behave parabolically, decreasing to

zero at the control depth, taken as 9 feet for this example outside the lee of the Reef. For








80



0.4
47. Diverted
20%
0 .3 .-. ..: .. :.. .. .. ...... ....... 407 .

------ 807
0.2 ------- -----
S-------------------------- 91ft/
1.43 9t/s
........................ 0.95 ft/s
0 .1 4t 3-*0.48 fts....
0 0.0
0 250 500 750 1000 1250 1500 1750 2000
Distance from Reef Centerline (ft)

Figure 4.9 Ponding Levels For P.E.P. Reef Prototype Scale. H = 3.28 ft, T = 6 s.
Velocities Shown Are Exit Plane Values (x = 2,000 ft.).



comparison, the method by Longuet-Higgins (1967) predicts a maximum setup of 0.27 inches.

This would indicate that the Midtown Palm Beach Installation is sufficiently long to reach the

'potential setup' predicted by the two-dimensional momentum approach. The difficulty in both

approaches presented herein is that the resulting exit plane velocities seem too high to be realistic.

The exit velocities calculated for each percent divergence case are noted in Figure 4.9. The

lowest velocity (for 20% divergence) is 0.48 ft/s. In the Longuet-Higgins approach, the set-up

predicted by a simple Manning's equation calculation would result in an exit velocity of roughly

0.6 ft/s, which is on the order of magnitude of the longshore current measured in the area. Such

a high current would definitely be noticeable in the field. Such a high current has not been

observed by the UFCOE monitoring team nor by lifeguards patrolling the area. It is noteworthy

to recall that with the low freeboard ratio of the Midtown Palm Beach Installation (roughly -0.6),

the percentage of the flow that is diverted alongshore is most likely closer to 20 to 40% and

certainly not 80 or 100%.








81

Several possibilities exist for the discrepancies in the velocity calculations. One

assumption made in the model is that of linear wave mass transport. Obviously waves in the

prototype are irregular and non-linear. The linear assumption can lead to an overestimation of

the mass transport of as much as 15% depending on the non-linear representation used to describe

the mass transport and the nature of the waves. Another possibility is the relief of the return

current in the upper levels of the water column. The mass transport profile shown in Figure 4.4

is a simplistic view of the profile. It is possible that the return current is relieved in part at the

surface, creating a situation in which the incoming waves are propagating against an adverse

current. This phenomenon was occasionally observed in the laboratory via the use of dye streaks.

However, this behavior was not observed on a consistent basis, nor was the effect widespread

in the laboratory basin. The result of this possibility would be an even smaller percent

divergence of the return flow, leading to smaller, more realistic exit velocities at the ends of the

structure.



4.4 Comments

The current patterns generated by a submerged breakwater in the nearshore zone have

been investigated, both experimentally and analytically. The purpose of the investigation was to

verify the patterns and provide some means of predicting the magnitude of the currents generated

in the vicinity of such a structure. The existence of a 'pumping current,' hypothesized from field

data, has been verified in the laboratory. Currents that flow from the centerline of a submerged

breakwater to its ends are most likely a contributing factor to the erosion patterns seen at the

Midtown Palm Beach Installation. Analytical approaches to predicting the magnitudes of these

currents yield reasonable results in comparison to laboratory data, however, these methods

overestimate the structure-induced longshore currents in the prototype. The analytical models and








82

previously published literature do indicate that there is a fundamental hydrodynamic basis for

such currents. A fundamental question arises as to how to accurately model the amount of

volumetric flow diverted by the barrier in the prototype, where measurements of the velocities

along the line of the structure are unavailable.

From a practical standpoint, the designer of such a structure needs to be aware of the

potential problems associated the generation of the pumping currents discussed herein. The loss

of a substantial amount of sediment in the lee of a submerged breakwater significantly

compromises its main objective, which is the protection of the beach and upland development

behind it. If the beach in the lee of a structure has very little or no sand, such as the Midtown

Palm Beach Installation, the smaller waves that pass over the structure, while having been

reduced in size and energy, may still produce a similar amount of damage to the shoreline. The

structure and the sandy beach act as a system to provide defense of upland developments.

The results of the field monitoring and the laboratory suggest that segmenting and

offsetting a submerged breakwater installation may provide some relief from the structure induced

longshore currents. It is, however, not possible to separate wave attenuation over such structures

and the generation of these currents. Each design must anticipate the wave climate and the

desired amount of wave attenuation, and plan appropriately to mitigate the currents created.

Further recommendations can be found in Chapter 5.















CHAPTER 5

CONCLUSIONS

Submerged breakwaters have become topics of considerable interest in coastal engineering

in recent years. Reactions to beach nourishment regarding environmental concerns and the

expense of periodic renourishment have turned the attention of coastal engineers to more

permanent solutions to the beach erosion problem. Interest in the state of Florida has been high

in light of two experimental field projects currently in place in the state and a third project under

consideration. While data exist regarding the performance of these structures in some aspects,

comprehensive performance data and field results are sparse. The purpose of this study was to

provide general design guidance for the installation of a submerged breakwater, particularly a

narrow-crested breakwater, such as the Midtown Palm Beach Prefabricated Erosion Prevention

(P.E.P.) Reef.



5.1 Midtown Palm Beach Installation

Field data from a comprehensive monitoring program of the Midtown Palm Beach P.E.P.

