• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 Abstract
 Introduction
 Approach
 Analytical methodology
 Numerical methodology
 Wave characteristics
 Analytical results
 Numerical model results
 Refraction due to currents and...
 Conclusions
 Bibliography














Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 89/024
Title: Prediction of shoreline changes near tidal inlets
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Permanent Link: http://ufdc.ufl.edu/UF00076121/00001
 Material Information
Title: Prediction of shoreline changes near tidal inlets
Series Title: UFLCOEL
Physical Description: xi, 130 leaves : ill. ; 28 cm.
Language: English
Creator: Douglas, Barry D
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal & Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1989
 Subjects
Subject: Shore protection -- Florida   ( lcsh )
Inlets -- Florida   ( lcsh )
Beach erosion -- Florida   ( lcsh )
Coastal and Oceanographic Engineering thesis M.S
Coastal and Oceanographic Engineering -- Dissertations, Academic -- UF
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Bibliography: Includes bibliographical references.
Statement of Responsibility: by Barry D. Douglas.
General Note: Originally presented as the author's thesis (M.S.)--University of Florida, 1989.
Funding: This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
 Record Information
Bibliographic ID: UF00076121
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 22191403

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Table of Contents
    Front Cover
        Front Cover
    Title Page
        Title Page
    Acknowledgement
        Acknowledgement
    Table of Contents
        Table of Contents 1
        Table of Contents 2
        Table of Contents 3
        Table of Contents 4
        Table of Contents 5
        Table of Contents 6
        Table of Contents 7
    Abstract
        Abstract 1
        Abstract 2
    Introduction
        Page 1
        Page 2
        Page 3
    Approach
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
    Analytical methodology
        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
    Numerical methodology
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
    Wave characteristics
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
    Analytical results
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
    Numerical model results
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
    Refraction due to currents and varying depth
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
        Page 124
        Page 125
        Page 126
    Conclusions
        Page 127
        Page 128
    Bibliography
        Page 129
        Page 130
Full Text




UFL/COEL-89/024


PREDICTION OF SHORELINE CHANGES NEAR
TIDAL INLETS






by


Barry D. Douglas






Thesis


1989
























PREDICTION OF SHORELINE CHANGES NEAR TIDAL INLETS


By

BARRY D. DOUGLAS




















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


UNIVERSITY OF FLORIDA


1989














ACKNOWLEDGEMENTS


I would like to thank my advisor Dr. Robert G. Dean for all of his assistance in

completing this thesis; I value him as both a teacher and a friend. The assistance of my other

committee members, Dr. Ashish Mehta and Dr. Max Sheppard, is greatly appreciated.

This work was sponsored by Florida Sea Grant; their continued support of the study

of coastal problems is appreciated. The data used in this investigation was furnished by

the Florida Department of Natural Resources; without this data this study would not have

been possible.

I would like to acknowledge my parents for their love and support. They have always

encouraged me, even if they did not understand why or what I was doing.

Greg and Margo, Dananimal, Howie, and Bro J are appreciated for their continued

friendship. Everyone at the "G": Sue, Kim, Jode, Michelle, Steverino, Rich, Don Juan,

Disco, and Will were my family in Gainesville. Thanks for sharing all the good times and

bad times. Dud's, the Porp, and Farrah's are appreciated for providing a means to keep

my sanity while in school. My fellow coastal students were a source of friendship and help

Paul, Steve, Ahn, Kyu-Nam, and Jei. Special thanks go to my fellow LAS members: Sam,

Gusty, and Jeff.

Finally, I would like to dedicate this thesis to Orville and Ethel Douglas, and Frank

and Roberta Soper. They were not afforded many opportunities in their lives. But because

of their hard work and the love they instilled in their families, I have been able to live my

life to its fullest extent. I hope they would like what I have achieved so far.















TABLE OF CONTENTS




ACKNOWLEDGEMENTS ... ................ ..... .. ...... ii

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

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

ABSTRACT ......... ......... ......... .... .......... vi

CHAPTERS

1 INTRODUCTION ............... ..... ............... 1

1.1 Purpose of Study ................................. 1

1.2 Background ................ ....... .... ......... 2

2 APPROACH ..................................... 4

2.1 Shoreline Change Data ...... .......... ..... ......... 4

2.2 One Line Theory ............. ................... 4

2.3 Pelnard-Considere Solution ........................... 6

2.4 Numerical Modeling ...... ................ ... ......... 8

2.5 Refraction ......... .. ... ... ....... ...... 10

2.6 Diffraction ....... ........ .. .. ..... .... ........ 11

2.7 Shoaling Processes at a Tidal Inlet ................ ....... 11

3 ANALYTICAL METHODOLOGY ......................... 15

3.1 Combined Continuity and Transport Equation ..... ........ 15

3.2 Predicted Results .... ......... ..... .. ............ 20

3.3 Least Squares Analysis ......... ............ ......... 21

3.4 Even and Odd Analysis ....... ....... ............... 24









4 NUMERICAL METHODOLOGY ................ ...... 29

4.1 Explicit Model ................................. 29

4.2 Implicit Model ................................. 30

4.3 Wave Refraction ........ ........... ........ ......... .. 33

4.4 Refraction Due to Currents . . . . . . 37

4.5 Wave Diffraction ......................... ....... .. 39

5 WAVE CHARACTERISTICS ............................. 43

5.1 Introduction .................................... 43

5.2 Wave Heights ....................... ............ 43

5.3 Wave Direction .................................. 44

5.4 Modified Wave Angles ............................. 46

6 ANALYTICAL RESULTS .... .......................... 52

6.1 Introduction .................................... 52

6.2 Sebastian Inlet ................................. 52

6.3 Fort Pierce Inlet ...... ......................... 55

6.4 St. Lucie Inlet ................................. 60

6.5 South Lake Worth Inlet ............................ 66

6.6 Boca Raton Inlet ................................. 71

6.7 Baker's Haulover Inlet ............................. 73

6.8 Venice Inlet .................................... 77

6.9 St. Andrews Bay Entrance .......................... 84

7 NUMERICAL MODEL RESULTS ......................... 91

8 REFRACTION DUE TO CURRENTS AND VARYING DEPTH ....... 105

8.1 Tidal Flow Field ................................ 105

8.2 Effects of Refraction on Longshore Transport . . . ... 109

8.3 Current Refrartion Sensitivity Test . . . . . .. 109

8.4 Current Refraction Effects on Net Longshore Transport . . ... 116









9 CONCLUSIONS ....................... ............ 127

BIBLIOGRAPHY ......... .. .......................... 129

BIOGRAPHICAL SKETCH ............................... 131














LIST OF FIGURES


2.1 DNR Monuments Located in St. Lucie County ............... 5

2.2 Shoreline Near Littoral Barrier . . . ..... ... 7

2.3 Numerical Model Grid System . . . ..... ... 9

2.4 Diffraction Patterns Behind a Jetty . . . ..... 12

2.5 Flood Current at an Inlet .......................... 14

2.6 Ebb Current at an Inlet ........................... 14

3.1 Control Volume Along the Shoreline . . . ..... 16

3.2 Shoreline Orientation and Wave Angle . . . ..... 18

3.3 Comparison of Shorelines for Different G and tan 0 Values ...... .. 22

3.4 Contour Plot of Error for St. Lucie Inlet 1928 to 1970 . ... 25

3.5 Even Function . . . . .. . ... .. 26

3.6 Odd Function ................... ............ 26

3.7 Predicted Solution with Background Rate of Erosion . ... 28

4.1 Refraction Grid System ................... ........ 35

4.2 Definition Sketch for Wave Diffraction . . . ... 40

5.1 Example Littoral Drift Rose . . . ..... ...... 45

5.2 Modified Monthly Breaking Wave Angles for Ft. Pierce . ... 49

5.3 Modified Transport for Ft. Pierce . . . ..... 50

6.1 Shoreline Changes for Sebastian Inlet 1946 to 1970 . . ... 54

6.2 Shoreline Changes for Sebastian Inlet 1928 to 1946 . . ... 56

6.3 Shoreline Changes for Ft. Pierce Inlet 1883 to 1928 . . ... 58








6.4 Shoreline Changes for Ft. Pierce Inlet 1928 to 1967 . . ... 59

6.5 Predicted Net Shoreline Change for Ft. Pierce Inlet 1928 to 1967 61

6.6 Shoreline Change for St. Lucie Inlet 1883 to 1948. . ... 63

6.7 Shoreline Change for St. Lucie Inlet 1948 to 1970. . . 64

6.8 Predicted Shoreline Change for St. Lucie Inlet 1928 to 1970 . 65

6.9 Predicted Shoreline Change for St. Lucie Inlet 1948 to 1970 . 67

6.10 Shoreline Changes for South Lake Worth Inlet 1883 to 1927 . 69

6.11 Shoreline Changes for South Lake Worth Inlet 1927 to 1942 ... 70

6.12 Shoreline Changes for South Lake Worth Inlet 1942 to 1970 ... 72

6.13 Shoreline Changes for Boca Raton Inlet 1927 to 1970 . ... 74

6.14 Shoreline Changes for Boca Raton Inlet 1974 to 1985 . ... 75

6.15 Shoreline Change for Baker's Haulover 1851 to 1919 . . ... 78

6.16 Shoreline Change for Baker's Haulover 1919 to 1945 . . .. 79

6.17 Shoreline Changes for Baker's Haulover 1945 to 1962 . .. 80

6.18 Shoreline Changes for Baker's Haulover 1935 to 1945 . ... 81

6.19 Shoreline Changes for Venice Inlet 1883 to 1942 . ..... 83

6.20 Shoreline Changes for Venice Inlet 1942 to 1978 . . ... 85

6.21 Shoreline Changes for St. Andrews Bay Entrance 1855 to 1934 ... 87

6.22 Shoreline Changes for St. Andrews Bay Entrance 1934 to 1977 ... 89

6.23 Predicted Shoreline Change for St. Andrews Bay Entrance 1934 to 1977 90

7.1 1930 Offshore Contours ................ .......... 93

7.2 Predicted Shoreline for 1930 Bathymetry . . . ... 94

7.3 Predicted Shoreline Positions From 1930 Bathymetry . .. 96

7.4 Shoal Due to Inlet Cutting ....... ....... ........... 97

7.5 Shoreline Change Due to Ebb Shoal . . . .... 8

7.6 Predicted Shoreline Positions From Ebb Shoal. . .. 100









7.7 Predicted Shoreline Change for Ft. Pierce . . . ... 101

7.8 Idealized Shoal at Ft. Pierce, Centered 5000 Feet North of Inlet .. 102

7.9 Idealized Shoal at Ft. Pierce, Centered at Inlet . . . 103

7.10 Idealized Shoal at Ft. Pierce, Centered 9000 Feet South of Inlet . 104

8.1 Offshore Tidal Velocity Component . . . . . 107

8.2 Alongshore Tidal Velocity Component . . . ... 107

8.3 Resultant Tidal Velocity Field . . . . . ... 108

8.4 Shoal Used for Cases 1 and 2 . . . . . 110

8.5 Current Velocity Field for Case 1 . . . . 111

8.6 Current Velocity Field for Case 2 . . . . ... 111

8.7 Longshore Transport for Cases 1 and 2 . . . ... 113

8.8 Shoal Used for Case 3 .................... .... 114

8.9 Current Velocity Field for Case 3 . . . . . 114

8.10 Longshore Transport for Cases 1 and 3 . . . . 115

8.11 Shoal Used for Case 4 ............................ 117

8.12 Current Velocity Field for Case 4 . . . . ... 117

8.13 Longshore Transport for Cases 1 and 4 . . . ... 118

8.14 Net Transport for Case 1 .......................... 120

8.15 Net Transport Relative to Ambient Transport for Case 1 . . 121

8.16 Net Transport Relative to Ambient Transport for Case 4 . ... 122

8.17 Net Transport Relative to Ambient Transport for Case 5 . . 124

8.18 Net Transport Relative to Ambient Transport for Case 6 . . 125













LIST OF TABLES




7.1 Wave Heights and Angles for Ft. Pierce .................. 92














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 Science

PREDICTION OF SHORELINE CHANGES NEAR TIDAL INLETS

By

BARRY D. DOUGLAS

December 1989

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

It is well known that tidal inlets tend to cause accretion on updrift shorelines and

erosion on downdrift shorelines. This study documented the shoreline changes near several

tidal inlets along Florida's east and west coasts. An analytical and a numerical method

were used to attempt to predict the shoreline changes downdrift of these inlets.

The analytical method is based on Pelnard-Considere's solution for the combined con-

tinuity and transport equation. This solution used simple boundary conditions and a con-

stant breaking wave height and wave direction. It was found that this solution could predict

shoreline changes associated with rapidly eroding downdrift shorelines. If refraction over

offshore shoals of diffraction around jetties influenced the downdrift shorelines, this solution

could not predict accurately the shoreline changes.

