• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 Symbols
 Abstract
 Introduction
 Literature review
 Method for determining delta volume...
 Results
 Conclusions
 Appendix A
 Appendix B
 Appendix C
 References






Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 94.010
Title: Ebb tidal delta evolution and navigability in the vicinity of coastal inlets
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00085001/00001
 Material Information
Title: Ebb tidal delta evolution and navigability in the vicinity of coastal inlets
Series Title: UFLCOEL-94.010
Physical Description: xv, 96 leaves : ill. ; 29 cm.
Language: English
Creator: Dombrowski, Michael Richard, 1960-
University of Florida -- Coastal and Oceanographic Engineering Dept
Publication Date: 1994
 Subjects
Subject: Coastal and Oceanographic Engineering thesis, M.S   ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (M.S.)--University of Florida, 1994.
Bibliography: Includes bibliographical references (leaves 89-95).
Statement of Responsibility: Michael Richard Dombrowski.
General Note: Typescript.
General Note: Vita.
Funding: This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
 Record Information
Bibliographic ID: UF00085001
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 33343981

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
        Page iv
        Page v
        Page vi
        Page vii
        Page viii
    Symbols
        Page ix
        Page x
        Page xi
        Page xii
        Page xiii
    Abstract
        Page xiv
        Page xv
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
    Literature review
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
    Method for determining delta volume and growth
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
    Results
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
    Conclusions
        Page 61
        Page 62
        Page 63
        Page 64
    Appendix A
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
    Appendix B
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
    Appendix C
        Page 87
        Page 88
    References
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
Full Text



UFL/CQEL-94/010


EBB TIDAL DELTA EVOLUTION AND NAVIGABILITY
IN THE VICINITY OF COASTAL INLETS






by



Michael Richard Dombrowski






Thesis


1994















EBB TIDAL DELTA EVOLUTION AND NAVIGABILITY
IN THE VICINITY OF COASTAL INLETS
















By

MICHAEL RICHARD DOMBROWSKI


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

1994














ACKNOWLEDGEMENTS


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

supervisory committee chairman, Professor Ashish J. Mehta, for his continuous support, guidance

and friendship throughout my study at the University of Florida. My thanks are also extended

to Drs. Robert G. Dean and Robert J. Thieke for serving as members on my supervisory

committee. Special thanks go to Dr. D. Max Sheppard for serving on my committee on such

short notice. Many thanks go to Yigong "Wally" Li for his computer programming expertise and

to Al Browder for his secretarial skills.

I would also like to thank Brett Moore and Ken Humiston for their inspiration and

continued encouragement throughout this adventure. Finally, I am most grateful to my wife, Pat,

for her patience and support through these times.














TABLE OF CONTENTS


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

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

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

KEY TO SYMBOLS ............................................. ...................... ix

ABSTRACT .................................................................................. xiv

CHAPTERS

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

Navigability at Coastal Inlets ........................................ 1
Seafloor Evolution ...................................... ............. 2
Study Objectives and Tasks ........................................... 7

2 LITERATURE REVIEW ............................................ 8

Overview .................................................................. 8
Ebb Delta Studies ........................................................ 8
Dean and Walton (1973) ................................... 8
Walton and Adams (1976) .................................. 10
Marino (1986) .............................................. 11
Oertel (1988) .................................... ........... 12
Hayter, Herandez, Atz and Sill (1988) ................. 13
Sediment Transport Studies ............................................. 15
Gole, Tarapore and Brahme (1971) ....................... 15
Sarikaya (1973) ...................................... ....... 16
Galvin (1982) .................................................. 17
Buckingham (1984) .......................................... 19
Ozsoy (1986) .................................... .......... 20
Walther and Douglas (1993) ................................ 21
Inlet Stability Studies .................................................. 23
Bruun and Gerritsen (1960) ................................ 23
O'Brien (1971) .............................................. 24
General Conclusions .................................... ........... 24








3 METHOD FOR DETERMINING DELTA VOLUME AND
GROWTH ......................................... ................ 26

Database ............................................ ................... 26
Ebb Delta Volume ............................................ 26
Tidal Prism .................................... ............ 27
Cross-Sectional Area ......................................... 27
Significant Wave Height and Wave Period .............. 27
Spring Sea Tidal Ranges ................................... 28
Ebb Delta Volume Estimates ........................................... 28
Ebb Delta Volume .................................... ..... 28
Sensitivity Analysis .................................... .... 29
Diagnostic Examination of Seafloor Evolution ................... 31
Model Development ........................................ 31
Model Parameters ........................................... 40
Ebb delta area ....................................... 40
Suspended sediment concentration ................ 41
Friction factors ...................................... 41
Sediment grain size ................................ 43
Deep water height and period ................... 43
Tidal inlet characteristics .......................... 43
Effects of Significant Physical Parameters on Delta Growth .... 43
Variation in Suspended Sediment Concentration ......... 44
Variation in Sediment Grain Size ........................... 44
Variation in Deep Water Wave Height .................. 47

4 RESULTS .......................................... ................. 48

Ebb Delta ........................................... .................. 48
Estimated Delta Volumes ................................... 48
Delta Volume Sensitivity Analysis ........................ 49
Delta Volume versus Tidal Prism ......................... 51
Time Evolution of Delta Volumes ......................... 54
Jupiter Inlet .......................................... 56
South Lake Worth Inlet ........................... 56
Boca Raton Inlet .................................... 57
Bakers Haulover Inlet .............................. 58
Influence of a on delta growth .................... 59

5 CONCLUSIONS ...................................... ............. 61

Estimated Ebb Delta Volumes ........................................ 61
Ebb Delta Volume versus Tidal Prism ............................. 61
Effects of Significant Physical Parameters on Delta Growth .... 62
Effects of a on Equilibrium Delta Volume ........................ 62
Influence of a on Navigability ....................................... 63
Future Investigations ..................................... .......... 63
Note of Caution ...................................... .............. 64









APPENDIX A EBB DELTA DATABASE ....................................... 65
APPENDIX B FORTRAN MODEL ALGORITHM AND INPUT FORMAT 80

APPENDIX C DATA USED TO CORRELATE TIDAL PRISM-BASED
AREA, Ap, TO MEASURED DELTA DEPOSITION AREA, AD 88

REFERENCES ................................................. ......................... 89
BIOGRAPHICAL SKETCH ......................................... ............... 96














LIST OF FIGURES

I-1 General sectional view of an inlet channel through a barrier
island and associated ebb delta ....................................... 3

1-2 General characteristic of an ebb jet and delta ..................... 5

III-1 Schematic of three "no-inlet" contour conditions in estimating
ebb delta volumes. Seaward exaggerated contours, A (dashed
lines), "best-fit" contours, B (solid lines) and landward
exaggerated contours, C (thick dotted lines) ..................... 29

111-2 Schematic of the initial grid and enlarged grid cell patterns
used in estimating ebb delta volumes ............................... 30

111-3 Seafloor growth diagrams illustrating the evolution of an ebb
delta: A) initial condition, B) transient condition and C)
equilibrium condition ..................................... .......... 32

III-4 Plan view of A) tidal prism-based area, Ap, and B) delta
deposition, AD ........................................................... 36

III-5 Cross-sectional view and plan view through the inlet and
idealized ebb delta ...................................... ............ 38

III-6 Ebb delta area, AD, versus tidal prism based area, Ap, for
twenty-one inlets based on data of Davis and Gibeaut (1990) ... 40

111-7 Ebb delta volume versus time comparing the effects of three
suspended sediment concentrations, C,, 0.00005, 0.00010 and
0.00020 kg/m3. Runs 1, 2 and 3 ................................... 45

III-8 Ebb delta volume versus time comparing the effects of three
grain size diameters, dso, 0.2, 0.3 and 0.4 mm. Runs 4, 5
and 6 ............................................. .................... 45

III-7 Ebb delta volume versus time comparing the effects of three
deep water wave heights, Ho, 0.0, 0.4 and 0.8 m. Runs 7, 8
and 9 ............................................. .................... 47

IV-1 Ebb delta volume versus tidal prism for mild energy coasts
(0-30 m2s2) ......................................... ................ 53








IV-2 Ebb delta volume versus tidal prism for moderate energy coasts
(30-300 m2s2) ..................................................... 53

IV-3 Ebb delta volumes versus year with model-calculated volume
ranges for Jupiter Inlet .............................................. 56

IV-4 Ebb delta volumes versus year with model-calculated volume
ranges for South Lake Worth Inlet .................................. 57

IV-5 Ebb delta volumes versus year with model-calculated volume
ranges for Boca Raton Inlet.......................................... 58

IV-6 Ebb delta volumes versus year with model-calculated volume
ranges for Bakers Haulover ......................................... 58