Reef installation have been collected and compiled for one year of the three year monitoring

program. Wave data collected during that time indicate a 15 to 35% reduction in significant

wave height between wave gages located offshore and onshore of the P.E.P. Reef. Additional

wave gages installed at the site verify the amount of wave height reduction calculated by the

permanent wave gages and provide an indication of the background reduction provided by wave

breaking. This reduction would occur irrespective of the presence of the Reef. Control








84

measurements taken outside the confines of the Reef indicate a 5 to 20% reduction in wave height

due to natural wave energy dissipation. Consequently, the Reef appears to be responsible for

approximately 10 to 20% of the wave height reduction, whereas the combined Reef and natural

effects are 15 to 35%. Comparisons of storm wave data inside the Reef confines and away from

the Reef support the conclusion that a substantial portion of the storm wave height reduction

measured over the Reef (roughly 40%) is attributed to natural effects such as wave breaking that

would occur in the area anyway.

Hydrographic surveys indicate that the area immediately in the lee of the Reef lost a

substantial amount of material (35,000 yds3) during the first four months after installation of the

full P.E.P. Reef. This loss was accompanied by a substantial gain of material (16,800 yds3)

immediately north and south of the Reef, predominantly to the south. Dean et al. (1994b)

proposed that this behavior of the sedimentation patterns was attributable to a 'pumping current'

generated in the lee of the Reef. This current flows from the centerline of the structure to the

ends of the breakwater where the current is dissipated much like a jet flow. The current

increases the amount of sediment carried from the lee of the Reef and causes the sediment to be

deposited at the ends of the Reef. In the case of the P.E.P. Reef, the predominant direction of

sediment transport is to the south, in the direction of the most accumulation of sediment. The

pumping current becomes superimposed on the longshore current, augmenting the sediment

transport to the south during storm events, which are times when the suspended sediment

transport is highest.

The presence of a pumping current was documented in laboratory experiments, verifying

the hypothesis presented above. Waves transport water and possibly sediment forward over the

structure. This transport is usually offset by a seaward return flow in the lower portions of the

water column. The presence of the structure impedes the return flow, diverting it alongshore








85

where it flows to the ends of the structure. In the Midtown Palm Beach installation case, the

introduction of the P.E.P. Reef parallel to shore seems to have created a longshore 'channel'

along which the longshore current and the pumping currents flow. It appears that the addition

of the pumping currents on the previously equilibrated system enhanced the southerly sediment

transport, whereas the net transport previously was in approximate dynamic equilibrium. The

result appears to have been a scouring of the channel until it reached a new equilibrium cross

sectional area where the average suspended sediment concentration was lower. The initial losses

seen at the site in the first four months support this conclusion. Surveys conducted during the

coming winter months at the site will shed more light on the problem. If the area in the lee of

the Reef remains fairly stable over the energetic winter season then it would be assumed that the

Reef and the beach have reached a new equilibrium. If more substantial losses occur, then the

system has not yet reached an equilibrium situation. If this is the case, consideration must be

given for the level of protection now afforded to the upland structures since the beachface will

be further eroded.



5.2 Vero Beach Laboratory Study

Physical model tests of the P.E.P. Reef were conducted on a 1:16 scale in the laboratory

of the Coastal & Oceanographic Engineering Department of the University of Florida to study

the three-dimensional hydrodynamics of the submerged breakwater. The tests were performed

to provide design guidance as part of a permit request to the state for permission to install a

P.E.P. Reef submerged breakwater off Vero Beach, FL.

Wave height transmission coefficients were determined for each test conducted. The

coefficients indicated less than ten percent wave height reduction for the freeboard ratios similar

to the Midtown Palm Beach installation. The results were compared to laboratory studies








86

published by Ahrens (1987) which compared well to these data. The data indicate that a

submerged barrier must occupy at least 80% of the mean water depth in order to effect a

transmission coefficient of less than 90%. Any transmission higher than that would be ineffective

in providing substantial protection to the shoreline. The arrangements with full coverage of the

shoreline (no large longshore gaps) provided the best wave height reduction along the entire

shoreline. Wide gaps along the shore would allow unattenuated waves to pass through the gaps

and strike the beach with more energy than the stretches protected by the structure. The result

would be an irregular shoreline, with more erosion in the unprotected areas.

It was found in the laboratory that the wave height reduction by a submerged breakwater

was directly linked to the generation of pumping currents in the lee of the structure. The

blockage of return flow and the transfer of momentum into the water column in the lee result in

an elevation of the water level which drives a flow from the center of the structure to the ends

of the structure. The linking of these two mechanisms prompted the desire to find a compromise

solution. Different planform arrangements were tested to determine an arrangement that would

reduce the incident wave heights and minimize the longshore pumping currents.

The laboratory studies were unable to provide an "ideal" solution to the problem in which

the wave heights were attenuated sufficiently and no significant adverse currents were generated.

Some compromise solutions were recommended, but no solution reduced the wave heights and

simultaneously removed the pumping currents. Recommended values of relative freeboard were

determined to provide at least a ten percent reduction in incident wave height, and planform

suggestions were offered to offset the longshore flow generated by the structure. To reduce wave

heights sufficiently, a relative freeboard ratio, f/Hi, of -1.3 or greater is recommended. This

value must take into account any settlement of the structure that may increase the freeboard. To

offset the pumping currents generated by the structure, the structure should be constructed in

segments so as to provide some means of offshore return flow along the line of the structure.




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