An implicit numerical model was developed that used monthly wave heights and wave

directions to model transport reversals. The model also contained diffraction and refraction

routines. It was found that the best results were obtained for Ft. Pierce Inlet for an offshore

bathymetry which represented the pre- and post-inlet cutting contours. This model could

not predict accurately a sheltered zone adjacent to the south jetty due to a lack of wave

breaking on the offshore shoal.








A detailed qualitative analysis of the effects of refraction due to tidal currents on the

net longshore transport was also completed. It was found that the currents affect the net

longshore transport for a considerable distance updrift and downdrift of the inlet. The

currents tend to increase updrift accretion and decrease downdrift erosion.














CHAPTER 1
INTRODUCTION



1.1 Purpose of Study

The Florida coastline consists of long, narrow barrier islands separated by inlets, main-

tained by tidal flows. These inlets are openings which connect sheltered areas behind the

barrier islands to the open ocean. This thesis presents methods to predict shoreline changes

near tidal inlets, with emphasis placed on shorelines downdrift of the inlets. Tidal inlets

are dynamic features which in most cases affect adjacent shorelines. The inlet is dynamic

because of changing conditions of tidal flow, wave action, sediment transport, and human

modifications for navigation purposes. The inlet and associated processes interfere with

the natural movement of the longshore transport of sediment. The usual result, for jet-

tied inlets, is that the downdrift shorelines experience erosion and the updrift shorelines

experience accretion. This results in shorelines in the vicinity of inlets to be subject to con-

siderable change as compared to shorelines on the open coast away from the influences of

inlets. Reported rates of shoreline erosion near inlets indicate that they can be on the order

of one to two times higher than areas remote from inlets (Walton and Adams, 1976). This

study investigated methods to predict the erosion of the downdrift shorelines, and further

understand the natural processes affecting the inlet.

The first method used is an analytical solution developed by Pelnard-Considere. This

solution was adapted to fit the case of an inlet which would block a net longshore transport.

This solution uses a constant wave height and wave direction, and assumes simple boundary

conditions. The second method used is a numerical model with very specific boundary

conditions. This model incorporates refraction and diffraction. Monthly wave heights from

wave gages and wave directions from littoral drift roses are also used as inputs. Many inlets







2
are studied and comparisons are made for inlets with different coastal processes affecting

them.

1.2 Background

Along Florida's eastern coast there are 19 tidal inlets from St. Mary's Entrance at the

Florida-Georgia border to Government Cut at Miami beach. Along Florida's west coast

there are a total of 37 inlets from Pensacola Bay Entrance near the Alabama border to

Caxambas Pass at the south end of Marco Island. On the east coast the predominant drift

is to the south and generally decreases from north to south, along the west coast transport

varies in magnitude and direction.

At natural inlets shallow, wide offshore bars exist which act like sand bridges that allow

the sediment to flow across the inlet mouths. A quasi-equilibrium exists at these natural

inlets, between the updrift and downdrift shorelines. An inlet would stay open in a location

where the tidal flow was sufficient to maintain the opening against longshore transport

which acts to close the inlet (Bruun and Gerritsen, 1959). Natural inlets migrated and

posed serious navigation hazards, most 'of these inlets have been modified for navigation

or water quality purposes. These modifications include deepening of entrance channels,

construction of jetties, and dredging. All of these modifications are intended to maintain

a deepened fixed channel. While maintaining the inlet, these modifications interfered with

the quasi-equilibrium that existed at the natural inlet, resulting in changes to the adjacent

shorelines. The modified inlet interrupts the longshore transport and can act as a sediment

sink.

The maintenance of navigational channels will also affect the adjacent shorelines. Deep-

ened channels cut through the natural offshore bar which transferred sand across the inlet

mouth. The inlet system will attempt to refill the channel and return to its quasi-equilibrium

state. Sediment which is deposited in this deepened channel is removed from the longshore

transport system. This removed sand results in a deficit of sand from the adjacent shores;

erosion will have to occur to make up for this deficit. Often dredging is used to maintain







3
the channel, if the dredged material is not reintroduced to the system downdrift of the inlet,

erosion will also occur to account for the deficit of material.

Jetties also affect the inlet and adjacent shorelines. All the inlets on the east coast

except Nassau Sound and Matanzas Inlet have been jettied. Jetties generally cause an

impoundment of sand updrift of the structure and erosion downdrift. The jetties decrease

the amount of sediment entering the inlet and also move sediment offshore. The effect is the

same as mentioned above, a sediment deficit occurs which will result in downdrift erosion

to account for the missing volume of sand.

The above-mentioned modifications work together with other factors such as shoals and

transport reversals to make an inlet and adjacent shores a very complex physical system.














CHAPTER 2
APPROACH



2.1 Shoreline Change Data

The Division of Beaches and Shores of the Florida Department of Natural Resources

(DNR) maintains permanent monuments along counties with predominantly sandy shore-

lines. These monuments are spaced approximately every 1000 feet along the shoreline, a

total of 3,428 monuments have been established. As an example, figure 2.1 shows St. Lucie

County with the locations of the DNR monuments noted. Surveys using these monuments

were started in 1971 and continue up to the present. Historic shoreline maps and aerial

photos which pre-date 1971 have been digitized and combined to yield shoreline positions

referenced to the DNR monuments. The resulting data base available from DNR consists

of shoreline positions given in state plane coordinates which date back to before the turn

of the century and continue up to the present.

These DNR shoreline change data were compared to analytical and numerical results in

this study. Shoreline changes were calculated using the first post cut survey and the most

current pre-nourishment survey. Shoreline positions were referenced with the inlet center

as x = 0.0, y = 0.0. Shoreline positions from this reference were determined for each survey.

These positions were then interpolated to common evenly spaced intervals. The resulting

data were a set of shoreline changes at evenly spaced longshore increments with the origin

at the inlet.

2.2 One Line Theory

Both the analytical and numerical models presented in this paper are based on what is

known as one line theory. The beach profile is assumed to maintain its equilibrium form.



















- R-1


- R-10



-R-20


Figure 2.1: DNR Monuments Located in St. Lucie County







6
This implies that the profile is displaced horizontally without change of form. The entire

profile moves uniformly when responding to changes, therefore only "one line," usually taken

as the shoreline needs to be considered. One line theory attempts to describe long term

variations in shoreline positions.

One line theory can not predict accurately short term variations such as storm condi-

tions which are regarded as disturbances superimposed on the long-term general trend.

2.3 Pelnard-Considere Solution

The analytical solution used in this study is adapted from a solution to the combined

transport and continuity equation first developed by Pelnard-Considere (Pelnard-Considere,

1956). The Pelnard Considere formulation can be applied to the prediction of the accu-

mulation of sand updrift of a littoral barrier extending perpendicularly from an initially

straight and uniform shoreline. Waves of uniform height and direction arrive obliquely to

the shoreline and cause a transport of sediment. At the littoral barrier the transport equals

zero, trapping all sediment up to bypassing. This requires the local shoreline at the barrier

to be oriented parallel to the incoming wave crests. At large distances updrift and downdrift

of the barrier the shoreline is unaffected by the presence of the structure.

Figure 2.2 shows the resulting shoreline evolution of accumulation updrift and erosion

downdrift with increasing time. Note that the planforms on the two sides of the barrier are

antisymmetric, at all times the accreted volume of material updrift of the barrier equals the

eroded volume of material downdrift of the barrier. This is an indication that the Pelnard

Consider solution is an odd solution and has no even component.

This solution was used to predict shoreline positions downdrift of an inlet. It was

assumed that an inlet acts very similar to a littoral barrier by interrupting the longshore

transport. The boundary condition was interpreted to be that no transport would pass

through the inlet; this would be analogous to an infinitely long littoral barrier which never

achieves bypassing. Tihe same restriction, that at large distance away the shoreline would

be unaffected by the presence of the inlet remained, and the local shoreline at the inlet













































Increasing Time


Increasing Time


Figure 2.2: Shoreline Near Littoral Barrier








would be parallel to incoming wave crests. The positive accretional shoreline change values

for the littoral barrier are equal to the negative erosional values downdrift of an inlet.

2.4 Numerical Modeling

Shoreline evolution can be predicted by the use of a finite difference numerical model.

It is not possible to develop analytical solutions for the full equations of transport and

continuity. The analytical solution mentioned previously was also limited by very broad

or general boundary conditions. Physical parameters such as variable wave direction and

height, sediment loss to the inlet, and diffraction could not be accounted for with the

analytical solution. Also the solution was odd, resulting in the updrift and downdrift

shorelines being antisymmetric images of each other. The use of a finite difference technique

to approximate the governing equations allows arbitrary boundary conditions and inputs.

The simplest form of a shoreline evolution model is the explicit model, in which the

transport and continuity equations are solved sequentially. The region of interest is di-

vided up into an incremental longshore grid system (see fig. 2.3). Shoreline positions are

determined at the grid centers and the transport values are calculated for the grid lines.

Transport is calculated using two adjoining grid mid points to determine the local shoreline

orientations from the previous time step. The shoreline positions at the grid midpoints for

the present time step are calculated using these transport values with the continuity equa-

tion. Simply stated, if the transport leaving a grid is greater than the transport entering

the grid the shoreline position erodes, and if the transport leaving the grid is less than the

transport entering the grid the shoreline accretes.

Since the explicit model relies on information from the previous time step, it can be

susceptible to stability problems. If the time step is large a substantial shoreline change can

occur for a relatively small difference in transport values. This large change in shoreline

position will result in an offset from the adjacent grids. These offsets would tend to transport

sediment in the opposite direction during the next time step, thus leading to the possibility

of an oscillating unstability. With successive time steps the displacement would grow and
































Reference Baseline
for Shoreline


Figure 2.3: Numerical Model Grid System







10
alternate as accretion and erosion. This oscillation will tend to propagate throughout the

grid system and cause the entire region to become unstable. To prevent this instability

from occurring there are limits to the size of time step and the length of the incremental

grid spacing that can be used.

An implicit model does not have the stability problem of an explicit model and therefore

has no restrictions on grid spacing or time step used in the model. The major difference

between the implicit and explicit model is that the implicit model solves the transport

and continuity equations simultaneously instead of sequentially. The continuity equation is

expressed in terms of the average of the transport for the present time step and the next

time step. The transport equation is expressed in terms of the average shoreline positions

for the present and next time step. Both of these equations then can be represented as an

expression of known quantities at the present time step, equated to unknown quantities of

the next time step. The result is four unknowns and two equations. With the introduction

of two auxiliary equations and appropriate boundary conditions a double sweep algorithm

can be used to solve simultaneously the transport and continuity equations.

2.5 Refraction

Wave celerity is dependent upon the water depth in which the wave propagates. Wave

speed and wave length decrease as the depth decreases, while the wave period remains

constant. When a wave moves over varying bathymetry, the wave crests which pass over

the shallower depths will slow down. This decrease in wave speed will cause the waves to

bend, becoming more parallel to the bottom contours. This bending of waves is known as

refraction. The change in depth will also cause a change in wave height through the process

of wave shoaling. These changes result in a convergence or divergence of wave energy.

At inlets a common feature is an offshore shoal. Incoming waves, regardless of direction,

will refract around the shoal. The resulting longshore currents will be directed towards the

region centered behind the shoal, causing a accumulation of sediment in this region. If the

waves are sufficiently large relative to the water depth over the shoal, wave breaking will







11
occur resulting in a local sheltering of the shoreline. Wave interaction with currents can

also cause refraction to occur. If currents interact with waves, the refraction has similar

effects of altering wave height and direction.

2.6 Diffraction

Diffraction of water waves is an event in which energy is transferred laterally along a

wave crest. It is most common when a regular train of waves is interrupted by a barrier

such as a jetty or a breakwater. If transfer of energy did not occur, straight waves passing

the tip of the barrier would leave an unaffected calm region in the lee of the barrier. Past

the edge of the barrier the waves would travel unchanged, creating a line of discontinuity.

Diffraction will alter both the wave height and wave direction.

When waves approach a jetty at an angle, a shadow zone will be created in the lee of

the structure as shown in figure 2.4. This shadow zone will be an area of sheltering, with

decreased wave energy and altered wave direction and reduced longshore transport.

2.7 Shoaling Processes at a Tidal Inlet

The tidal flows which keep an inlet open are the ebb tide which directs tidal currents

seaward and the flood tide which directs tidal currents landward. The flood tide removes

material from the longshore drift and deposits it in the calm bay or lagoon behind the

inlet. The ebb tide pushes material back through the inlet, also removing sediment from

the longshore drift, and deposits it seaward of the inlet.

The ebb flow pushes sediment offshore, while wave attack tends to drive material back

towards the inlet. This material is usually deposited in a crescent or kidney shape planform.

The ebb currents have a central core with a high velocity, producing an ebb jet which

can carrying sediment a considerable distance offshore. Jetties and deepened channels

concentrate the ebb flow and move the ebb shoal even farther offshore (Marino and Mehta,

1989). The net longshore currents will move the sediment downdrift from the inlet. The

resulting feature is an offshore shoal which is offset offshore and downdrift from the inlet.