IV-7 Ebb delta volumes versus wave to tidal power ratio, a .......... 60














LIST OF TABLES

II-1 Coefficients of Eqn. 2.1 obtained by linear regression for the
relationship of tidal prism with ebb delta volume ............... 11

11-2 Bruun's stability criterion of sandy coastal inlets related to
ebb delta size and bypassing ......................................... 23

III-1 Initial input parameters for examining the effects of variation
in suspended sediment concentrations, C,, grain size diameter,
dso, and deep water wave height, Ho on ebb delta growth ....... 46

IV-1 Ebb delta volume for the "best-fit", "no-inlet" contours ......... 48

IV-2 Ebb delta volumes and percent differences due to changes in
the "no-inlet" contours .............................................. 49

IV-3 Ebb delta volumes and percent differences due to changes in
the grid cell size ....................................... .............. 51

IV-4 Initial input parameters and resulting wave to tidal energy
ratio, ......................................................... .......55

IV-5 Comparison of wave to tidal energy, a, and the corresponding
ebb delta volumes ...................................... ............. 59

A-i Ebb delta related parameters for coastal entrances along the
Florida coast ....................................... ................ 66

A-2 Ebb delta related parameters for coastal entrances along the
Georgia coast ........................................ ............... 74

A-3 Ebb delta related parameters for coastal entrances along the
South Carolina coast ..................................... .......... 75

A-4 Ebb delta related parameters for miscellaneous coastal entrances
along the Atlantic and Pacific Ocean coasts ....................... 76

C-1 Data used to correlate tidal prism area, Ap, to measured ebb
delta deposition area, A ............................................... 88














KEY TO SYMBOLS


Ac cross-sectional area at the inlet throat

A, ebb delta area based on tidal prism

AD ebb delta area based on regression analysis

a,a, regression coefficients, Eqns. 2.1 and 3.1, respectively

a, spring sea tidal amplitude

b,b1 exponential correlation coefficients, Eqns. 2.1 and 3.1, respectively

bo distance between two adjacent deep water wave rays

b, distance between two adjacent nearshore wave rays

C shallow water wave celerity

C CjC,

C, concentration of suspended sediment entering the settling basin

CD drag coefficient

Co deep water wave celerity

C, depth-averaged suspended sediment concentration

d delta accumulation height

de delta equilibrium height

-d incremental change in delta height

dso median grain size

E dimensionless wave energy density, Eqn. 2.7

Et tidal energy parameter

E, wave energy parameter








F, sediment settling flux

fc friction factor due to current

f, friction factor due to the combined current and waves

f, friction factor due to waves

g acceleration due to gravity

G parameter including the effects of dso, Ac, and specific gravity, Eqn. 2.4

h water depth at time, t

ha water depth adjacent to the dredged channel

hd water depth in the dredged channel

he equilibrium water depth

hi incremental change in the water depth

ho initial water depth at the inlet throat and over the seafloor

hp design project depth

hR reference water depth

H shoaled nearshore wave height

Ho deep water wave height

HR referenced wave height

H, significant deep water wave height

i time-step subscript

k1,2,3,4 intermediate Runge-Kutta method steps

k wave number

k' empirical coefficient, Eqn. 2.15

K coefficient of actual sedimentation to effective sediment load

L, length of dredged channel

L wave length

m suspended mass per unit delta bed area








m",m' empirical coefficients, Eqns. 2.12 and 2.15, respectively

M annual average littoral drift reaching the inlet

n Manning's n

p probability of sediment deposition

P spring tidal prism

Pbed bed stability parameter
Po total wave power

Q littoral transport rate

Qp pre-dredging littoral transport rate

R fraction of Q which reaches the dredged channel

re one-half the distance from the entrance mouth to the outer edge of Ap

rR sediment removal ratio

Re wave Reynolds number

S,n net sedimentation load

Sr shoaling rate

t time

At incremental time in number of tidal periods

tp time interval for an over-dredged channel to shoal to a design project depth

T wave period

TR sediment transport ratio

T, tidal period

Ua alongshore current velocity adjacent to the dredged channel

Uc current velocity

Ucb near-bed current velocity

Ucr critical velocity for erosion

Ud alongshore velocity across the dredged channel








U, flow velocity in the x1 direction

U, average inlet velocity over one-half tidal cycle

Um, maximum velocity through the inlet entrance for a spring tide

Uo characteristic velocity over the delta deposition area

U, total current velocity due to current and waves

U, orbital velocity due to waves

Uw, maximum near-bed orbital velocity due to waves

V ebb delta volume

VT shoaling rate

w width at the inlet throat

Wd dredged channel width

Ws particle settling velocity

W', effective settling velocity of the particles

W, settling velocity of a particle that reaches the seafloor at a distance from the inlet

y vertical distance from the bottom

Y ylh

xl distance in direction of mean flow

X xjlh

Zb distance above the profile origin

Zo theoretical origin of the logarithmic profile

ca wave to tidal energy ratio

E turbulent diffusion coefficient

Eo cross-sectional average of the turbulent diffusion coefficient

v kinematic viscosity of seawater

angle between current direction and wave direction

7, unit weight of sediment








7w unit weight of seawater

Pd dry bed density

p, particle density

Pw density of seawater

Tb shear stress due to waves superimposed on current

Tcr critical shear stress
'b maximum near-bed horizontal excursion














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

EBB TIDAL DELTA EVOLUTION AND NAVIGABILITY
IN THE VICINITY OF COASTAL INLETS

By

Michael Richard Dombrowski

December 1994

Chairperson: Ashish J. Mehta, Ph.D
Major Department: Department of Coastal and Oceanographic Engineering

For maintaining safe conditions for navigation in the vicinity of coastal inlets, the ebb

delta is frequently dredged. Previous investigations have established the dependence of the delta

volume on wave energy and tidal energy at sandy inlets. In this study, this dependence was

examined with respect to the rate of delta growth and the final equilibrium delta volume starting

with the opening of a new inlet when no delta is present.

A careful examination of the method to estimate delta volumes showed that the choice

of the "no-inlet" bathymetric contours and the grid cell size selected for estimating the delta

volume can measurably influence the volume obtained. In general, the greater the complexity

of the bathymetry, the larger the variation in the estimate.

A diagnostic model was developed for examining the influence of the ratio of wave

energy to tidal energy on delta growth. Model sensitivity tests showed that increasing the

suspended sediment concentration in the littoral zone caused the delta to approach equilibrium

faster, but did not affect the equilibrium volume. Increasing the wave height increased the time








of approach to equilibrium but decreased the volume. Finally, increasing the sand size increased

the growth rate as well as the equilibrium volume.

The model was applied to four Florida inlets. It was shown that the observed variability

in the delta volume can be due to the delta not achieving equilibrium and to the degree of

dominance of the wave energy relative to the tidal energy. This dominance also therefore

characterizes navigational access to the inlet.














CHAPTER I

INTRODUCTION



1.1 Navigability at Coastal Inlets

Navigation issues at coastal inlets for commercial and military purposes dates back to at

least 6,000 B.P. (Bruun and Gerritsen, 1960), and within modern times another consideration for

safe navigation has been added, namely recreation. Since early times naturally protected harbors

have been constructed to moor waterborne vessels and load and unload cargo and passengers.

Safe access is provided by inlet entrance channels from deep water through seaward protective

works such as jetties and breakwaters. The purpose of these structures is not only wave

attenuation for the protection of vessels during passage through the channel, but also to stabilize

the channel and interrupt excessive littoral drift from decreasing the channel depth. This problem

of depth decrease is of course not limited to improved channels, since it is also necessary for

unimproved inlet channels to have depths that are sufficient for the navigability of vessels. Thus,

in general, the problem of littoral sediment accumulation at inlets is linked to that of navigability

of the channel.

At the seafloor in the immediate vicinity of the inlet the interrupted littoral sediment tends

to accumulate and raise the floor, leading to the formation of an ebb delta. Thus, the conditions

for navigation, specifically in terms of water depths and wave action, are contingent upon the size

and shape of the ebb delta. At new inlets, or ones which have been closed for a period of time,

the rate at which the seafloor is modified by deltaic formation depends on the prevailing physical








2

conditions, availability of littoral sediment and geologic setting. Thus, from the standpoint of the

requirements for designing and maintaining the entrance channel, it is necessary to develop an

understanding of the mechanisms and means by which delta evolution occurs. The aim of this

study is therefore to examine the inter-dependence between significant physical parameters

governing sediment transport and the rate of delta formation at coastal inlets. The focus is

restricted to those cases where the bottom material is in the sand size range.



