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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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