Wave Crests


Zone


Figure 2.4: Diffraction Patterns Behind a Jetty







13
The local longshore currents adjacent to the inlet are directed towards the inlet during

both flood tide and ebb tide (O'Brien, 1966). On the flood tide, sediment is moved towards

the inlet from all directions. On the ebb tide, the momentum of the strong ebb jet entrains

adjacent waters forming eddies. These eddies cause circulation cells which move sediment

towards the inlet, even though the ebb flow is directed away from the inlet. The currents

associated with the ebb and flood tide are shown in figures 2.5, 2.6. Refraction around this

outer bar will also move sediment towards the inlet from both sides. The ebb shoal alters

incoming waves and tidal currents in such a way to affect the transport systems near an

inlet. The presence of the ebb shoal is important in investigating the shoreline evolution

near inlets.

The shoaling that occurs at inlets is due to the forces of tidal currents and wave action.

After a period of time these forces become somewhat balanced and an equilibrium shoal

system will be formed. In an area of high wave energy the offshore shoal volume will be

relatively small, while in areas of small wave energy the shoal volumes will tend to be

larger (Dean and Walton, 1973). Marino and Mehta (1989) have estimated that 420 10 6

meters3 of material is stored in ebb shoals along Florida's east coast. The general trend

is for decreasing shoal size from the Georgia border south towards Government Cut. This

also corresponds to decreasing shelf width, decreasing wave energy and decreasing longshore

transport. These authors also reported that most of the volume is stored in shoals north of

St. Lucie Inlet.






14











, -

)



-






Figure 2.5: Flood Current at an Inlet








.






".


Figure 2.6: Ebb Current at an Inlet














CHAPTER 3
ANALYTICAL METHODOLOGY



3.1 Combined Continuity and Transport Equation

The analytical method used in this study is a solution to the combined continuity and

transport equations. As shown in figure 3.1 for an incremental length, Ax, of shoreline

the change in volume of sand can be expressed as the product of the change in transport

through the region, AQ, and time. This change in volume is


AV = (AQ)(At) (3.1)

This change in volume can also be expressed as a product of the length dimensions of the

region.

'AV = (Az)(Ay)(D) (3.2)

In this equation Ay is the change in shoreline position, and D is the vertical dimension of

the active profile.

These two expressions (eqns. 3.1 and 3.2) both represent the same change in volume

and when equated, the one-line continuity equation results (eqn. 3.3).

1 a9Q ay
S aQ_ a (3.3)
D ax at

The other equation needed to form the combined continuity, dynamic equation is the

equation for transport, a common expression for transport is equation 3.4.


Q = Qo sin (20) (3.4)

where
(KH (gT) (3.)
Qo = 1 (3.5)
16(s 1) (1 p)
















Qi ln


Qout


Figure 3.1: Control Volume Along the Shoreline


I
D








K =0.77, sediment transport factor

g =acceleration due to gravity
Hb =breaking wave height
K =0.78, the ratio of breaking wave height to breaking depth
s =2.65, specific gravity of sediment

p =0.35, porosity of the sediment
0 =angle between wave crests and the shoreline

The angle between the breaking wave crests and the shoreline can be expressed as the
difference between, f8 the shoreline orientation, and ab the breaking wave angle.


0 = P ,b (3.6)

The shoreline orientation, f can be expressed as the change in the local shoreline position,
as shown in figure 3.2.

= tan- (Z (3.7)

Substituting this into the transport equation (eqn. 3.5),

Q = Qo sin [2 (- tan-1 (ay) ab)] (3.8)

If the angles involved are small the inverse tangent term can be approximated by equa-

tion 3.9.
By
a= (3.9)

The continuity equation (eqn. 3.3) contains the derivative of transport with respect to the
longshore direction. This derivative can be expressed as the following:

S= Qo2 cos[2 (P ab)] (3.10)
ax

If the cosine term is assumed to be unity for small angles the derivative can be simplified.

)Q a2y
aQ =Q (2)(---) (3.11)
ax -ax2













0

CJ
o
I
*


N











Reference ,
Base Line


+Qs


Figure 3.2: Shoreline Orientation and Wave Angle






19
Substituting this derivative into the continuity equation (eqn. 3.3) results in the linearized

combined continuity and dynamic equation.

ay 2y
S=Ga (3.12

2Q. KH: g1
G- (3.13)
D 8(s- 1)(1- p)D
Equation 3.12 is the heat conduction equation for solids, also known as the diffusion

equation. G has the dimensions of length squared per unit time, and expresses the time

scale of shoreline change. In the english unit system G has the value of 0.0214(H/2)ft2/sec,

for a closure depth of 27 feet. This equation has many solutions depending on the boundary

and initial conditions used. The solution by Pelnard Considere, mentioned earlier, has the

following form and is valid up to the occurrence of bypassing around the structure.

tan 0[ -z2 e
y(x,t) 4Gtexp ( ) z erfc( V (3.14)

The last term contains erfc, which is the co-error function and is defined as the following.

erfc = 1 erf (3.15)

erf(z) = = exp (-u2)du (3.16)

The error function equals zero when the argument is zero, and approaches unity for large

arguments.

The boundary conditions are that at points far updrift and downdrift of the barrier the

shoreline remains unaffected, y = 0.0 at z = oo. The initial condition is that the shoreline

is straight and uniform. The shoreline at the barrier is parallel to incoming wave crests.

This condition can be seen by taking the derivative of equation 3.14 with respect to x.

The derivative of the error function with respect to its argument is the following.

derf(z) 2 dz
d ( )( ) exp (-z2) (3.17)
du exdu( ) )p G
The derivative -r y with respect to z is the following.

ay tan0 -2x -22 2-
ex =t Vexp ( ) f ) + texp (3.18)
az 4Gt 4 GLt 2G-t 4Gt







20
By substituting zero for x in equation 3.18 the derivative will equal the slope of the shoreline

at the barrier.

_y tan 1[0.0 +0.0) (3.19)

( )=o= -tan0 (3.20)
ax
Thus showing that the shoreline at the barrier is parallel to incoming wave crests.

3.2 Predicted Results

Equation 3.14 presented in the last section was used to predict shoreline changes which

were compared to measured DNR data for several inlets. The comparisons of predicted

results and measured data were made for shoreline change values; not actual shoreline

positions. This method was used because the analytical solution assumes a straight and

uniform initial shoreline and then determines shoreline change from this initially straight

shoreline. Thus only a change from the shoreline at the time of the cut could be computed.

The comparison procedure was to compute the shoreline changes between two post-cut

DNR surveys and to determine predicted shoreline changes using equation 3.14 for the

corresponding time spans. For example, St. Lucie Inlet was cut in 1892 and the surveys

used are for 1928 and 1970. The 42 year shoreline change measured, was determined as

the change in shoreline position from 1928 to 1970.

The predicted shoreline change, Ypredicted, was determined as the difference between the

shoreline computed for 1970 and the computed shoreline for 1928.


ALpredicted = y(x,78years) y(z,36year,) (3.21)

Where the zero reference time in the above equation is 1892. The form of the solution used

produces negative or erosional shoreline positions, therefore the change is represented by

its difference from 1970 to 1928.

The measured DNR data were in the form of nothing and eating positions for each

monument, an azimuth of the survey, and a nothing and eating position of the mean high

water line.







21
3.3 Least Squares Analysis

The last step needed to compare the measured data to the predicted results was to

determine the proper values of G and tan 0 to be used in the analytical solution. This

solution uses a constant G and 0 for a specified time value to predict the shoreline position.

The only unknowns in this equation are G and tan 0, and these unknowns are held constant.

G is a function of the wave height to the 5/2 power; small changes in the breaking wave

height cause large fluctuations of this constant. It was found that the solution was very

sensitive to changes in either G or 0. Figure 3.3 shows three predicted shoreline planforms

about a littoral barrier for a time span of ten years with no bypassing. The updrift shore

is represented by negative distances, and the downdrift shoreline is represented by positive

values. A shoreline was calculated for a constant G for a wave height of 1 foot and a 0 of

5 degrees, for the second case the 0 was held constant and the wave height increased to 2

feet. The last case examined used a G for a wave height of 1 foot and increased the breaker

angle 0 to 10 degrees. By increasing the variables, drastically different shorelines resulted.

Doubling the wave height increased the G constant by a factor of approximately 5.5, and

doubling the wave direction doubles the tan 0 constant. It can be seen that by doubling

either variable increased the shoreline change at the barrier by more than a factor of two.

Accurate values of G and tan 0 were needed to predict the shoreline change.

One G value and one 0 value had to be chosen to represent the entire shoreline region

for the entire time span studied for each inlet. It was decided that determining a net wave

height and direction for large time spans of up 50 years would be very inaccurate and a

better approach would be to determine best fit values of G and tan 0. A non-linear least

squares method was developed to determine a G, tan 0 pair that would yield the best fit

possible for the predicted results.

An iterative procedure was used that assumed the predicted shoreline position was the

position of the last iteiation plus an increment due to the tanO and another increment due



































z
0 80
0-4

0





-160
-LJ









-e80


-560
-560


-640


-10000 -7500 -5000 -2500 0 2500 5000 7500 10000

DISTANCE FROM BARRIER(FT) HB=IFT.THETA=5
.................. HB2FT.THETA f5
.. .HB-IFT.THETl-10



Figure 3.3: Comparison of Shorelines for Different G and tan 0 Values








to the G constant (eqn. 3.22).


Yk+ = Y + L G + ta (tan ) (3.22)
aG a tan 0

In equation 3.22 the superscript k denotes the iteration level. The least squares error then
becomes the following.

C2 = + [(y + AG + A tan 0 ym.e (3.23)

I denotes the total number of points and k represents the iteration, and the unknowns are
AG and Atan0.

An initial G and tan 0 value had to be assumed. Using these values, derivatives of y with
respect to G and tan 0 were calculated. These derivatives were then used to compute AG
and A tan 0. The next step was to calculate the new G and tan 0 to be used to determine

Predicted values. This was an iterative process and ceased when the least squares error from
two successive iterations differed by less than a specified value.
The least squares expression (eqn. ,3.23) was differentiated with respect to AG and
A tan 0, these derivatives were set equal to zero to determine minimum error values. The
derivative with respect to AG follows.
ae2 / ayp A { ayp yp (_ ayp ayp ayp
G + AG + A tan 0 ) )
aAG a aGGG aa n \tano8 aGa
(3.24)
This is minimized by setting the derivative equal to zero, resulting in an equation of two
unknowns; AG and A tan 0. The subscripts p and m denote predicted and measured shore-
line positions. Equation 3.24 can be rewritten with the known quantities set equal to the
unknowns.

AG y 2 + A tan 0 y- ) ay (3.25)
\ aG E a tan o ao / aG J

if this same procedure is applied for the derivative of the error with respect to A tan 0 a
second equation results which can be solved simultaneously with equation 3.25 to determine








AG and A tan O. This second equation is

AG () atan ata2 (= m Yp) (3.26)

As stated earlier, AG and A tan 0 are the only unknowns, yp is computed from the previous
step. Equations 3.25 and 3.26 are solved with G and tan 0 values from the previous

iteration. The measured shoreline change,ymeas,,ed, is known and the predicted values are

computed from the G and tan 0 from the previous step. The derivatives of predicted with
respect to G and tan 0 must be known to solve for AG and A tan 0; expressions for these

derivatives follow:
ayp, tan 0 1 -(3.2
= 4t / exp( (3.27)
ay aG V 2( 4Gt
[v,=Gtexp ( eerfc( x) (3.28)
8 tan 0 /4Gt N t
This process is repeated until the error converges to a minimum value. Figure 3.4 shows a
contour plot of error for different values of G and tanO, used to fit the analytical solution
to data for St. Lucie Inlet.

3.4 Even' and Odd Analysis

The shoreline changes about the inlet were analyzed to determine an odd and an even
component of the net change. An even signal is symmetric about its mid-point; at points
equidistant from the center the even component has the same magnitude and sign. An odd

signal is antisymmetric and at points equidistant from the origin the signal has the same

magnitude but opposite signs. As examples, the sine is an odd function and the cosine is an
even function. Figures 3.5 and 3.6 show other examples of purely odd and even functions.

Any function, f(t), regardless of its form can be written as the sum of odd and even
components. An even function is defined as any function which satisfies the following
condition

f(-t) = f(t) (3.29)
and a function is odd if


f(-t) = -f(t)


(3.30)













ERROR X 1000


0.05 0.10 0.15
G FT 2/SEC)


Figure 3.4: Contour Plot of Error for St. Lucie Inlet 1928 to 1970


0.30





0.25





0.20




I.--
UJ
S0.15
z
CC
I--




0.10





0.05


0.00
0.00


0.20















Figure 3.5: Even Function


Figure 3.6: Odd Function


j*







27
The net, f,(t), is the sum of the odd fo(t), and the even, fe(t).


fA(t) = f.(t) + fo(t) (3.31)

For a negative value of t, the net would equal


f,(-t) = f(-t) + fo(-t) (3.32)

Equation 3.32 can be rewritten as


f,(-t) = fe(t) f(t) (3.33)

Equations 3.31 and 3.33 are solved simultaneously with f,(t) and fo(t) as unknowns and

fn(t) and f,(-t) as known quantities. The solutions for the even and odd components in
terms of the net function are

f (t) + f(-t) (334)
2
f,(t) fn(-t) (335)
fo(t) W 2 (3.35)
2
The measured shoreline change was used as the net function, fn(t), and equations 3.34

and 3.35 were used to determine odd and even components of the net. The inlet midpoint

was used as the origin, with the downdrift shore as positive z and the updrift shore as

negative x. The least squares analysis discussed in the last section was performed on the

odd component to determine a best fit predicted odd component.