1.2 Seafloor Evolution

As noted, ebb deltas are accumulations of material at the seaward side of coastal inlets

(Figure I-i); the development of these deltas is typically a product of littoral suspended sediment

acted on by tidal and wave forces. Walton and Adams (1976) found that flood deltas on the bay

side of the inlet tend to reach an equilibrium volume over a period of time, and indicated that ebb

deltas volumes also achieve an equilibrium state. At the same time these investigators recognized

that due to changing wave and tidal energy conditions, the volume of ebb delta may be

episodically influenced, thus resulting in the growth of the delta at a new inlet approaching and

fluctuating about some equilibrium volume. Walton and Adams (1976) found the equilibrium

volume to be dependent on the tidal prism and, furthermore, the empirical coefficients

characterizing this relationship were themselves found to depend on the wave energy. For a

given tidal prism, the equilibrium yolume decreased with increasing wave energy. To examine

this important issue of the influence of wave- and tide-induced forces on the rate of growth of

sandy ebb deltas, a semi-quantitative approach has been attempted in this study. To begin, the

underlying issues in ebb delta development are described first.

The opening of a tidal inlet channel is primarily a result of the break-through of a barrier

island (Brown, 1932). This breach can occur during storm conditions when water mass









3

associated with the storm surge and waves is transported across the barrier island, consequently

eroding the beach, the dune system and providing a low relief where tide-induced currents may

contain enough energy to maintain a permanent channel across the barrier island. There are also

cases where coastal inlets are intentionally relocated for the purpose of erosion control along the

down-drift shoreline (Kana and Mason, 1988).

Barr I er
Is I and
s nd -- Ebb De I ta





Inlet
Channe I


Figure I-1. General sectional view of an inlet channel through a barrier island and
associated ebb delta.



Although barrier island break-through is the primary reason for the natural opening of

tidal inlets, many of the resultant openings tend to be unstable, and lead to closure after a

comparatively short period of time. Escoffier (1940) considered the relationship between the

maximum flow velocity through the inlet throat and the throat cross-sectional area to determine

if the inlet is stable or unstable. This criterion was based on the sediment depositional conditions

which would either enlarge or reduce the initial cross-sectional area. Bruun and Gerritsen (1960)

proposed a stability criterion in which the ability of the channel current to remove the littoral drift

deposited in the channel is considered for the condition for the inlet to remain open. The ratio

of the spring tidal prism to the littoral drift, P/M, is thus a measure of inlet stability. Bruun

(1977) later quantified this relationship for inlets ranging from unstable "overflow channels" to

stable channels with little ebb delta formation and good flushing characteristics. O'Brien (1971)








4

noted that wave-transported material deposited near a coastal inlet may close the inlet depending

on the relative strengths of wave and tidal forces. A greater wave energy would be required to

close a larger inlet than a small one due to the larger tidal prism of the former.

The essential approach to describing the evolution of a ebb delta is to begin with a new

inlet or one that has been closed for a period of time and therefore has no delta. As noted, the

break-through of a barrier island by a storm event or artificial means provides an initial opening

between the back barrier bay or lagoon and open water. Once the inlet breaks-through, a free

jet forms on the seaward side of the inlet as a result of tidal current (Oertel and Dunstan, 1981).

A free jet may also form on the landward side if it discharges into an unrestricted basin. In any

event, due to the initial opening and the formation of the jets, an initial accumulation of material

both on the landward side (flood delta) and the seaward side (ebb delta) of the inlet will occur.

For this study, only the ebb delta accumulation is investigated.

The accumulation of the ebb delta material can be derived from the initial formation of

the cut, especially in areas where the littoral drift is comparatively small. Thus, for example

Oertel (1988) found that approximately 78 percent of the 31.6 x106 m3 of material in the ebb

delta of Quinby Inlet in Virginia consisted of the sediment derived from the newly opened

channel.

A theoretical approach by Ozsoy (1986) presented a model whereby the mass transport

of material is the result of turbulent free jet issuing from the inlet. Thus, a portion of the

suspended sediment supplied by littoral transport is entrained into the inlet opening during the ebb

(as well as flood) phases of flow is ultimately deposited on to the ebb delta (Figure 1-2). The

depositional pattern of the ebb delta is dependent on the characteristics of the ebb flow jet and

on the wave energy. A low wave energy sandy coast may be characterized by marginal sand bars

advancing seaward and consist of greater quantity of material as compared to high wave energy









5

coasts where the increased wave forces transport the material toward the inlet and nearshore area

(Walton and Adams, 1976).



Ebb Jet -- Ebb De Ita
Boundary




I n I et
Channe






Entra I nment of
IIttoral current
and associated
suspended sediment

Figure 1-2. General characteristics of an ebb jet and delta.



The sediment deposited in the ebb delta can be considered to be contained within a

seafloor area characterized by the area obtained by dividing the spring tidal prism by the water

depth. In Oertel's (1988) conceptual model, material is deposited over an area just beyond the

distal end of the "near-field" jet as the flow velocity decreases below a certain critical value.

This deposition area, defined as the "far-field", tends to be fan-shaped resulting from the lateral

spreading of the jet in the presence of landward approaching waves.

According to O'Brien (1969), the capacity of tidal current in maintaining the channel is

characterized by the maximum velocity in the inlet throat as determined by the tidal prism and

cross-sectional area of the inlet opening, whereas, as noted, the current velocity further seaward

governs the deposition or erosion of material within the delta footprint. This characteristic








6

current velocity can be assumed to occur at a point between the inlet mouth and the outer edge

of the ebb delta. This location thus delineates the shoreward end of the "far-field" defined by

Oertel (1988).

The deposition or erosion of material within the confines of the delta footprint is due to

the bottom stress produced by the tidal current. Superimposing oscillatory currents due to wave

action complicates sediment motion near coastal inlets (O'Brien, 1969). The primary result of

wave action is the suspension of material which is then transported by the tidal current. The

critical shear stress for resuspension and transport is dependent on the diameter of the sediment.

If the critical shear stress is exceeded by the combined hydrodynamic stress due to current and

waves, then the seafloor can be expected to be eroded. However, if the combined stress is less

than that of the critical value then material will deposit within the confines of the delta area.

Thus, starting with a situation in which waves are absent, the rate of sediment deposition, hence

delta growth, decreases as waves appear and increase in intensity, until such a condition when

there is no deposition. Further increase in wave action would then cause the delta volume to

decrease due to bottom scour.

As the seafloor elevation rises, and decreases the water depth, not only does the ebb

current velocity increase over the delta in comparison with that at the inlet mouth by continuity,

but the decreased depth also results in increased wave shoaling, thereby increasing orbital velocity

and the wave shear stress contribution. Thus, under constant tide and wave conditions, the

seafloor can only rise to an elevation where there is no further deposition when the combined

hydrodynamic stress equals the critical shear stress. At this stage the ebb delta will have evolved

to an equilibrium volume and shape.








7

1.3 Study Objectives and Tasks

From the above description it is seen that in a given geologic setting, the rate of growth

of ebb delta and its ultimate equilibrium volume depend both on tidal energy and wave energy.

The ebb jet serves to deposit littoral material at a distance from the inlet where the flow velocity

is small enough to be conducive to deposition. Conversely, waves tend to enhance resuspension

and transport of deposited material away from the ebb delta. Thus, as noted, with increasing

wave action one may expect the rate of ebb delta growth to decrease, and the equilibrium volume

to decrease as well. It is the main objective of this study to examine the dependence of the inlet

ebb delta growth rate and the equilibrium volume on tidal, wave and sedimentary characteristics.

This objective is met by completion of the following tasks:

1. Development of a database consisting of inlet ebb delta volumes, throat cross-sectional

areas, spring tidal prisms, significant deep water wave heights and wave periods, and

spring tidal ranges.

2. Re-examination of the procedure for ebb delta volume estimation developed by Dean and

Walton (1973) to determine the variation in the estimated delta volumes arising from the

interpretation of bathymetric conditions.

3. Examination of the influence of wave energy on the ebb delta volume-tidal prism

relationship following the work of Walton and Adams (1976).

4. Development of a diagnostic model to examine the role of tidal energy and wave energy

in influencing the ebb delta volume-time curve, starting with the no-volume condition.

5. Examination of model sensitivity to important governing physical parameters.

6. Examination of the trends in the time-variation of the delta volume with the help of the

model at selected inlets.