An example of an even component of shoreline change could be the background rate of

erosion. If the background rate of erosion is constant over a certain region, the shoreline

will be affected by the same change. Figure 3.7 shows the shoreline about a littoral barrier

predicted by the analytical solution with a background rate of erosion of two feet per year.

By adding in the background erosion the shoreline is no longer antisymmetric about the

barrier. The odd and even components of the net change have also been plotted The odd

component is the predicted shoreline without the background rate. The even component is

a straight line at minus 20 feet which represents the background erosion.




























































30 -7500 -5000 -2500 0 2500 5000 7500 10000

DISTANCE FROM BARRIER(FT) INITI-L SHORE
................. 0D0
.. EVEN


Figure 3.7: Predicted Solution with Background Rate of Erosion


300






200






I-- 100
U-

Z



0






- 100
C)




-200
v,


-300













CHAPTER 4
NUMERICAL METHODOLOGY


4.1 Explicit Model

Numerical procedures can be used to solve the continuity and transport equations.

Numerical methods have the advantage of being able to model specific physical processes

such as refraction or diffraction. Numerical models also have much greater flexibility with

boundary conditions and model inputs. Variable wave heights or irregular shorelines are

examples of this flexibility. The derivation of the equations for the numerical method will

follow.

Derived earlier was the continuity equation

oy 1Q (4.1)
at D ax

Using a grid system set up along the shoreline with y at the midpoints this equation can

be represented as the following:

Ayi 1 (Qi+1 Qi) (4.2)
At D Axi

The change in shoreline position, Ayj, then can be written as

(Qi+i Qi)(At) (4.3)
hy; = ((4.3)
(D Azx)

The transport is determined using the transport equation of the previous chapter, computing

the shoreline angle f referenced to north, from the shoreline position.


= tan 1 yi- (4.4)
2 Azi /

Qi = H/7 '2sin2 -tai n-i (4.5)
Q' 16(8- 1)(1 p) t Azji







30
The initial shoreline positions are input as the initial yi values. Then transport is

computed using appropriate wave heights and wave angles. These transport values are used

to compute the change in shoreline position, Ay, for the specified time step. This procedure

is repeated for the time interval desired. Boundary conditions are that the transport, at a

barrier such as an inlet, is either zero or some specified value. Another boundary condition

could be a specified shoreline change value at an outer grid point.

These two equations (eqns. 4.3, 4.5) are solved sequentially making this an explicit

model. Explicit models have an inherent stability limit, due to this sequential procedure.

The stability parameter is
G At 1
(A t < 1 (4.6)
(Az)2 2
If this relationship approaches one half, the shoreline position values start to oscillate. To

satisfy this stability condition grid spacing must be large or the time step must be made

small. A large grid spacing will not show detailed shoreline evolution, therefore to ensure

stability the explicit model must use a small time step. Small time steps have the obvious

disadvantage of taking considerably more computer time.

4.2 Implicit Model

The implicit solution used here is based after Perlin (1982), and solves for continuity

and transport simultaneously. The method consists of determining four equations to solve

for four unknowns; Ay'+1, Ay'1, Q~41, and Q!+1. The superscript n denotes time step.

Continuity is expressed in terms of the forward difference of the transport, averaged for the

present and the next time steps.

At 1 [ Q +1+ Q Q+ Q (4.7)
Ayn+l x 2 2 (4.7)
Azi D 2 2

This equation is then rewritten to equate unknown quantities at time step n + 1 to time

step n.


(2 + (1 1- ( tD) =+ [ Q ,)] (4.8)
k AxD) 1 '+- 22 AxD








This equation can be expressed as

AiQ",+ + BiAyj"+1 + CiQ+1= Di (4.9)

where
At
A 2 AD (4.10)

Bi = 1 (4.11)

C, = -A, (4.12)
At
S= 2 AxD (Q Q ) (4.13)

The transport is expressed as the sum of the transport for the previous time step plus

an increment due to time.

Q+l = Q ~ + At (4.14)

Expanding the partial derivative of Q with respect to time and neglecting higher order

terms, results in the following:

SAt = aQ At + 8aQ Ay+' At (4.15)
at ay, at ayi-i at

The transport can now be expressed as

Q+l = Q + an Ay+l + aQaI (4.16)
ayi ayi-1
where
aQi" K7 H 1 2 cos 2 [r/2 tan-1 ) a
= (4.17)
By [16(s- 1)(1 p)J Ax [1 + ( )2]

aQ = -- (4.18)
ayi-1 ayi
As with the continuity equation, the transport equation can be expressed in terms of coef-

ficients.

A:Ay?"+ + B'Q"1+ + CAyiJ-j1 = Df (4.19)

where
aQ,
A= (4.20)
ayi







32

B; = 1 (4.21)

C; = -A: (4.22)

Dj = Q"% (4.23)

There are now four unknowns and two equations. The solution procedure used is known

as a double sweep (Abbot,1971) and introduces two auxiliary equations. The two auxiliary

equations used were:

Ayn+1 = EiQ?+1 + Fi (4.24)

Qf+1 = Ei Ay'"+11 + FR* (4.25)

Solving these four equations (eqns. 4.9, 4.19, 4.24, 4.25) simultaneously yields the

following results for E, F, E*, and F*.
C-
E = ----- (4.26)
A. Ei*+ + B

F = Di AF+ (4.27)
AiEZ+1 + Bi

E-* C, (4.28)
Af Ei + B4
Df A*F-
F D = 1 (4.29)
S Af Ei + Bj;
During the first sweep, the coefficients E, F, E*, and F* are conditioned. Sweeping

from large values of i to smaller values, the coefficients are determined. These coefficients

are then used in the auxiliary equations 4.24 and 4.25 to solve for Ay and Q by sweeping

from small values of i to large values of i.

The grid system places, i = imax, at the inlet. This results in i = 1, being the farthest

grid point away from the inlet. Qimaz+l is the transport entering the grid closest to the

inlet, and assumed zero. This allows no transport across the inlet regardless of transport

direction. For the downdrift shore studied here, this boundary condition allows no southerly

transport across the inlet, and traps all northerly transport. Using this boundary condition,

Efmaz and Flmaz were determined from equation 4.25.

E*,,zAy? .1- + Flm, = Qn+, = 0.0 (4.30)








therefore

Ei*aZ = 0.0 (4.31)

Fmaz = 0.0 (4.32)

If E* and F* are known for grid i + 1, then E and F can be determined for grid i (see

eqns. 4.26 and 4.27). The transport boundary condition at imax has yielded E,,maz and

Fimaz, now Eimaz-1 and Fimaz- can be determined. This procedure continues to determine

the coefficients as i decreases. After the first sweep has been completed, the second boundary

condition allows the auxiliary equations to be solved. The second boundary condition

assumes that at grid i = 1 the shoreline is unaffected by the presence of the inlet, or Ayi

is equal to zero. By substituting this in equation 4.25, the transport can be calculated for

grid i = 2, then Ay2 can be determined using equation 4.24. This sweep is continued up

to imax, solving for all the transports and shoreline changes.


Qn+1 = F2 (4.33)


Ay?+ = E2 + F2 (4.34)

This implicit method does not have the stability problems of the explicit procedure

and allows for both large and small time steps and grid spacings. A continuity check was

introduced, to verify that the stored volume of sediment over the computational domain

as calculated from the change in shoreline positions equaled the accumulative difference in

transport at i = imax and i = 1.

4.3 Wave Refraction

As a wave approaches the shoreline, changes in depth cause the wave crests to bend.

The waves tend to become parallel with the bottom contours, and the changing depth also

will cause a change in wave height because of shoaling. These changes in wave direction

and wave height were incorporated into the mcel through a wave refraction routine.






34
The two governing equations for the refraction routine were irrotationality of wave

number (eqn. 4.35) and conservation of wave energy flux (eqn. 4.36).

Vx k=0 (4.35)

S[EC] = 0 (4.36)

Expansion of the governing equations results in the following two expression which were

solved by finite difference schemes.

a (k sin 0) (a cos) )
y 0 (4.37)
ax ay
a (EC, cos 0) a (EC, sin) = 0 (4.38)
ax ay
The development of the solution of the refracted wave angle for each grid point will follow,

the solution for the wave height is similar and only the final solution will be presented.

A grid system is developed for offshore bathymetry, the longshore direction is repre-

sented by the i axis and the offshore direction is represented by the j axis. The finite

difference form of the solution uses eight adjacent grid points to the point of interest,(i,j)

(see figure 4.1). Equation 4.37 can be rewritten as the following expression in finite differ-
ence form.

(k cos 0)d+l (k cos O)i 1 [(ksin) -ksin O)i.1, +
Ay 2 2 sinAx
(k sin O)i+l+ (ksin O)i + (439)


Solving for (k cos Oi,) results in

(kcos )i,, = (k cos 0),, -+ (2 ') ([(ksin)i+,, (ksin0),_ ,] +

[(k sin O),+1,y+1 (k sin 0)i-_i+]) (4.40)

A smoothing parameter,r, is now introduced. The (k cos 0) terms for i, i + 1, and i 1 for

the offshore grid one step seaward are smoothed to yield.


(kcos 0)i,i+ = r (k cos O),,i+l + r (k cos 0)i-,i+1 + (1 2r) (k cos O)i,i+l


(4.41)
























































Figure 4.1: Refraction Grid System






36
Substituting equation 4.41 in equation 4.40 results in the finite difference solution for
(kcos ).

(kcos ), = r [(kcos 0)+1+ + (k cos 0)-_1+1] +

(1 2r) [(k cos 0),,] -

I ( A ) ([(k sin 0)+i (k sin O)i-lj] +
[(ksin )+,j+l (k sin O)-,j+,]) (4.42)

The field is originally initialized using wave angles from Snell's law, which relates the
grid points with the wave angle at the most seaward grid. Then an iterative procedure was
used that swept from the outermost grid at j = jmax towards the most shoreward grid at
j = 1. This iterative procedure was repeated a number of times until the wave angle for
each grid point converged to a steady value.
Equation 4.38 was solved in similar fashion to determine the wave heights. From linear
wave theory; wave energy was expressed as the wave height squared. The wave height field
is initialized with values determined frorri conservation of wave energy flux with the wave
height at the most seaward grid offshore.



(H2C sin 0)i = T [(H'C, sin B)ii + (H2C sin ),j+] +

(1 2r) [(H2 min 0i +
1 ( y) (HCcosO) (H 2CcosO +
2 (2A) ([( [') +lj \ / i-ij]
[(H2Ci cos) (H2C cos0e) i-1]+ (4.43)

It was found that for large bathymetric changes or incoming waves that differed from
the shore normal by a large angle, the refraction routine would become unstable. The
steady values of wave height and wave direction would need to be approached at a gradually
increasing rate. To accomplish this, a damping factor was added to equations 4.42 and 4.43.
To simplify the presentation of this damping procedure equation 4.42 is expressed in terms






37
of coefficients B1, B2, B3, and B4. The damping factor, r, was determined as a function

of the hyperbolic tangent, tanh.


r = tanh (m 0.05) (4.44)

Where m is the step of the iteration loop which is run until all values of height or direction

converge to steady values.


B1 = r [(k cos 0)i++1+ + (kcos 0),_1,i+i] (4.45)

B2 = (1 2r) [(k cos ),,i+] (4.46)

B3 = Y [(ksin 0);+lj (ksinO)i-1j] (4.47)

B4 = -2 [(ksin )i+lJ+l (ksin 0)i-j+lj (4.48)

The solution then becomes


(k cos O),, = B1 + B2 + r [0.5 (B3 + B4)] (4.49)

4.4 Refraction Due to Currents

In the same manner as changes in depth refract waves, currents interacting with incom-

ing waves also will cause refraction to occur. This wave and current interaction will cause

wave crests to bend and wave height will also be altered. For example an ebb tidal jet will

oppose incoming wave crests, causing waves to steepen and bend towards the inlet. The

flood tide will generate a current which will reinforce the incoming wave crests, tending to

decrease wave heights and cause the waves to bend away from the inlet. The wave refraction

routine discussed in the previous section was modified to incorporate the effects of currents.

An intrinsic wave frequency (or) is used which is the frequency apparent to an observer

riding with the current.

a = w i. (4.50)


where w is the absolute frequency and u is the current vector.