CHAPTER II

LITERATURE REVIEW



2.1 Overview

This chapter provides a literature review of relevant studies on ebb delta volumes, inlet

sediment transport and inlet stability. The review of ebb delta volume studies and the physical

processes effecting the inlets in Section 2.2 include 1) measurements of ebb delta volumes; 2)

capacity of deltas to store sand; 3) coastal physical parameters influencing ebb deltas; and, 4)

potential sources of ebb delta material. The second portion of this review in Section 2.3 focuses

on studies on sediment transport relevant to the deposition or erosion of the ebb delta, including

5) prediction of sedimentation in entrance (approach) channels; 6) sedimentation within inlet

channels; 7) erosion/deposition in entrance channels; 8) determination of the removal ratio of

suspended matter in settling basins; and 9) a procedure to quantify the rate of shoaling after ebb

delta dredging. Section 2.4 examines the stability of coastal inlets. Finally, in Section 2.5,

findings based on this review that are relevant to the modeling effort in Chapter IV are

summarized.



2.2 Ebb Delta Studies

2.2.1 Dean and Walton (1973)

Dean and Walton (1973) provided a qualitative description of the hydraulic and

sedimentary processes in the vicinity of coastal inlets. These authors compared inlets to the








9

idealized form of a surface nozzle, where the ebb jet is analogous to the turbulent jet issuing from

the nozzle. On the other hand, the flood flow conforms to a uniform concentric sink flow

converging toward the inlet. Thus, the laterally spreading ebb jet entrains water from the

adjacent shoreline toward the inlet, while during the flood flow water is transported both toward

and into the inlet. As a result, the combination of the ebb and flood flows causes the current to

transport sediment toward the inlet from the adjacent shoreline during all tidal stages. The

sediment thus transported is ultimately removed by the ebb flow and is deposited offshore. Dean

and Walton (1973) noted that the forces acting to transport sediment are not only dependent upon

the effects of ebb and flood currents, but also on waves forces which tend to drive the material

deposited as an delta towards the inlet. These forces have no net effect when the delta volume

reaches a state of equilibrium, at which point it does not exhibit growth or reduction in its

volume.

Twenty-three Florida inlets were investigated to estimate the quantities of sand in the ebb

deltas. A method was developed for estimating the volume of accumulated sand. The first step

was to construct a bathymetric record of the inlet and its adjacent shores. A representative shore-

normal profile was then determined from contour lines on either side of the inlet corresponding

to the bathymetry of a "no-inlet" condition. Contour lines connecting these two profiles were

overlain on the delta and a grid superimposed on the chart. The depth differences at each corer

of the square were measured and averaged for the square. Finally, the summation of the

averaged grid depth differences multiplied by the grid area yielded the ebb delta volume.

Since the estimated delta volumes may be subject to individual interpretation bias, each

author calculated the same eight ebb delta volumes from their individually interpreted "no-inlet"

contours. This exercise resulted in delta volume differences of less than 30 percent, with the

inlets with the large volumes having differences of less than 10 percent.










2.2.2 Walton and Adams (1976)

These authors investigated the capacity of deltas at inlets to store sand. The volumes for

six flood tidal deltas were calculated from comparative surveys ranging over time periods from

seventeen to seventy-seven years. Preliminary analysis showed that the flood deltas may reach

an equilibrium size over a period of time. It was considered by the authors that the ebb deltas

also reach an equilibrium state. By knowing the volume of sand deposited in the flood and ebb

deltas would give an estimate of the volume of material that would be removed from the adjacent

beaches, thus providing an approximation of the effects to the adjacent shoreline due to the inlet.

Ebb delta volumes for forty-four tidal inlets around the United States were calculated

using the method described in Dean and Walton (1973). The volume of each of the deltas was

calculated two or more times to obtain a range of values due to the individual interpretation of

the "no-inlet" contour lines. This exercise generally resulted in a volume deviation of less than

10 percent.

Tidal prisms were correlated with ebb delta volumes categorized by three wave energy

levels in an effort to explain any effects on the volumes due to differences in the wave energy.

The square of the product of the deep water wave height and period was used to parameterize the

wave energy, thus providing a quantitative description of the available energy to modify the ebb

delta. The wave energy parameter ranges were arbitrarily chosen from 0-30 (mildly exposed),

30-300 (moderately exposed) and > 300 (highly exposed). The data were plotted on a log-log

scale with a linear regression line equation of


V = aP1 (2.1)

where V = ebb delta volume (m3) and P = spring tidal prism (m3). The coefficients a and b

found for the three wave energy regimes are given in Table II-1. The dependence of these

coefficients on the wave energy regime in Table II-1 implies that the relationship between the








11

delta volume and tidal prism is not unique in the sense that it depends measurably on the

prevailing wave energy.



Table II-1. Coefficients of Eqn. 2.1 obtained by linear regression for the relationship of tidal
prism with ebb delta volume.

Wave energy regime Coefficient, a Coefficient, b
High 5.33 x 10-3 1.23
Moderate 3.77 x 10-3 1.08
Mild 8.76 x 10-3 1.24

Source: Walton and Adams (1976)



2.2.3 Marino (1986)

This investigator described the general development of ebb deltas using a geomorphologic

perspective through inlet case studies on the east coast of Florida. These inlets were chosen due

to the unique morphology of each inlet and the associated differences in the development of the

deltas. This examination revealed some of the problems that are encountered in determining the

ebb delta volumes for those inlets where the bathymetric conditions are less than "ideal". For

example, at Ft. Pierce Inlet the updrift and downdrift profile lines have substantially different

slopes, so that the "no-inlet" contour lines had to be interpolated between the updrift and

downdrift shorelines. Also, where inlets had significant shoreline offsets with respect to each

other, the grid size had to be decreased from 305 m2 to sizes ranging between 76 and 152 m2,

so that a greater bathymetric detail could be covered. Another example of the problems

encountered was the presence of offshore reefs at St. Lucie Inlet, Hillsboro Inlet, Port Everglades

Inlet and Government Cut. In these cases, the estimated ebb delta volumes may have been

measurably different than actually present, since the reef areas could not be distinguished from

sandy areas.








12

A dimensional analysis was done to determine the physical parameters that are important

in characterizing the ebb delta volume. Dimensionless parameters were found and the functional

relationship was reduced to


V Pw Ac Ei
f [- p 1- = 0 (2.2)
W W3 hoI a, Et

where V = ebb delta volume, w = width at the inlet throat, ho = depth at the throat, P = spring

tidal prism, Ac = cross-sectional area at the inlet throat, aos = spring sea tidal amplitude, E, =

tidal energy parameter, and E, = wave energy parameter. Marino (1986) eliminated E,/E,, the

ratio of wave energy to tidal energy, because the wave energies considered were found to be

within the "moderate" range defined by Walton and Adams (1976). The non-dimensional V/P

ratio, when plotted against the aspect ratio, w/ho, for different values of A/al did not produce

any strong trends. However, from the relationship, the investigator asserted that as w/ho

decreases, the ebb delta volume tends to increase, leading to the credence that delta volume

depends on not only of tidal prism but also on the aspect ratio.

The relationship of the ebb delta volume (m3) to the spring tidal prism (m3) was

determined by linear regression:


V = 5.59x10-4 p.39 (2.3)



2.2.4 Oertel (1988)

This investigator considered the ebb jet to be divided into two zones. The first, the near-

field, was described as the zone of flow establishment extending from the inlet mouth to a certain

transition point. Within this zone the maximum ebb flow velocities occur. As the jet extends

past the near-field flow, its boundaries spread out laterally from the inlet. The decrease in flow








13

velocity at the end of the near-field results in material being deposited in the far-field. The

associated decrease in the water depth compresses the jet vertically and further increases the

lateral spreading resulting in a continual reduction in the flow velocity and a build up of the delta

material.

During a flood tide, the return flow toward the inlet does not form a reverse flow pattern

of the ebb tide; rather the flow distribution radially converges toward the inlet. The velocity field

is distributed over a greater near-field area than during the ebb flow, thus resulting in lower near-

field flood velocities than ebb velocities. Consequently, the summation of the near-field flood

and ebb velocity vectors results in flood- and ebb- dominated zones. Oertel (1988) suggested that

the difference between the axially ebb-dominated flow and the flood-dominated marginal flow be

termed "net tidal delta flow". It is within this region that a spatial asymmetry in the shear

stresses tends to develop ebb marginal deltas.

Oertel (1988) described how resultant vectors of inlet and littoral currents may effect the

flow jet, thus re-orientating the inlet gorge and the marginal delta for different types of inlet

situations. Thus, littoral sediment can be deposited in spits at the end of the barrier island, or

transported into the inlet. In the inlet, the material may accumulate in the inlet gorge or, if the

critical shear stress for scour is exceeded, be transported bayward to the flood delta, or seaward

to the ebb delta. Material that accumulates in the ebb delta may remain there to build the delta

itself or may be by-passed downdrift or updrift via marginal deltas and channels.



2.2.5 Havter. Hernandez. Atz and Sill (1988)

These investigators performed a study using a movable bed model to evaluate the effects

of tidal flow and wave action on ebb delta formation and to estimate the effects of shoal mining

on the delta and the adjacent shoreline. The results of the experiment were normalized to include








14

the effects of sediment size, specific gravity, and inlet cross-sectional area via the parameter, G:


G = whd,(y, -y) (2.4)

where dso = median grain size, y, = unit weight of sediment, and 7, = unit weight of sea

water. The relationship of the delta volume (m3), to the tidal prism (m3), was determined by

linear regression:


V = 4.8x10-4 -1340 (2.5)
G

and


V = 6.9x104' P -1870 (2.6)
G G

where Eqns. 2.5 and 2.6 correspond to the experiments effected by no wave action and by wave

action, respectively. It was found that the data corresponding to the presence of waves was more

scattered than without waves. The two regression lines (Eqns. 2.5 and 2.6) also indicate that

experiments with waves formed larger deltas as compared to deltas without waves. The

explanation provided by the investigators was that more material moved offshore from the inlet

mouth as a result in the increased shear stress induced by the combination of waves and currents.

Secondly, the littoral transport of material into the inlet from the adjacent shoreline was enhanced

by wave action. This observation was however contradicted when the normalized tidal prism,

VIG, was compared to a normalized tidal prism, P/GE, where E is the dimensionless wave

energy density:


E H (2.7)
8h2


where H, = significant deep water wave height and h = inlet water depth.










The resulting regression line is


V = 4.76x10-3 (2.8)
G |y GE

The data plotted in Hayter et al. (1988) and Eqn. 2.7 indicate that the delta volume will increase

with an increase in the tidal prism or with a decrease in the wave energy.



2.3 Sediment Transport Studies

2.3.1 Gole. Tarapore and Brahme (1971)

A method was developed by these investigators to predict sedimentation in entrance

channels based on the analysis of prototype and model data, and analytical studies. This method

was developed to estimate the quantity of material required to be removed from the channel

during maintenance dredging.

The total suspended load crossing a shore-normal channel in the alongshore direction was

calculated from the prototype and hydraulic model data. The prototype data were obtained during

seasonal conditions to account for the variation in tides, wave climate and seasonal sedimentation.

The subsequent analytic step was to determine if a sediment particle will settle out of the water

column and be deposited in the channel or cross over the channel. This criterion was derived

in terms of particle fall velocity. This procedure ultimately determined the fraction of the total

sediment load which contributes to the sedimentation of the channel. It was assumed that the

suspended sediment carrying capacity of the current is proportional to the square of the flow

velocity. Thus, as a result of dredging and the associated increase in the depth of flow, the

alongshore flow velocity across the channel decreases. This decrease in flow velocity results in

the net sedimentation load of the dredged channel (S,):











S = KL, U C, t hd d (h (2.9)
[Udh hChJ

where K = coefficient of actual sedimentation to effective sediment load derived from dredging

records of existing channels, L, = length of dredged channel, Ua = alongshore current velocity

adjacent to dredged channel, Cs = depth-averaged suspended sediment concentration, t = time

(months), hd = water depth in the dredged channel, wd = dredged channel width, W, = particle

settling velocity, ha = water depth adjacent to the dredged channel, and Ud = alongshore

velocity across the dredged channel.



2.3.2 Sarikaya (1973)

This study investigated the removal ratio of suspended sediment in settling basins. This

ratio, rR, is defined as the settled suspended sediment within the deposition area to the suspended

sediment entering the area:


r = l-_C (2.10)

where C, = uniformly distributed suspended sediment concentration and Cb = concentration of

suspended sediment entering the settling basin. The differential equation for suspended sediment

transport in a settling basin was derived from the law of conservation of sediment mass. Written

in dimensionless form:


dC _W d 1 d d (2 )
dX U, dY Uh dY dY

where X = xl/h, xl = distance in direction of mean flow, h = water depth, Y = y/h, y =

vertical distance from the bottom, C = C/Cb, U, = flow velocity in the x1-direction, and e =








17

turbulent diffusion coefficient. The removal ratio was obtained by employing a finite difference

method, with the initial conditions assuming a uniformly distributed sediment concentration at the

inlet, no re-entrainment of sediment particles from the seafloor, and no sediment is introduced

at the water surface. The removal ratio was determined as a function of Whz/2e, where e,

cross-sectional averaged turbulent diffusion coefficient, and WF/WV, where Wo = settling velocity

of a particle that reaches the seafloor at a distance from the inlet, if turbulence is neglected. This

relationship indicates that as the effect of turbulence increases Wzh/2e decreases thereby reducing

the removal ratio resulting in comparatively smaller sediment deposition volumes. Conversely,

higher values of the parameter WF/W increase the removal ratio indicating the dependence of

sedimentation on the settling velocity.



2.3.3 Galvin (1982)

This investigator presented a method to determine the channel shoaling rate and a time

estimate to shoal the entrance channel from an initial over-dredged depth to a project design

depth. The shoaling rate of the channel was considered to be dependent on the littoral sediment

deposited in the dredged channel. The shoaling rate (Sr) was given as



w ,= e Wd h, (2.12)



where L, = dredged channel length, wd = dredged channel width, Q = littoral transport rate,

R = fraction of Q which reaches the dredged channel, ho = initial water depth, h = water depth

at time t, and m" = exponent depending on whether the dredging increases the cross-sectional

area resulting in a reduction in the channel velocity (m" = 5/2), or whether the velocity is the

same compared to pre-dredging condition (m" = 3/2). The time interval, t,, for an over-dredged








18

channel to shoal to a project design depth, hp, is defined as


p -w (hd-h)+ (InA-InB (2.13a)


where

(h,-h)
A (h-h (2.13b)
(h h)

and


Sm" -1 hd-ho
1+-
2 h
B h(2.13c)
+ -1 [h-h]
2 h

Channel depth during shoaling versus time after dredging for three combinations of the

natural controlling depth and dredged channel depth were plotted in order to obtain a quantitative

evaluation of the effect of bypassing on channel shoaling for three initial depths dredged to 4

meters. It was found that: a) the curves of channel depth versus time indicated that the maximum

rate of shoaling occurred immediately after dredging; b) the channel shoaled faster when the post-

dredging velocity was reduced (m" = 5/2) as compared to when post-dredging velocity was not

reduced (m" = 3/2); c) the channel shoaled faster when no bypassing occurred (m" co); and,

d) a shallow dredged channel approached the natural controlling depth at a slower rate than a

deep dredged channel.

It was shown in this study that this method can be used to compute the duration that a

channel will be maintained at a certain project depth, test if a proposed dredging depth will last

a desired length of time, and estimate the decreased rate of bypassing as a result of the dredged

channel.










2.3.4 Buckingham (1984)

Buckingham (1984) studied the erosion of tidal inlet channels and the associated

sedimentation in the vicinity of the channels. A study was conducted using a fixed bed,

undistorted model that combined penetrating oceanic waves and tidal currents in the channel of

Jupiter Inlet, Florida. A bed stability parameter was used to evaluate the sediment

erosion/deposition potential at selected locations within the inlet entrance and interior waters.

This parameter quantitatively relates the flow velocities of the model data to the

erosion/deposition potentials. The bed stability parameter, Pbed, was defined as


P -1 (2.14)
-cr

where Tb = bed shear stress due to waves superimposed on current and Tr = critical shear stress.

When b > Tr, (positive Pbd) erosion will occur and when Tb < cr (negative Pbed) material will be

deposited. Under turbulent conditions, the bed shear stress is proportional to the square of the

velocity. Thus, the velocities due to waves and current can be substituted in Eqn. 2.13 to obtain

the following equation for the stability parameter:

2


S l+k2 H m1 j 2 (2.15)
Pbe = 1k'e-1
h H U -

where k' and m' are empirical coefficients found to range between 2 to 8 and 1.3 to 1.7,

respectively, HR = reference wave height, hR = reference water depth, H = wave height at the

site in question, h = water depth, U, = current velocity, and Ucr = critical velocity for erosion.

Two limiting assumptions were made in the development of this relationship. First, the critical

shear stress to erode the seafloor was considered to be equal to the shear stress below which








20

sediment will deposit, and secondly, the critical shear stress under waves and current was

considered to be equal to that obtained from Shields' (1936) relationship for incipient grain

motion under steady flow. Thus, the second assumption neglects the shear stress contribution

from wave action. The bed stability parameter was found to produce reasonable results when

interpreting hydrodynamic data to compare the erosion and deposition potentials using fixed bed

models involving both waves and currents within the inlet.