38
Irrotionality of wave number and conservation of wave energy flux are still used as the

governing equations, but are expressed to take into account the current. The wave number

is now expressed in terms of the intrinsic frequency.


a2 = gk tanh (kh) (4.51)


Vx ,=0 (4.52)

g- 0[f + 6, 0 (4.53)

The group velocity, Cg, is now expressed in terms of the intrinsic frequency (Mei, 1983).

1 2 kh
C, = sinhkh (4.54)
2 k smh 2 kh

The solution of the wave angle remained the same, except the wave number was now solved

using equation 4.51. For the case of no current and only depth changes, the wave number

is a function of depth and period only. The wave number for each grid point is then a

constant and does not change. For the case of refraction due to currents, the wave number

is related to the intrinsic frequency. The intrinsic frequency is a function of depth, period,

and the current angle relative to the wave angle. When the refraction routine was modified

for currents, the wave number had to be recalculated inside the loop which ran until steady

values of wave direction were converged upon.

The wave heights were solved in a similar fashion as in the last section but with the

modified conservation of wave energy equation. The intrinsic frequency (eqn. 4.50) cam be

simplified to

a T = V2 + v2k cos (0, 0,) (4.55)

Where O0 is the angle between the current and the shoreline and 08, is the angle between the

wave crests and the shoreline. The current component in the alongshore direction is u and

v is the current component in the offshore direction. Coefficients T1 and T2 are introduced

to simplify the presentation of the solution for wave height. For the case of refraction due






39
to currents and varying depth, the conservation of wave energy flux was expressed as

a [ (u+c cos e,) a [ (v+C sin w)]
x + ay=0 (4.56)

TI = (u + C cos 0w) (4.57)

H2
T2 = (v + Cg sin 0,) (4.58)

The coefficients B1, B2, B3, and B4 are now expressed in terms of T1 and T2.

B1 = r [T2i-lj+1 + T2i+1,,+u] (4.59)

B2 = (1 2r) [T2i,j+] (4.60)

B3= 2 [Tli+lj T1i-1J (4.61)

B4 = 2 [Tli+lj+l Tli-lj+1 (4.62)

The solution for wave heights with shoaling due to varying depth and the presence of current

then became.

S(v + sin ) BI + B2 + r [0.5 (B3 + B4)] (4.63)

4.5 Wave Diffraction

When wave crests pass a barrier a lateral transfer of energy occurs. In this model a
diffraction routine was included to model the effects of wave diffraction due to the presence

of a jetty. A shadow zone would be created in the lee of the jetty which would have

lower wave energy than the shoreline farther away from the jetty. The diffraction routine

used in this study is based on a solution by Perlin (1978) which used the previous work

of Penny and Price (1952). The solution determines a diffraction coefficient KD, which

will alter the incoming wave heights in the shadow zone of a jetty. A definition sketch of

the variables involved is shown in figure 4.2. The angle 0o is the angle between incoming

waves and the jetty axis. The angle OD is the angle between the jetty and the location

where the diffraction coefficient will be calculated. The wave height at the tip of the jetty

is Ho. The other variable needed is r, which is the radial distance from the tip of the








































Shadow Zone


Figure 4.2: Definition Sketch for Wave Diffraction






41
jetty to the location where the diffraction coefficient will be calculated. The solution uses

a dimensionless parameter, p', which is the product of the radial distance and the wave

number. The quantity L to calculate this parameter is the wave length. The solution

also uses Fresnel integrals CF, and S, which were approximated by a numerical expansion

(Abramowitz and Stegun, 1965).

P= r (4.64)


Suml = cos [p'cos (OD 0o)] (1 + C + S) +

sin [p' cos (OD o0)] (S CF)] +

cos [p' cos (OD + 0o)] (1 + C + S)] +

sin [p'cos ( + o)] (S -CF) (4.65)


Sum2 = cos[p'cos (OD o)] (S C) -

sin [p' cos (OD Go)] (1 + CF + 5) +

cos [p' cos (0D + 0o)] (S CF) +

sin [p' cos (OD + Go)] (1 + CF + S) (4.66)

The diffraction coefficient is the modulus of Sumi and Sum2.


KD = (Suml)2 + (Sum2)2 (4.67)

The diffracted wave height is the product of the diffraction coefficient and the wave height

at the tip of the jetty.

H = KD Ho (4.68)

The wave direction is determined assuming a circular wave crest pattern along any radial.

The diffraction solution was modified to calculate a diffracted wave height which would

be the breaking wave height. For grid points within th,; shadow zone, diffractce wave heights

were computed for different offshore distances until the diffracted wave heights were equal







42
to the product of the depth and a constant, = 0.78.


Hb = nv (Depthb) (4.69)

A simple bisection procedure was introduced to ensure that the diffraction routine converged

to the offshore location where the diffracted wave height would be the breaking wave height.

The bisection routine used a lower bound and an upper bound, and would determine a wave

height at a location at half the distance between the bounds. For each iteration either the

upper or the lower bound would change until the breaking wave height is converged upon.

If the initial bounds represented locations shoreward and seaward of the breaking location,

the bisection routine would absolutely converge to the breaking location. The initial lower

bound was the shoreline with a depth of zero, and the initial upper bound was the outer edge

of the shadow zone at that alongshore grid point. If the computed diffracted wave height

was greater than the quantity, r- (Depthb), the present guess became the next lower bound.

If the computed wave height was less than the quantity, x (Depthb), the present guess

became the next upper bound. This procedure was repeated until the guesses converged

to the breaking height. A limitation to this method was that the combined processes of

refraction and diffraction could not be modelled. In nature the diffracted waves in the lee

of the structure would also be refracted due to changes in water depth, as the wave crests

approached the shoreline.














CHAPTER 5
WAVE CHARACTERISTICS



5.1 Introduction

The model requires as inputs an original shoreline and wave characteristics. The wave

characteristics needed are the breaking wave height and the breaking wave direction, these

are used to compute transport. The model uses a deep water wave height and deep water

wave direction and transforms these to shore over a specified offshore bathymetry. Diffrac-

tion around the jetty tip and refraction over an offshore ebb shoal will alter these deep

water wave characteristics. This chapter will discuss the wave heights and wave angles used

for the model and the effects of diffraction and refraction.

5.2 Wave Heights

The wave heights used in this study were obtained from the Coastal and Oceanographic

engineering Department's Coastal Data Network (CDN). The CDN consists of eight stations

that have been installed around the coast of Florida. These stations collect data at approx-

imately six hour intervals. The breaking wave heights used were obtained by an analysis

discussed in Phlegar (1989). This analysis assumed that the breaking wave heights can be

represented by a Rayleigh Probability Distribution. Using this distribution a breaking wave

height could be determined from a root mean square wave height from the CDN stations.

The resulting wave parameter was a H' for each month, using three years of data. This

is an appropriate wave parameter because the wave height used to compute transport is

raised to the 2.5 power.







44
5.3 Wave Direction

The wave directions used in this study were obtained from littoral drift roses (Walton,

1973). The drift roses use a large source of ship wave observations to compute littoral

drift along Florida's coast. The wave data were from the U.S. Naval Weather Command,

Summary of Synoptic Meteorological Observations (SSMO). These wave data were used to

produce plots of transport as a function of shoreline orientations (see figure 5.1). Knowing

the shoreline orientation, transport in directions to the right and left when looking offshore

could be obtained. Q+ is directed to the right when looking offshore, and Q- is directed to

the left. For a specified shoreline orientation, a net transport was calculated as


Q(net) = Q(+) Q(-) (5.1)

These values are estimates of transport and often do not agree with reported Corps of

Engineer transport values. It is also stated in Walton (1973) that transport values south of

Ft. Pierce may be in error due to wave sheltering by the Bahamian Bank, and the effects

of the Gulf Stream.

The main advantage of using the littoral drift roses (LDR) was that a net transport

could be obtained on a monthly basis for each site. Using these data and monthly wave

heights from the CDN data transport reversals could be modeled. The shore normal for

each site was determined, and a net drift for each month was obtained from the LDR. A

breaking wave angle was calculated using the LDR transport and the CDN wave height.

The transport equation developed earlier was


Q = K*H/ sin 2(f ab) (5.2)


K* = KVg (5.3)
16(s 1)(1 p)

Solving 5.2 for the breaking wave angle results in the following expression.


a = p sin 5K/2 (5.4)
KH (5.4)





























LEGEND
--- Negative Drift (to Left)
Positive Drift (to Right)


800 900


Figure 5.1: Example Littoral Drift Rose


100,


S140"



150"


160"


170


180"


800 600 400 200 0 200 400 600 800
Average Littoral Drift in Cubic Yards Per Day






46
These breaking angles were then brought out to deep water using Snell's Law (eqn. 5.5).

sin (8 Qb) sin ( ao)
= (5.5)
Cb Co
Co (5.6)
to = P sin- ( b)C (5.6)
Cb
The wave heights were also brought out to deep water. Conservation of wave energy

flux (Dean and Dalrymple, 1983) can be expressed as


[EC, cos (/ a)], = [EC, cos (/ a)]o (5.7)

E is the wave energy and is a function of the wave height squared. Cg is the wave group

velocity. The conservation of flux (eqn. 5.7) can be rewritten as:


H2C,, cos (38 cb) = H,2C, cos (/ co) (5.8)

Equation 5.8 is solved for Ho.

H2C cos (g-ctb) 1/2
Ho = cos a) (5.9)


Cb = Cb = (5.10)

C = C = T (5.11)

The variable h is the breaking depth, and T is the wave period.

Values are now known for the deep water wave height and deep water wave angle for

each month. These values were then used as inputs to a refraction routine which calculated

a breaking height and direction for each grid point.

5.4 Modified Wave Angles

A net transport value, Qm, was calculated for each site from the measured shoreline

change data, by considering the inlet jetty system to be a complete barrier. This measured

transport value was an average net transport value. The monthly LDR transport values

were averaged to determine a predicted average net transport value, Qp. In particular, the

predicted values did not agree with the measured values. It was also found that the deep






47
water wave angles determined from the LDR transport data could vary greatly from the

shore normal. The refraction routine used in the numerical model could operate only with

gradually changing bathymetry and wave characteristics. If the wave approach was too

large relative to the shore normal the refraction routine would become unstable and not

function properly.

The wave angles determined from the LDR transport were modified to yield the calcu-

lated transport and to represent a more natural wave climate with a wave approach that

approximated the shore normal. A procedure was developed that modified the mean break-

ing angle to generate the measured transport, and modified the deviation from the mean

to make angles closer to shore normal.

The following discussion will describe this modification procedure; all angles mentioned

refer to breaking angles. The breaking angles determined from the roses were assumed to

be a mean value plus a fluctuation from this mean.

Op; = p, + O' (5.12)

0' is the fluctuation for each month from the mean value. The objective was to determine

a new angle Omod, which consisted of a modified mean, mod which would generate the

calculated transport plus the fluctuation 0' determined form the LDR's multiplied by a

factor from zero to one.

,mod; = mod + K'(O) (5.13)

Ofi = O, (5.14)

The transport could now be expressed as

T Q = K*H sin 2 [ od + K'O) ]At (5.15)

where T is equal to one year and At is equal to one month. Equation 5.15 can also be

expressed as equation 5.16 when the sine term is expanded, and coefficients A and B are

introduced.
[TQ- cousin o (5.16)
L At = A cos 2,mod + B sin 2Lmod (5.16)






48
A = HSK'l sin 2 ( K') (5.17)

B = H g* cos 2 (p K'D ) (5.18)

This simplified form of the transport (eqn. 5.16) can also be expressed as


lA = C cos (2mod ) (5.19)

Solving for 0mod yields
1 TQ
mod = + COS-'1 (5.20)

Equation 5.19 can also be expressed as


At =C cos 2mod cos e + C sin 20imo sin e (5.21)

Equating equation 5.21 with equation 5.16, C and e can be expressed in terms of A and B

which are known quantities.

A = C cos E (5.22)

B = C cos e (5.23)

C = A2 + B2 (5.24)

e = tan- () (5.25)

The procedure was now to set Q in equation 5.20 equal to the measured transport Qm,

then specify a value of K'. A and B were determined using equations 5.17 5.18, once

these values were known a 0mod could be calculated. It should be noted that each value

of K' would result in a different Omod value. But every combination of K' and 0mod would

generate an average net transport equal to the calculated transport. If K' equals zero, the

breaking angle for each month would be the same, and if K' equals one then the fluctuation

value 0' would equal the deviation from the unmodified LDR angle values.

Figure 5.2 shows the modified monthly breaking angles for Ft. Pierce for K' values

of one, zero, and one half. Figure 5.3 shows the resulting transport generated by these

wave angles. It was found that even though it appears that different K' values change the















85.000


80.000


75.000



(r)
LJ
A-
LUJ
CD

6 70.000








65.000


\~~ /


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





V


I I I
1.0 2.0 3.0


I I


I I I I I
4.0 5.0 6.0 7.0 8.0

MONTH


I I I
9.0 10.0 11.0
_SHORE
................. K I.0

-.-.-. K-0.0
-----__.-O.O


Figure 5.2: Modified Monthly Breaking Wave Angles for Ft. Pierce


60.000


12.0
NORMAL


2













0.600




0.500




0.4100




0.300

OJ
Un

Cr) 0.200




C
U-




E:
-0.100


-0.200

Z 0.000
(:I
I--


-0.100




-0.200


-0.300


MONTH MEAN
................. 0 LOR
-._. .K-1.0
S---- .Kr0.5
.K-0.0



Figure 5.3: Modified Transport for Ft. Pierce







51
breaking angles and transport considerably the effect on the final predicted shorelines run

for several years was negligible. This was because regardless of the value of K, the net

transport generated would always equal the measured net transport.














CHAPTER 6
ANALYTICAL RESULTS



6.1 Introduction

This chapter will present the measured shoreline changes for several inlets on Florida's

East and West coasts. A wide range of physical processes are represented by these data. The

inlets studied differed in wave climate, transport, number of jetties present, and shoaling.

The comparison of these inlets results in a better understanding of the processes occurring

at tidal inlets. A brief history of each inlet and plots of the shoreline changes are included.

An attempt was made to show shoreline changes for updrift and downdrift shorelines, but

for some inlets complete data sets were not available. For inlets with complete data sets,

the shoreline change plots present the net change, and the even and odd components of the

net change. Unless otherwise stated negative distances from the inlet are to the north, and

positive distances are to the south. When applicable the analytical solution developed in

this study was fitted to the downdrift net shoreline change.

6.2 Sebastian Inlet

Sebastian Inlet is a man made inlet located at the Brevard and Indian River County

line on Florida's East Coast. The inlet is approximately 45 miles south of Cape Canaveral

and 23 miles north of Fort Pierce Inlet. Sebastian Inlet connects the Indian River lagoon to

the Atlantic Ocean. Several attempts were made to make a cut through the barrier island in

this area from 1886 to 1924, but these efforts failed to create a minimum flow cross section

required to maintain a stable inlet (Mehta, et al., 1976). In 1886, using shovels a cut known

as Gibson's Cut was started. This work stopped before the cut was complet--d. Tn 1895

a cut was completed, but was closed by a storm. The first attempt to make a cut with a







53
dredge was undertaken in 1918, a channel was completed and two jetties were constructed

out of local rock. Four hours after the cut was completed a northeaster closed the channel

(Mehta, et al., 1976). Construction was again started in 1924, this time as the work drew

near to completion a storm entered the area and opened the cut. The channel shoaled

quickly and a 1,500 feet bulkhead was constructed on the south channel bank in 1931, to

direct tidal flows to erode the inner channel shoals. Efforts to maintain the shoaling failed

and the cut closed in 1941-1942.

In 1948, the present inlet was dredged, this channel was orientated 43 degrees to the

south of the old 1924 channel, with the former shoals now forming islands along the new

northern bank. A new northern jetty was constructed in 1952, and this jetty received major

extensions in 1955 and 1970. A sand trap was dredged in the inner channel in 1962, this

trap was re-dredged and enlarged in 1972. During both of these sand trap dredgings, spoil

was placed on the downdrift beaches.

The inlet channel has various sizes of rocks in it, and Sabellariid worm reefs are also

present. This hard rock underlayer has created a throat cross section which is approximately

one half the size of the cross section associated with a similar inlet with a sandy bottom

(Mehta, et al., 1976). This smaller cross section has resulted in unusually high tidal currents

through the inlet, these currents probably have contributed to the very high shoaling rates

and the associated dredging. The almost constant dredging at this inlet indicates that large

amounts of material are passing into the inlet.

Figure 6.1 shows the shoreline changes for Sebastian Inlet from 1946 to 1970, these

data would indicate the shoreline changes associated with the present inlet location. The

net shoreline change shows the extensive downdrift erosion and the updrift accumulation of

sediment. It appears that Sebastian Inlet is affecting shorelines for approximately 5 miles

updrift and downdrift of the inlet. The most severe erosion has occurred 2 to 3 miles south

of the inlet. The downirift shorelines have ~. .ded an average of 72 feet for this time span;

or an erosion rate of approximately 3 feet per year. The updrift shorelines have accreted































































10000 -20000 -10000 0 10000 20000

DISTANCE FROM INLET (FT) NET
................. D
....-... EVEN


Figure 6.1: Shoreline Changes for Sebastian Inlet 1946 to 1970


200.0





150.0





100.0


50.0


z
Cc
U
Z



0.0
LJ

-IJ
U


r-1




-100.0


-150.0







55
an average of approximately 55 feet; resulting in an accretion rate of 2.3 feet per year. The

even component indicates a loss of sediment over this region for the time span considered.

Figure 6.2 shows the shoreline changes for Sebastian Inlet for 1928 to 1946, a time pe-

riod which includes the shoaling and closure of the 1924 cut. The 1928 shoreline would still

be experiencing the effects of the 1924 cut, and the 1946 shoreline would be experiencing

recovery from the inlet closure in 1941-1942. The shoreline change from 1928 to 1946 shows

accretion for 3 miles updrift and downdrift of the inlet. the average accretion was approx-

imately 52 feet. The even component of shoreline change is positive over the entire region

indicating a very large net gain of sediment over this region for the time span considered.

The odd component of shoreline change is difficult to interpret in that it does not have

any noticeable maximum or minimum values, but rather a general trend of decreasing in

magnitude from north to south. The lack of an offset between the updrift and downdrift

shorelines is most likely the cause of the behavior of the odd component. The odd com-

ponent indicates that the updrift shorelines are gaining more sediment then the downdrift

shorelines, but there is no discontinuity at the inlet.

6.3 Fort Pierce Inlet

Ft. Pierce Inlet is located in St. Lucie County, and connects the Indian river to

the Atlantic Ocean. Ft. Pierce Inlet is located between Sebastian and St. Lucie Inlets,

Hutchinson Island is directly to the south of the inlet. Prior to the cutting of this inlet,

Indian River Inlet existed 2.7 miles to the north of the present location of Ft. Pierce Inlet.

This inlet shoaled and eventually closed in the early 1900's, most likely due to the opening

of St. Lucie Inlet in 1892 which took much of the tidal flow from Indian River to the ocean

(Walton, 1974). Ft. Pierce Inlet was cut in 1920, the original cut was 350 feet wide and

the design depth was 25 feet. The original construction also included a pair of 400 feet

long jetties, these jetties were too short and were lengthened in 1926. The north jetty was

lengthened to 1800 feet an, the south jetty was lengthened to 1200 feet. Rapid shoaling

occurred in the inlet channel after construction and the channel was dredged often.































































5000 -12000 -8000 -4000 0 4000 8000 12000

DISTANCE FROM INLET (FT) NET
................. ODD
.. EVEN



Figure 6.2: Shoreline Changes for Sebastian Inlet 1928 to 1946


150.0




125.0




100.0




75.0
t-


j 50.0
LL-



Z
I:
r--
0 25.0
LUJ
Z

_J
LL 0.0
CE



-25.0




-50.0


-75.0







57
Ft. Pierce Inlet is affected by an offshore reef and porous jetties. A reef is located

approximately 1250 feet offshore in 10 to 14 feet of water. This reef forms an almost

horizontal platform. Both the north and south jetties are permeable and allow sediment to

pass through and over them into the inlet. A study of this inlet by the Coastal Engineering

Laboratory at the University of Florida in 1957 presented evidence of these jetties acting

to drain sediment into the inlet. Profiles near the jetties were found to have a gentler slope

compared to profiles farther away form the inlet, and the shoreline for 1500 feet north of

the inlet was very stable. It was determined that sand would accumulate at the north jetty

and also flow through the jetty to the inlet, causing the inlet to act as a drain. Sediment

was found to also pass through the southern jetty, but at a lesser rate than the north jetty.

This same study also hypothesized that a natural sand bypassing system existed at the

inlet. The ebb tidal currents would bring sediment out of the channel and deposit a large

portion of this material on the offshore reef, this material would then migrate along the reef

by longshore transport. Wave action on the reef would push some of this sediment back

towards the shoreline near the south jetty. If the jetty had been longer this material most

likely would have been transported offshore and lost to the longshore transport system.

Figure 6.3 shows the measured shoreline change for Ft. Pierce Inlet from 1883 to 1928,

this time period includes pre-cut up to 8 years after the initial cut. Shoreline recovery from

the closing of Indian River Inlet can be seen at 8000 to 16,000 feet to the north of the inlet.

Updrift accretion and downdrift erosion at the inlet can also be seen. Additionally evident

is that the shorelines to the south of the location of the cut were generally accreting during

this time period. The even component shows a net increase of sediment over this region

during this time span.

Figure 6.4 shows the measured shoreline changes for Ft. Pierce Inlet from 1928 to

1967, this time span is post-cut and includes no beach nourishments. The effects of the

inlet .,re clearly present in this figure, the downdrift shorelines are experiencing erosion for

approximately 6 miles and the updrift shoreline is accreting sediment north of the inlet. The




























































2000 -24000 -16000 -8000 0 8000 16000 24000

DISTANCE FROM INLET (FTI NET
................. ODD
...... EVEN


Figure 6.3: Shoreline Changes for Ft. Pierce Inlet 1883 to 1928


600.0






450.0


300.0


Li
Z



z

-J
CC




r
U














-150.0
-150.0


-300.0















400.0





300.0





200.0

I-
LL


U 100.0





0.0
z





(_)
'-1
-J
OC
0 -100.0





-200.0





-300.0


-400.O


-32000 -24000 -16000 -e000 0 8000 16000 24000

DISTANCE FROM INLET (FT) NET
..............0... 00
-....... EVEN



Figure 6.4: Shoreline Changes for Ft. Pierce Inlet 1928 to 1967







60
maximum erosion was located approximately 1.5 miles downdrift. For a time span from 1928

to 1945 this maximum erosion was one mile downdrift, showing that this point is migrating

to the south with time. The effects of the inlet can also be seen by noticing that the odd

component of shoreline change is almost identical to the net change for approximately 3

miles north and south of the inlet. The even component of shoreline change indicates a net

loss of sediment over this region during this time span, it has been reported that 80,000

cubic yards of sediment per year are lost to the inlet (Coastal Engineering Laboratory Staff,

1957).

The analytical solution was fitted to the net shoreline change for 1928 to 1967, these

results are shown in figure 6.5. In both of these figures a sheltered zone next to the inlet

is present, a more thorough discussion of this zone is presented in the numerical results

chapter of this report. Two predicted shoreline changes are presented in figure 6.5, one uses

the entire data set, and the other only uses the portion of the data south of the sheltered

zone. For the net shoreline changes the analytical solution yielded a wave height of 2.29

feet and a breaker angle of 1.62 degrees, for the odd shoreline changes the solution yielded

a breaking wave height of 1.72 feet and a breaker angle of 2.41 degrees. The CDN data for

Ft. Pierce indicate an average yearly (H ) of 2.26 feet.

6.4 St. Lucie Inlet

St. Lucie Inlet is an opening from the Indian and St. Lucie Rivers to the Atlantic

Ocean. The inlet is located between Hutchinson Island to the north and Jupiter Island to

the south. The inlet was opened by local interests in 1892, the original inlet dimensions

were a width of 30 feet and a depth of 5 feet. The inlet widened quickly and by 1898 the

dimensions of the cut were 1700 feet by 7 feet. In 1926 to 1929 a 3,325 feet long jetty

was constructed on the north side of the inlet. After the initial cut and up to the time

of construction of this jetty the northern shoreline retreated. After jetty construction the

updrift ..horelin- stabilized anu accretion began to take place. The southern shoreline has

experienced continual erosion since the cutting of the inlet. Before jetty construction there
















0.0





-50.0





-100.0
Ii-

LLU

Z

L:)
CE -150.0


UJ
Z

S-200.0
LLj
c-:


"U-)

-250.0





-300.0


-350.0


0 4000 oo00 12000 16000 20000 24000 28000 32000

DISTANCE FROM INLET (FT) NET.
................. G-0.2118. TAN0.0221
G-0.1705. TRN0.0282


Figure 6.5: Predicted Net Shoreline Change for Ft. Pierce Inlet 1928 to 1967







62

was transport across an offshore bar but this transfer of sediment was irregular (U.S.

Army Corps of Engineers, 1971). The shoreline south of the inlet along Jupiter Island has

experienced one of the most severe erosion problems in the state, with erosion rates of up

to 40 feet per year (U.S. Army Corps of Engineers, 1968). The measured shoreline change

data indicate an average erosion rate of 14 feet per year for a time period from 1928 to 1970

for 1.5 miles south of the inlet to 6.5 miles south of the inlet.