2.3.5 Ozsoy (1986)

This investigator examined transport and sedimentation processes in the vicinity of a tidal

inlet through analytic modeling of sediment transport associated with the turbulent jet produced

by ebb tidal flow. The jet was divided into a "zone of flow establishment" (ZOFE) and a "zone

of established flow" (ZOEF), where the ZOFE is defined from the inlet mouth to a seaward

location where the flow is not fully influenced by the jet boundary shear, hence has a constant

jet centerline velocity and the ZOEF extends seaward of that point, with decreasing jet centerline

velocity.

The analytic model produced a non-dimensional distribution of the settlement rate within

the boundaries of the jet. It was found that two maxima and a minimum at the center-line

occurred. The two maxima correspond to the marginal shoals located along both sides of the jet

center-line. Sediment settling was comparatively small along the center-line of the jet due to the

high current velocity. There was no deposition of material outside of the jet boundaries due to

the small or zero ambient sediment concentration.

It was found that bottom friction, bathymetry, sediment settling velocity and the initial

inlet velocity influence the depositional patterns within the jet boundaries. As bottom friction

increased, jet flow sediment concentrations were more rapidly reduced. This resulted in material








21

deposition relatively close to the inlet mouth in building a fan-shaped delta. A change in the

bottom slope did not result in any significant change in the concentration within the jet, but did

transport the material further seaward resulting in elongated marginal shoals. The settling

velocities, on the other hand, played a significant role in determining sediment distribution.

Sediments with larger settling velocities (coarser material) were deposited closer to the inlet and

the marginal shoals, while low settling velocity, finer material was jetted further offshore. Flow

velocities were also shown to be influential on sedimentation patterns. When the initial velocity

was less than the critical velocity for erosion, larger deposits of material were found to occur at

the mouth or within the jet core (in ZOFE). When the initial velocity was equal to the critical

velocity, it was found that material is deposited further seaward in the marginal shoals. Finally,

when the initial velocity was greater than critical, scouring occurred and material deposited

further offshore than the marginal shoals, outside the active zone of sediment transport. Ozsoy

(1986) found that the predicted depositional patterns resulted in reasonable qualitative similarity

to those at prototype coastal inlets under certain hydrodynamic conditions.



2.3.6 Walther and Douglas (1993)

These investigators developed a procedure to quantify the shoaling rate within an offshore

dredged area within the ebb delta and sediment transport rate across the inlet after dredging. The

post-dredging of the ebb delta will reduce bypassing rate around the inlet, hence the estimation

of this reduction is a matter of considerable engineering interest. The quantity deposited in the

dredged area is determined by the sediment transport ratio, TR, from the work of Gole et al.

(1971) expressed in terms of pre- and post-dredging depths:












T = h[ 1 (2.16)


where ho = initial water depth, hd = water depth in the dredged channel, and m" = 5/2. The

bypassing rate can then be determined from an estimate of the pre-dredging littoral transport rate.

The shoaling rate (VT) within the dredged area is estimated as the difference between the pre- and

post-dredging transport rates:

V = QP,(1-T,) (2.17)

where Q, = pre-dredging littoral transport rate. As sediment is deposited in the dredged area,

the depth and the trapping rate will decrease, while the sediment bypassing rate will increase.

A comparison of two hypothetical examples were presented to illustrate the recovery and

bypassing rates for a deep and a shallow sand borrow area within the ebb delta. The rate of

littoral material to the ebb delta, the pre-dredged depth and the dredged volume were considered

constant for both cases, with a variation in the borrow area dimensions. The bypassing rate and

the cumulative volume of sand bypassed versus time were determined. The investigators found

that the initial bypassing rate of the shallow cut was approximately twice the rate for the deep cut.

However, the bypassing rate increased faster for the deep cut with the bypassing rate-time curve

intersecting the shallow cut curve by the fifth year, for the particular set of parameters chosen.

The increased bypassing rate for the deep cut resulted in full recovery to the pre-dredging

condition by the ninth year as compared to the fourteenth year for the shallow cut. The

cumulative volume bypassed at the end of the fourteen years was within one percent of each other

for the two cases. It was concluded that the results using this method were sensitive to the

assumed sediment transport rate to the dredged area. As noted, it was also shown that, initially,

the deeper cut trapped more sediment and reduced the bypassing rate compared to the shallow

cut, but eventually the same cumulative sand volume was bypassed in both cases.








23

2.4 Inlet Stability Studies


2.4.1 Bruun and Gerritsen (1960)

Bruun and Gerritsen (1960) proposed a stability criterion in which the condition for the

inlet to remain open was considered to be dependent on the ability of the channel current to

remove the littoral drift deposited on the ebb delta. The ratio of the tidal prism passing through

the inlet during a one-half tidal cycle to the annual average littoral drift reaching the inlet, P/M,

was proposed as a measure of inlet stability. Bruun (1977) later quantified this relationship for

sandy coastal inlet (Table 11-2). As the tidal prism increases relative to the littoral drift, thus

increasing the stability ratio, P/M, the inlet entrance has the tendency of maintaining itself.

Conversely, as the stability ratio continues to decrease, the seafloor elevation rises until the inlet

is subject to closure.



Table 11-2. Bruun's stability criterion of sandy coastal inlets related to ebb delta size and
bypassing.


Ratio range, P/M


P/M > 150

100 < P/M < 150


50 < P/M < 100

20 < P/M < 50

P/M < 20


Inlet conditions with respect to navigability and stability


Conditions are relatively stable and good, little ebb delta formation
and good flushing.
Conditions become less satisfactory, and ebb delta formation
becomes more pronounced.
The ebb delta may be rather large, but they can usually still be
navigated by shallow draft vessels ....
.... all inlets are typical "delta-bypasses" .... For navigation, they
present "wild-cases", unreliable and dangerous.
.... entrances appear as unstable "over-flow channels" rather than
permanent inlets.


Source: Bruun (1977)


I










2.4.1 O'Brien (1971)

O'Brien (1971) reviewed the report by Saville et al. (1957) on a moveable bed hydraulic

model study of an inlet and noted that an inlet that is in equilibrium is due to a balance between

the wave energy which tends to close an inlet and the tidal energy which maintains the opening.

Thus, the ratio, a, of normal incident wave energy over one tidal period to the tidal energy

through the inlet over a tidal period can be used to evaluate the stability of an inlet:


a = T, (2.18)
2 a., ,P

where Po = total wave power, w = width at the inlet throat, T, = tidal period, y, = unit weight

of seawater, P = spring tidal prism, and 2ao, = spring tidal range. Given a single representative

deep water wave height Ho, Po is defined as:


P = 'Yg H2T (2.19)
32vr

where g = acceleration due gravity and T = wave period. Mehta and Hou (1974) and Sedwick

(1974) found a to be a reasonable indicator of inlet stability. The stability coefficient, a, was

plotted against the tidal prism and a line separating relatively low values of a representing

stability from a region of high values of a representing instability was drawn.



2.5 General Conclusions

With regard to the objective of the present study and the modeling effort described in

Chapter IV, the studies reviewed in this section lead to the following relevant observations:

1. Inlets can be modeled as an idealized form of a surface nozzle, where the ebb jet is

analogous to the turbulent jet issuing from the nozzle, and the flood conforms to a

uniform concentric flow converging toward the inlet (Dean and Walton, 1973; Oertel,

1988; and Ozsoy, 1986).








25

2. The relationship between the delta volume and the tidal prism depends measurably on

prevailing wave energy (Walton and Adams, 1976; Hayter et al., 1988).

3. Suspended sediment concentration, grain size, sediment settling velocity and the initial

inlet velocity influence the depositional patterns with the ebb jet boundaries (Gole et al.,

1971; Sarikara, 1973; Ozsoy, 1986)

4. Flow velocities due to waves and current related through the bed stability parameter,

Pbd, determine the sediment erosion/deposition potential (Buckingham, 1984).

5. Ebb jet spreads out laterally and the flow velocity decreases at the end of the near-field

resulting in the material being deposited in the far-field (Ozsoy, 1986; Oertel, 1988).

6. Curves plotting the water depth during shoaling versus time after dredging indicate that

the maximum rate of shoaling occurred immediately after dredging (Galvin, 1982).

7. Deeper dredged cuts trap more sediment and reduce the bypassing rate as compared to

a shallow cut, but eventually the same cumulative sand volume is bypassed (Walther and

Douglas, 1993).

8. The ratio of the tidal prism to the annual average littoral drift reaching the inlet is an

indicator of conditions for navigation through the entrance. As the tidal prism decreases

relative to the littoral drift, the ebb delta grows and ultimately hinders navigation (Bruun

and Gerritsen, 1960).

9. The stability coefficient, a, defined as the ratio of longshore wave power to the tidal

power can be a reasonable indicator of stable versus unstable inlets (O'Brien, 1971;

Sedwick, 1974; Mehta and Hou, 1974).