Figure 6.6 shows the net shoreline change from 1883 to 1948, and figure 6.7 shows

the net shoreline change from 1948 to 1970. The odd and even components of the net

change are also presented in these figures. The net change from 1883 to 1948 shows the

massive erosive power associated with the cutting of this inlet. The updrift region shows

signs of accretion after the jetty construction in 1928, by 1948 this shoreline has almost

returned to the 1883 position. Unfortunately the 1928 survey does not include any data

north of the inlet. The accretion north of the inlet is more clearly seen in the data from

1948 to 1970. The maximum erosion is located 8,000 to 16,000 feet south of the inlet. This

maximum erosion region is spread over ,a region approximately one mile long. This one

mile region has a erosion rate of 27 feet per year. For both time spans the even component

denotes a loss of sand over the region considered, this loss could either be to the inlet

or offshore shoals. At the inlet the even component changes sign, in figure 6.6 the even

component is negative,in figure 6.7 the even component has become positive. The negative

even component is associated with the widening of the channel and the westward migration

of the northern end of Jupiter Island. By 1948 the inlet region has started to stabilize its

orientation and the positive even component is indicating some build up of material in this

region. It should also be noted that the odd component in figure 6.6 is almost identical to

the shoreline change signature of the analytical solution.

Figure 6.8 shows the predicted shoreline change and the measured data for surveys of

1928 a" 1970. This time period encompasses the jetty construction up to the first major

beach nourishment project. There were no survey data directly south of the inlet, causing















1250


1000


750 -


500


250


I-0 _________________-------....A --
0-


S-250 -


L :-
z
C -500


-750 -
z

U_-i ooo

C -1250


-1500


-1750


-2000


-2250


-2500 -
-40000 -30000 -20000 -10000 0 10000 20000 30000

DISTANCE FROM INLET (FT) NET
................. OD 0
EVEN


Figure 6.6: Shoreline Change for St. Lucie Inlet 1883 to 1948







64






500







250




U-

-250 .' |







-50







-2500







-40000 -30000 -20000 -10000 0 10000 20000 30000
DISTANCE FROM INLET (FT) NET
.................... 00D
.. ". 7 EVEN

Figure 6.7: Shoreline Change for St. Lucie Inlet 1948 to 1970
z A
\ /


"F INLET : /-

























Figure 6.7: Shoreline Change for St. Lucie Inlet 1948 to 1970
















0






-200











U
6-- --o







z
-4



LLJ
Cc
E -800






-1000






-1200
0


V
'/











/'


I I I I I I I 1
5000 10000 15000 20000 25000 30000 35000 40000

DISTANCE FROM INLET (FT) MEASURED NET
................. ANRLTT TCRL


Figure 6.8: Predicted Shoreline Change for St. Lucie Inlet 1928 to 1970







66

a gap of approximately a mile and a half to occur. The maximum erosion was at the first

survey data point south of the inlet, and the erosion decreased as distance from the inlet

increased. The analytical solution yields an average breaking wave height of 1.95 feet and

a breaker angle of 10 degrees. These wave parameters would produce a longshore transport

of approximately 617,000 cubic yards per year, a reported gross transport rate for St. Lucie

is 523,000 cubic yards per year (Walton, 1973). The measured data show a loss of sediment
---572"0-
of 512,000 cubic yards per year. The CDN wave data indicate a (H ) wave height of

2.18 feet.

Figure 6.9 shows the predicted shoreline and measured data for 1948 to 1970. Two

predicted shoreline change results are shown, one using all the data and one excluding the

sheltered zone immediately south of the inlet. Excluding the sheltered zone, the analytical

solution yields an average breaking wave height of 1.73 feet and a breaker angle of 16

degrees. The transport produced by these values is 711,000 cubic yards per year. This was

a complete data set and extended up to the inlet.

6.5 South Lake Worth Inlet

South Lake Worth Inlet is located in Palm Beach County on Florida's east coast. Lake

Worth Inlet is to the north and Boca Raton Inlet is to the south. Lake Worth Inlet was

cut in 1918 to form a connection from Lake Worth, a salt-water sound, to the Atlantic

Ocean. The southern end of Lake Worth was becoming stagnant, and South Lake Worth

Inlet was cut in 1927 to increase flushing. South Lake Worth Inlet has also been referred to

as Boynton Inlet. A pair of 300 feet long jetties was also constructed at this time. Sediment

quickly built up next to the northern jetty, and shoals formed in the inlet. This shoaling

threatened to close the inlet, and a sand transfer plant was constructed on the north jetty in

1937. This sand transfer plant has operated continually except from 1942 to 1945 because

of fuel shortages during World War II. The sand transfer plant is estimated to transfer

approximately 7b ..-ubic yards per hour (U.S. Army Coips of Engineers, 1953), it has also

been estimated that prior to 1958 one million cubic yards of material had been transferred
















0








-150 y


-300






uJ
z
Z
CE





S-450
0

CD




-600 -


I I I I
5000 10000 15000 20000

DISTANCE FROM INLET


I
25000

(FT)


I I I
30000 35000 40000
H MEASURED NET
................. GO .1296.TAN=0.1764
-.-.-.-. G=0.0851. TAN0.2878


Figure 6.9: Predicted Shoreline Change for St. Lucie Inlet 1948 to 1970


-750







68
(U.S. Army Corps of Engineers, 1971). The transfer plant consists of a suction line on a

swinging boom and is operated for two to three hours a day. The sand transfer plant was

relocated in 1967, when jetty additions were made. Shorelines on both sides of the inlet

have been heavily armored with groins and seawalls.

Figure 6.10 shows the shoreline changes for South Lake Worth Inlet from 1883 to

1927. The shoreline near the inlet has accreted a considerable distance, with adjacent

shorelines generally eroding at differing rates. Notice that the shorelines south of the inlet

have built out more than the shorelines to the north of the inlet. The odd component of

shoreline change has a very unusual feature; the odd component directly south of the inlet

is much greater than the odd component directly north of the inlet. The usual odd shoreline

component has a maximum value updrift of an inlet and a minimum value downdrift of an

inlet. The odd component indicates that adjacent to the present location of the inlet the

shoreline to south was accreting and the shoreline to the north was eroding sediment from

1883 to 1927.

Figure 6.11 shows the shoreline changes for South Lake Worth Inlet for 1927 to 1942.

The effects of the inlet cutting can be seen as updrift accretion and downdrift erosion.

For 1883 to 1927 the updrift shoreline was experiencing more erosion than the downdrift

shorelines, from 1927 to 1942 almost the entire updrift shoreline is accreting. The decreased

erosion located approximately 10,000 feet south of the inlet, coincides with the location of a

groin field which fronts a seawall that was constructed during this time. The effects of the

sand transfer plant are not easily seen from these data. The odd component now exhibits

the usual pattern of a maximum value updrift of the inlet, and a minimum downdrift of the

inlet. It should also be noted that the odd component of shoreline change almost exactly

matches the net shoreline change for 10,000 feet north and south of the inlet. This matching

of the net change and the odd change is an indication of the overwhelming influence the

;'let cutting has had on the longshort transport in this r,.:n. The accretion starting

approximately 20,000 feet south of the inlet may be due to influences of Boca Raton Inlet.















250.0




200.0




150.0


i--
LL
S100.0


(3
50.0
U


z
0.0




(n -50.0 -




-100.0 v




-150.0 -




-200.0
-q0000 -30000 -2

DISTANCE


300 -10000 0 10000 20000 30000

FROM INLET (FT) NET
................ ODD
.. .EVEN


Figure 6.10: Shoreline Changes for South Lake Worth Inlet 1883 to 1927
















200.0





150.0





100.0

I-
LL


UI 50.0
C.J
Z



0.0
z




I-
CLU-
0 -50.0




-100.0





-150.0


-200.0


-40000 -30000 -20000 -10000 0 10000 20000 30000 4001

DISTANCE FROM INLET (FT) NET
................. 000
.. EVEN


Figure 6.11: Shoreline Changes for South Lake Worth Inlet 1927 to 1942








The effects of the sand transfer plant can be seen in figure 6.12, which shows the shore-

line changes for South Lake Worth Inlet from 1942 to 1970. Shorelines for approximately

15,000 feet north and south of the inlet are accreting during this time span. The even

component of shoreline change indicates a net gain of sediment for this region of plus or

minus 15,000 feet. For the entire region the even component of shoreline change indicates

a net loss of sediment for the time span considered.The maximum erosion has moved to

approximately 20,000 feet south of the inlet. The region from 10,000 feet to 20,000 feet

north of the inlet is also experiencing erosion.

6.6 Boca Raton Inlet

Boca Raton Inlet is at the southern end of Palm Beach County near the boundary

with Broward County on Florida's east coast. South Lake worth Inlet is to the north and

Hillsboro Inlet is to the south. Before the original cut was made in 1925, an occasional outlet

from Lake Boca Raton would open during heavy rainy seasons (Fluet, 1973). This opening

would then soon close because of wave action and shoaling. In 1925 a private corporation

purchased the rights to the waterway in the vicinity of this opening and improved the inlet

by dredging. This improved cut experienced shoaling and jetties were constructed in 1930 to

1931, after this construction an ebb shoal soon formed (Strock, 1979). This inlet frequently

closed due to shoaling, and in 1957 improvements by dredging were carried out again. Once

again the inlet was plagued by a severe shoaling problem. Boca Raton Inlet also had the

unique problem of whom had legal responsibility to maintain the inlet and jetties. These

legal problems often hindered efficient inlet maintenance. In 1972 the privately owned jetties

and the inlet waterway were deeded to the City of Boca Raton.

Because of the frequent dredging needed to maintain the inlet, the northern jetty was

extended in 1975. This extension was successful in maintaining a navigable waterway,

but caused severe erosion to the south of the inlet. Since 1972, the City of Boca Raton

has maintained a dedicated dredge at the inlet, and spoil has been placed on the downdrift

shorelines. To help alleviate the erosion problems at the inlet a weir section was constructed

















150.0





100.0





S50.0
U-



z
cI 0.0




C-5
LU





-100.0





-150.0
-150.0


-200.0


-40000 -30000 -20000 -10000 0 10000 20000 30000 4

DISTANCE FROM INLET (FT) NET
................. ODD
.EVEN


Figure 6.12: Shoreline Changes for South Lake Worth Inlet 1942 to 1970







73
in the north jetty in 1980. Sediment bypassing took place by dredging this sand trap at the

weir and placing the material south of the inlet.

Figure 6.13 shows the measured shoreline changes for Boca Raton Inlet for 1927 to

1970. These surveys span a time period from shortly after the initial cut and up to just

prior to the northern jetty extension. The shoreline changes are then representative of

the shoreline history of Boca Raton Inlet up to the 1975 jetty extension, and will include

effects of several openings, closings, and almost continuous series of channel dredgings. The

downdrift shorelines experienced erosion with a maximum retreat at approximately 12,000

feet south of the inlet. A groin field is located half a mile south of the inlet, and may be

the cause of the region of decreased erosion rate located about a mile south of the inlet.

The effects of bypassing can be seen as accretion just south of the inlet. The entire updrift

shoreline experienced accretion during this time span. The even component of shoreline

change indicates a net gain of sediment over this region for the time period considered.

A beach nourishment project was completed in 1980, in response to erosion due to the

northern jetty extension. The project length was approximately one mile, and approxi-

mately 44,000 cubic yards of material was placed over this project length (Stauble, 1986).

Figure 6.14 shows the downdrift shoreline changes for Boca Raton Inlet for 1974 to 1985.

The fill can be seen as the bulge in the shoreline changes centered at 10,000 feet south of the

inlet. The shorelines south of this fill are experiencing an increased erosion rate compared

to the 1927 to 1970 shoreline changes. The analytical solution was fitted for this erosion

region. The solution yielded a wave height of 1.27 feet and a breaker angle of 1.1 degrees.

6.7 Baker's Haulover Inlet

Baker's Haulover is located in Dade county and connects the Atlantic Ocean to the

northern end of Biscayne Bay. The inlet is nine miles north of Government Cut, and 14 miles

south of Port Everglades Harbor. The original cut was made in 1925 to rid the northern end

of Biscayne Bay Irom accumulating pollution. Due to the increased development of south

Florida this inlet has become increasingly important for navigation purposes. In September































































10000 -20000 -10000 0 10000 20000 3

DISTANCE FROM INLET (FT) NET
................. ODD
.... EVEN


Figure 6.13: Shoreline Changes for Boca Raton Inlet 1927 to 1970


200.0






150.0


100.0


W

Z
cc
a:


50.0
z

LJ
IL
"c
r
U) 0.0






-50.0


-100.0

































































)00 oo10000 15000 200 25000 30000

DISTANCE FROM INLET (FT) -MERSURED NET
................. ANALYTICAL




Figure 6.14: Shoreline Changes for Boca Raton Inlet 1974 to 1985


20.0



10.0



0.0



-10.0



-20.0



-30.0



-40.0



-50.0



-60.0



-70.0



-80.0



-90.0


~







76
1926 a severe hurricane passed over this area destroying all of the construction associated

with the inlet and causing massive erosion throughout the region. The hurricane had winds

up to 120 m.p.h and gusts up to 130 m.p.h, and a storm surge of 10.6 feet above mean sea

level (U.S.Army Corps of Engineers, 1946). By 1928 the inlet was repaired and two short

steel cellar jetties were installed, the inlet width was 300 feet. Steel sheet-pile bulkheads

were also constructed parallel to the shorelines for approximately 700 feet north and south

of the inlet.