CHAPTER III

METHOD FOR DETERMINING
DELTA VOLUME AND GROWTH



3.1 Database

Data included in this compilation of the relevant inlet parameters were primarily obtained

from existing sources, and secondarily calculated in this study. These parameters include ebb

delta volumes, inlet throat width, average water depth at the throat, throat cross-sectional area,

spring tidal prism, annual average deep water significant wave height and wave period, and the

spring sea tidal range. These parameters are tabulated, and when available, by year for each

inlet, in Appendix A. The majority of the data were obtained from the literature in the Coastal

Engineering Archives of the Coastal and Oceanographic Engineering Department (COE) at the

University of Florida. Specifically, reports and studies published by COE and other universities,

private engineering consultants, Florida Department of Natural Resources (FDNR), and the U.S.

Army Corps of Engineers. Information was also obtained from the periodicals and journals

housed in the Archives, as well as nautical charts and bathymetric surveys.



3.1.1 Ebb Delta Volumes

Ebb delta volumes were found for eighty-one inlets on the three coasts of the United

States, of which forty-five are in the State of Florida of the 189 volumes, 182 were found in the

literature and 7 estimated as described in Section 3.2.










3.1.2 Tidal Prism

Spring tidal prisms in Appendix A have either been reported in other documents or have

been obtained from Jarrett (1976) based on the formula of O'Brien (1969), knowing the throat

area. O'Brien (1969) found the following relationship between the throat cross-sectional area and

the spring tidal prism:


P = aA b(3.1)


where Ac = throat cross-sectional area (m2) and P = tidal prism (m3). The coefficients a, and

b, where found for sandy inlets in equilibrium under a semi-diurnal tide. Jarrett (1976) later re-

analyzed this relationship based on data from inlets along the Atlantic, Pacific and Gulf of
Mexico coasts. In this study, the tidal prisms for both the Atlantic and Gulf of Mexico inlets

were calculated with the coefficients determined for 0, 1 or 2 jetties given by Jarrett (1976).

Coefficients for the Atlantic inlets, a, = 1.94 x 104 and b1 = 0.95, and for the Gulf of Mexico,

a, = 4.06 x 103 and b1 = 1.19 were used to calculate tidal prisms.


3.1.3 Cross-Sectional Area

Minimum or throat cross-sectional area for the inlets are reported from existing

documents, or calculated from United States Geological Survey (U.S.G.S.) quad sheets or

National Ocean Service (NOS) Nautical Charts. Cross-sectional areas were obtained by

measuring across the distance across the inlet throat to obtain the inlet width. The width was

then multiplied by an estimated average depth across that line.


3.1.4 Significant Wave Height and Wave Period

Deep water significant wave heights, H,, were obtained from Hubertz and Brooks (1989)

and Hubertz et al. (1993). The hindcast wave information covers a twenty year period from 1956

to 1975 for 108 stations along the Atlantic coast and 51 stations along the Gulf of Mexico coast.

Yearly average height from the station closest to the inlet of interest was used for the year

corresponding to the volume.








28

Mean wave periods were obtained from U.S. Army Corps of Engineers, Coastal

Engineering Research Center (CERC) (Brooks, 1994a, 1994b unpublished) through a special

request. A twenty-year average characteristic value was calculated from these data for the same

stations for which wave heights were obtained.


3.1.5 Spring Sea Tidal Ranges

Spring tidal ranges, 2as, were calculated from Balsillie (1987a, 1987b, 1987c) for the

coast of Florida as the difference of the mean higher high water and mean lower low water

levels. Tidal ranges at locations outside Florida were obtained from two sources: 1) USGS quad

sheets; and 2) NOS Nautical Charts.


3.2 Ebb Delta Volume Estimates

The purpose of this exercise was to examine the procedure developed by Dean and

Walton (1973) for estimating the ebb delta volumes. The first task was to estimate the necessary

volumes, and the second to evaluate the effect of interpretation of bathymetric conditions on the

estimated volumes.


3.2.1 Ebb Delta Volumes

Seven bathymetric surveys were selected to estimate delta volumes. The next step using

each survey was to draw shore-perpendicular lines on either side of the inlet to obtain a

representative "no-inlet" profile. These two lines were located at a distance from the inlet in an

effort to minimize the influence of the inlet on the contours. Equal depths along the two lines

were connected to develop a "best-fit" contour configuration overlain on the survey (Figure III-1).

The "best-fit" contours, although drawn somewhat subjectively, represent the bathymetric

conditions as if no inlet was present. A grid pattern was then superimposed on the survey. The

size of the grid cells selected was somewhat subjective; however, the choice in general is

dependent upon the complexity of the bathymetric relief to detail the changes in elevation. If the









29

bathymetry shows depth undulations with irregular elevation changes or small pockets of sand

bars, then the grid cell size should be small. However, if the change in elevation is

comparatively smoother, more gradual, the grid cell size can be larger. The elevation differences

at each of the four intersections were estimated within 0.15 meters and averaged for the cell.

The average elevation of each of the grid cells were then summed and multiplied by the total

surface area of all the grid cells to obtain the ebb delta volume.

SNaturaI Contour

......... ............... ........... ... ...........
......... ...... ...............
... Se......... .......eward Contour CA)
....... --------------- ---------
Landward Contour CC- ..-'
.-" "Bet-rP-l Contour CB3



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




Barrie Brrir Is 1 3n




Figure III-. Schematic of three "no-inlet" contour conditions in estimating ebb delta
volumes. Seaward exaggerated contours, A (dashed lines), "best-fit"
contours, B (solid lines) and landward exaggerated contours, C (thick
dotted lines).



3.2.2 Sensitivity Analysis

Dean and Walton (1973) had each estimated the volumes of eight ebb deltas to evaluate

the differences in the quantities due to the individual interpretation of the natural "no-inlet"

contours. The intent of the following exercise was to examine changes in the volumes due to:

1) varying the position of the "no-inlet" contours, and 2) changing the grid cell size. For each

of the seven bathymetric surveys mentioned in Section 3.2.1, three "no-inlet" contour positions

(Figure III-1) were used to estimate the delta volumes. The first step was to determine the








30

volumes from the "best-fit" contours. Next, two additional volume computations were made for

each of the surveys by slightly exaggerating the contours landward and seaward, with the ends

remaining at approximately the same locations. The distance of the landward and seaward

exaggerated contours were subjective, but an attempt was made to retain a reasonable

representation of the "no-inlet" contours. The results of this exercise are given in Section 4.1.1.

The next issue was to examine the variation in the volumes due to a change in the grid

cell size (Figure II-2). This was undertaken by doubling the size of the initial grid cells for each

of the volumes computed as described above. The elevation differences of the initial grid cell

located at the intersections of the doubled grid size were used to calculate the average elevation

difference each of the grid cells.


Figure III-2. Schematic of the initial grid and enlarged grid cell patterns used in
estimating ebb delta volumes.








31

3.3 Diagnostic Examination of Seafloor Evolution

As noted in Section 2.2.2, with the opening of an inlet the ebb delta volume increases

as the inlet tidal current deposits material derived from the littoral system and ultimately reaches

an equilibrium volume when the condition of no net deposition is attained. This process of

monotonic accumulation is influenced by wave action and its seasonal as well as year-to-year

variation. To examine the influence of the effects of current and waves on the growth rate of ebb

deltas, a diagnostic approach is developed. The growth process of the delta will have an initial

condition of a new inlet with no delta present (Figure I-3.A). Delta accumulation height, d,

will be simulated by modeling tidal currents and superimposed waves to determine the combined

shear stress, 7b. The seafloor will continue to rise on the condition that the combined shear stress

is smaller than the critical value, rcr for scour/deposition (Figure III-3.B). The model must then

determine the delta volume when the seafloor reaches an equilibrium elevation, de, due to a

balance of the shear stresses, i.e. ,b = rcr (Figure III-3.C), and estimate the time for the

equilibrium condition to occur. Derivation of the model is presented in Section 3.3.1 and the

corresponding Fortran algorithm is found in Appendix B.

An important point to note is that for the model development, the tidal period will be

considered to be the smallest time-scale. In another words, processes which actually occur over

flood and ebb phases of flow will be treated in a composite manner over the duration of the tide.