This inlet has experienced a varying shoreline history of erosion and accretion. Because

of the influence of several inlets to the north the quantity of sand reaching this area is

far below the transport capacity of incoming waves. Estimates of net longshore southerly

transport are 50,000 cubic yard per year at the north county line and 20,000 cubic yards per

year at Government Cut (Coastal and Oceanographic Engineering Department, 1958). The

Little Bahama and Great Bahama Banks lay approximately 60 miles due east of the coast of

Florida from this shoreline. These banks shelter the coast from waves and also prevent some

long period swell that would arrive from the north east from affecting the area. These north

east waves are generally associated with winter storms and tend to transport sediment back

on shore (Coastal and Oceanographic Engineering Department, 1969). Another important

fact for this region is that for 4,500 feet south of the inlet an almost continuous line of

seawalls has been built by property owners. These structures were usually exposed to wave

action at high tide (Coastal and Oceanographic Department, 1958).

Unlike most inlets studied in this investigation, both the north and south shorelines

have experienced erosion. The jetties are very permeable and sediment leaks through them

and bypasses around both the south and north jetties. This region also has a hard rock

layer underlying the surface. This rock has prevented the inlet from scouring to a depth of

natural stability of a similar sandy inlet. This has caused high tidal currents to occur, the

flood tide draws sediment into the inlet causing large shoals. The Corps of Engineers reports

that 17,000 cubic yards of sediment were dredged from the inlet channel yearly (U.S. Army








77
Corps of Engineers, 1946), before the south jetty was extended. The ebb tidal currents are

strong enough to move most suspended sediment offshore. These tidal currents are also

large because of the relatively small size of the inlet compared to the size of Biscayne Bay.

The results are that both the north and south shorelines have experienced erosion due to

the inlet being both a barrier and a drain for sediment.

From 1851 to 1919 the shorelines for the region were accreting throughout the county,

the area where the inlet would be cut experienced some erosion (figure 6.15). From 1919

to 1927 the shorelines eroded due to the September 1926 hurricane. The shoreline change

from 1919 to 1945 is shown in figure 6.16. It can be seen that no dominant trend is present,

this is most likely due to the heavy armoring of the shorelines during this time period. The

next period for which survey data were available was 1945 to 1962, this time span includes

beach nourishments placed north and south of the inlet in 1960. The shoreline changes for

1945 to 1962 are presented in figure 6.17. A laboratory study in 1958 states that very little

shoreline change occurred between 1943 and 1957 (Coastal and Oceanographic Department,

1958). The shoreline advance from the nourishment projects can be seen, but it also evident

that the nourishment is spreading and erosion is starting to occur at the inlet.

A period of high erosion was found to occur from 1935 to 1945, for the region south

of the seawalls for approximately 5 miles (figure 6.18). The analytical solution agreed well

with the measured data for this time span, the solution yielded a breaking wave height of

2.22 feet and a breaker angle of 4.75 degrees.

6.8 Venice Inlet

Venice Inlet is located on Florida's West coast in Sarasota County, and separates Casey

Key from Manosota Key. Venice Inlet connects Little Sarasota Bay and Roberts Bay with

the Gulf of Mexico. This inlet has also been referred to as Casey Pass.

Venice Inlet is a natural inlet which migrated before a nine feet deep channel was

dredged in 1937 to 1938. Accompanying the channel dredging was the construction of a

pair of sheet-pile jetties. Because of severe erosion associated with the jetty construction,

















600.0





500.0





400.0

I-
l-


LJ 300.0

Z
(-


S200.0


-1
LU
0 100.0
I
U-



0.0





-100.0


-200.0


10000 20000 30000 40000

DISTANCE FROM INLET (FT) -MEASURED NET


Figure 6.15: Shoreline Change for Baker's Haulover 1851 to 1919


I

































































15000 -10000 -5000 0 5 10000ooo

DISTANCE FROM INLET (FT] NET
................. ODD0
-.--... EVEN



Figure 6.16: Shoreline Change for Baker's Haulover 1919 to 1945


50.0








25.0



I-
LL-

LU
" 0.0
Cc

U


LJ

LiJ
S-25.0





-50.0


-50.0


-75.0


















150.0




125.0




100.0


I-
U-
- 75.0

LJ
03
Z
(cc
r 50.0


LLJ
z
Z
S25.0
Ui
Cc
n-


(n 0.0




-25.0




-50.0


-75.0


-25000-20000-15000-10000-5000 0 5000 10000 15000 ZUUUU

DISTANCE FROM INLET (FT) NET
................. 000
-- EVEN


Figure 6.17: Shoreline Changes for Baker's Haulover 1945 to 1962









81







0.0



-25.0



-50.0 -




- -75.0
LLi




CI
U
-200.0 -


(-)
U -125.0








-175.0 ,/








-225.0 -
W


LU


















-250.0 I
5000 10000 15000 20000 25000

DISTANCE FROM INLET (FT) MEASURED NET
................. RNALTTICAL


Figure 6.18: Shoreline Changes for Baker's Haulover 1935 to 1945








82

flanking revetments and bulkheads were added to the jetties in 1938 to 1940. The south jetty

experienced severe erosion and the flanking revetment was constructed for approximately

1000 feet, this region south of the jetty has tended to remain stable and sometimes show

accretion due to the presence of this structure.

The net transport at Venice Inlet is towards the south. This improved inlet has never

had any maintenance dredging, indicating that the net transport across the inlet is very

small (U.S. Army Corps of Engineers, 1984). This lack of maintenance dredging also indi-

cates that the jetties are very sand tight and do not allow much sediment to pass through

them into the inlet channel.

Several features along this shoreline besides the inlet itself influence the shoreline evolu-

tion. Approximately 10,000 feet south of the inlet at Horse and Chaise Point there is a rock

outcropping; this region has been stable for several years compared to adjacent shorelines.

Groin fields are present 5,000 feet south of the inlet at Venice Beach and at 22,000 feet south

of the inlet at Caspersen Beach. These structures have stabilized the beach they front, but

by their very presence these regions must be high erosion areas. Bluff line erosion along

these shorelines has also added an unknown quantity of material to the longshore transport

system (U.S. Army Corps of Engineers, 1984).

Figure 6.19 shows the measured shoreline change for Venice Inlet from 1883 to 1942,

this time span includes a period before the inlet modifications and five years after the inlet

modifications. The severe erosion downdrift and the build up of material at the north

jetty is clearly evident; the maximum accretion and maximum erosion values both are

approximately 300 feet. This may be another indicator of very small net transport across

the inlet and sand tight jetties. The amount of background rates of shoreline change included

in these shoreline changes is unknown, because only one pre 1937 survey was available. The

maximum erosion was located south of the revetment flanking the southern jetty, the erosion

rate then decreased south of this point due to the effects of the groin field at Venice Beach

and the rock outcropping at Horse and Chaise Point. The even component of shoreline
































































-18000 -12000 -6000 0 6000 12000

OISTRNCE FROM INLET (FT) -NET
................. 000
-. -. EVEN


Figure 6.19: Shoreline Changes for Venice Inlet 1883 to 1942


300.0





200.0





100.0
U-







U
UJ








j -100.0



(U)
LL



Cc



-200.0






-300.0


-400.0








84
change indicates a loss of sediment in this region over the time span considered. The net

shoreline changes show that almost all of this loss is occurring downdrift of the inlet.

Figure 6.20 shows the shoreline changes for Venice Inlet from 1942 to 1978. The updrift

beaches during this time span accumulated much more material than during the 1883 to

1942 time span. The average shoreline change updrift of the inlet is plus 60 feet, this results

in a shoreline change rate of 1.67 feet per year. The downdrift beaches still experienced

erosion, with the maximum erosion occurring approximately 15,000 feet south of the inlet.

This location is between the rock out cropping at Horse and Chaise Point and the groin

field at Caspersen Beach. The rock out cropping is acting as a littoral barrier and the

updrift accretion effects of the groin field have not propagated quite this far north yet.

The stabilizing effects of the revetment at the south jetty can be seen as a small region of

accretion just south of the jetty.

The even component of shoreline change indicates approximately no net gain or loss

of sediment over this region for the time span considered. But the even component does

indicate that the region adjacent to the inlet was building up sediment, while the regions

farther away from the inlet were losing sediment. The odd component of shoreline change

has an unusual shape, in that this component has approximately the same slope for a

distance of 12,000 feet centered at the inlet. The usual behavior for the odd component is

to have maximum and minimum points which are very near the inlet. This indicates that

the shoreline changes from 1942 to 1978 are of generally the same magnitude over the entire

range of shorelines investigated. If the greatest changes are confined to an area centered

at the inlet, the odd component will have a large offset at the inlet, then tend to approach

zero as distance increases.

6.9 St. Andrews Bay Entrance

St. Andrews Bay Entrance is located in Bay County on Florida's West coast. The

inlet connects Panama City Harbor to the Gulf of Mexico. St. Andrews was cut in 1934

across a peninsula, 4 miles to the west of an existing natural channel known as East Pass.


































































000 -12000 -6000 0 6000 12000

DISTANCE FROM INLET (FT) NET
................. 000
.. EVEN


Figure 6.20: Shoreline Changes for Venice Inlet 1942 to 1978


150.0





100.0





50.0

I-
LL-


LU 0.0





-50.0
z
Z

-J
LU

3 -100.0

U'n



-150.0





-200.0


-250.0







86
This pass was abandoned after the new cut was made. St. Andrews Entrance created a

barrier island to the east, now known as Shell Island. The initial cut was to a depth of 32

feet, two jetties spaced 1500 feet apart were also constructed. The west jetty was 550 feet

long and the east jetty was 500 feet, wave action caused scour to the inner channel banks.

To protect the channel against this erosion, bulkheads and revetments were built as jetty

wings on both sides of the inlet, after the initial cut these jetty wings had to be repaired

and lengthened frequently (U.S. Army Corps of Engineers, 1948). The shoreline behind

these wings has continued to erode and the jetties have at different times had the potential

to become totally detached from the adjacent channel banks.

The predominant net longshore drift is to the west. Bay County has two or three

possible transport nodal points (U.S. Army Corps of Engineers, 1971). A nodal point may

exist at the jettied entrance, with drift to the east along Shell Island and drift to the west

along Panama City Beach. Another nodal point may exist between the eastern tip of Shell

Island at Lands End and the western tip of Crooked Island. This nodal point would be in

the middle of the abandoned East Pass.

Figure 6.21 shows the measured shoreline change for St. Andrews Bay Entrance from

1855 to 1934, this time period is pre-cut and should not include any effects of the inlet.

The negative distances from the inlet are to the west, and the positive distances are to the

east. The dominant feature of this region is the landward migration of the eastern end

of the peninsula at Lands End. It can be seen that the peninsula rotated landward from

a point located near the present location of the inlet. Shorelines east of the present cut

eroded at an increased rate as distance to the east increased, while shorelines west of the

present cut remained very stable. The even component of shoreline change indicates a net

loss of sediment over the region considered from 1855 to 1934. The odd component has

the unusual form of an almost straight line indicating accretion to the west with continuing

erosion as distance is increased to the east.

Figure 6.22 shows the shoreline changes for St. Andrews Bay Entrance for 1934 to 1977,
















1000.0 -



750.0



500.0



250.0
I-
LL




CC
= -250.0 ,- ..



-500.0 -
S-so.o/ ""\







-1000.0 -
-1250.0
LO






-1500.0







-1750.0
-17500.0 -- --- | --- --- i --- -- | -- ^ --- --


-24000 -18000 -12000 -6000 0 6000 12000 18000 24000

DISTANCE FROM INLET (FT) NET
................ 000
.. ... EVEN


Figure 6.21: Shoreline Changes for St. Andrews Bay Entrance 1855 to 1934








88
this time span shows the effects of cutting the inlet. This figure indicates net transport to

the west, with the western shoreline retreating and the eastern shoreline advancing. This

shoreline behavior is completely reversed from the shoreline changes observed before the

inlet was cut. The previously eroding shoreline east of the inlet is now advancing due to

sediment accumulating at the inlet, and the stable shorelines that existed to the west are

now experiencing severe erosion. The maximum erosion was located at the west jetty, with

the erosion decreasing as distance increased away from the jetty. The volume of material

eroded to the west almost equals the volume of material that accumulated to the east.

Figure 6.23 shows the predicted shoreline change for 1934 to 1977 compared to the

measured shoreline change. The predicted shoreline change for this 43 year time span

agrees very well with the measured changes. The analytical solution yields a breaking wave

height of 1.71 feet and a breaker angle of 1.56 degrees. These wave parameters would

indicate a net transport of 55,000 cubic yards per year.




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