3.3.1 Model Development

The net decrease of suspended sediment mass per unit delta bed area, m, with respect to

time is given by


= F (3.2)
dt '












A:) Barrier Island


UI U "
I
.. L0 'cr Seaf I oor

Inlet Channel
B)


U -- U Uc--- b <%cr




C)


U- Uo --- c--- r
ho r- ^//
F W MMIde

Incrementa I Deposition


Figure UI-3. Seafloor growth diagrams illustrating the evolution of an ebb delta: A) initial
condition, B) transient condition and C) equilibrium condition.



where F, = settling flux is defined as


F, = -i'C, (3.3)

where W', = effective settling velocity of the particles and C, = depth-averaged suspended

sediment concentration. The effective settling velocity is defined as


pW, (3.4)

where = probability of sediment deposition and W, = particle settling velocity. Krone (1962)

characterized p according to











p = (3.5)
Tcr

where Tb = combined bed shear stress due to waves and current, and cr = critical bed shear

stress. Deposition can occur only when Tb < Tr (p > 0). The settling velocity (Schiller etal.,

1933) can be expressed as



W, a P P, (3.6)
W 3CD Pw

where p, = particle density, p, = seawater density, dso = median particle size, g = acceleration

due to gravity, and CD = drag coefficient. The value of CD outside the Stokes range (Reynolds

number < 1) decreases rapidly then levels off and becomes nearly constant (e.g. 0.43 for spheres)

in the fully turbulent flow regime considered.

Equation 3.2 can thus be expressed as


=- Hf b)W, (3.7)



where Hf [x] = heavyside function such that Hf [x > 0] = x, and Hf [x 0] = 0. Next,


pd = AD ] (3.8)

where pd = dry bed density, AD = ebb delta deposition area, m = mass, and V = delta volume.

Furthermore,

dV = dhA, = d(d)AD (3.9)

where dh = change in water depth and d(d) = change in ebb delta height. Substituting Eqns.

3.8 and 3.9 into Eqn. 3.7 results in:











dh W. CIC, ib (3.10)
dt Pd cr)


Given W,, C,, and Pd, Eqn. 3.10 can be solved provided 7b and Tcr are determined.

Komar and Miller (1974) found that data for sediment threshold under oscillatory flows closely

agreed with Shields' (1936) relationship for incipient grain motion under unidirectional flows.

Thus, the work by Shields (1936) for fully turbulent flow can be used to determine the critical

shear stress, cr, for waves and current combined:

Tr, = 0.058(p,-p)gdso (3.11)

where p, = density of seawater. Grant and Madsen (1978) prescribed the following relationship

for shear stress, TI,, due to both current and waves:


4 = 0.5 p, f U (3.12)

where U, = total velocity due to waves and current at the seafloor. The friction factor due to

the combined current and waves, fw, is equal to


SIUc Ic f+ IlUb w (3.13)


where fc = friction factor due to current, f, = friction factor due to waves, Ucb = near-bed

current velocity over the delta, Uwb = near-bed orbital velocity due to waves can be obtained

from linear wave theory (Dean and Dalrymple, 1984a):

UWb H cosh(kh) (3.14)
T sinh(kh)

where k = wave number equal to 2r/L, L = wave length, T = wave period and h = water depth

at the delta. As a wave train propagates from offshore into shallower water, the wave height








35

changes as the depth changes. According to linear wave theory (Dean and Dalrymple, 1984b),

the shoaled wave height, H can be expressed as



H H = 2c b, (3.15)


where bo= distance between two adjacent deep water wave rays, b, = distance between two

adjacent nearshore wave rays, Co = deep water wave celerity equal to gT/2ir, C = shallow water

wave velocity equal to (gh)'2, and H,= deep water wave height. Waves approaching the

shoreline in shallower water begin to decrease in celerity and the wave crests tend to align

parallel with the contours of equal bathymetry. As the delta grows these contours are extended

seaward, thereby causing refracting waves to transport material from the adjacent updrift and

downdrift beaches toward the inlet. However, ignoring the refraction process for simplicity, for

the derivation of this model the contours are assumed to remain straight and parallel. Thus, the

refraction coefficient (bo/b,)u2, is set equal to unity.

Grant and Madsen (1978) define U,, the total current velocity due to waves and current

as


Ut = (U b+U,+2Ucb Uwbcos)2 (3.16)

where 4 = angle between the current and wave direction. During ebb flow, when 4 = 7, the

momentum of the ebbing water mass causes the incoming waves to break seaward of the ebb

delta. Conversely during flood flow, when 0 = 0, the waves are able to penetrate over the delta

and into the inlet channel. It is assumed that the combined effect of waves and current over a

tidal period is represented in this model by selecting 4 = 0.

The material is deposited over a certain area as the ebb flow velocity decreases. By

considering the ebb jet boundaries to remain attached to the shoreline, and the entrainment of









36

ambient water into the ebb jet small compared to the tidal prism, this area (Ap) is notionally

defined as the tidal prism divided by the depth of flow (Figure III-4.A). The relationship

between Ap and the ebb delta deposition area, AD, is developed in Section 3.3.2.1.

A) B3

AP
AD
I n let
Channe I









Figure 11-4. Plan view of A) tidal prism based area (Ap), and B) delta deposition area
(AD).



The first step to determine the current velocity over the ebb delta is to obtain the

maximum velocity through the inlet for a spring tide is found from O'Brien (1969):


U 0.86P (3.17)
-tA,

where P = spring tidal prism, T, = tidal period, and Ac = throat cross-sectional area of the inlet.

The average inlet velocity over one-half tidal cycle is then obtain from


2 U. (3.18)


As the flow exits the inlet channel it is considered to spread out from the inlet mouth.

To obtain a characteristic velocity, Uo, at the shoreward end of the deposition area, this velocity

is assumed to occur along an arc, one-half the distance, re, from the entrance mouth to the outer








37

edge of the area A, (Figure mI-4.A), where re is obtained from continuity according to



r 2A= p (3.19)


Thus, Uo is obtained from


Uo (3.20)
7r,

where w = width of the entrance.

As the seafloor rises, the water depth decreases with respect to the initial water depth,

whereby to maintain the continuity of flow, the current velocity over the delta, Uc, must increase

(Figures III-3 and 111-5). As Uc decreases with distance as the flow spreads out over the delta

from its inner to outer limit. For the present purpose, Uc will be defined as its value at the inner

limit of the delta. It should also be noted that the velocity profile of Uc is vertically uniform, it

is therefore necessary to apply a correction factor to obtain the near-bed velocity, Ucb.

From the logarithmic velocity profile (Mehta, 1978), the ratio of the near-bed velocity,

Ub, to the depth averaged current velocity, Uc, is defined as


Ub In(zbzo) (3.21)
U, Iln(h lz)-


where Zo = theoretical origin of the logarithmic profile, and zb = distance above profile origin

and is set here equal to 0.05 m. From the Manning-Strickler formula, zo can be obtained by


z, = 107n6


(3.22)
















Ebb de ta
outer limit


Figure 111-5.


Cross-sectional view and plan view through the inlet and idealized ebb delta.


Mehta and Ozsoy (1978) noted that a representative Manning's n value of 0.028 can be used for

sandy inlets, and with an initial water depth 4.0 m used in Chapter IV, the ratio of near-bed

velocity to the mean velocity was determined. Thus, the current velocity obtained by continuity

is multiplied by a correction factor of 0.40:


(3.23)


Ulb O0.40UOh


where ho = initial water depth. Note that when the equilibrium delta volume is attained, U =

Ucr, hence Ub = Ur = 0.40 Uo (holh), where h, = equilibrium water depth.

Inserting Eqns. 3.11, 2.12, 3.13, 3.14, 3.16, 3.17, 3.20 and 3.21, into Eqn. 3.10, results

in the governing equation for water depth variation with time, and is expressed as












dh W,C, p,,f (H)2coshkh U+0.16 h Hacoshkh Uho (3.24)
1 [ +0.16 +
dt pd 2~- 4sinh2kh h 2.5sinhkh h

Eqn. 3.24 can be functionally expressed as

h = F(h) (3.25)
dt

This equation was solved by using the 4-th order Runge-Kutta iteration method:

h,., = h,+ (k1+2k +2k,+k) (3.26)


k,=AtF(h,) (3.27)


k=AtF h,+ (3.28)


k,=AtF h+ -(3.29)


k,=AtF(h,+k) (3.30)

where h, = incremental change in water depth, for i= 0,1,2,..., j-1, kl,2,3,4 = intermediate

method steps, and At = time increment in number of tidal periods.

The incremental change in delta accumulation, Ad, can then be multiplied by the

depositional area, AD, to obtain the ebb delta volume, V. The cumulative volume change is then

plotted to illustrate the effects of waves and currents on ebb delta growth rate and estimate the

duration to achieve an equilibrium volume.









40

3.3.2 Model Parameters

3.3.2.1 Ebb delta area

It is necessary to identify the ebb delta area, AD, over which deposition occurs. This was

achieved by empirically correlating Ap defined in Figure III-4 with AD based on measurements.

Davis and Gibeaut (1990) digitized ebb delta features of Florida's lower Gulf Coast inlets from

aerial photographs, and estimated the delta surface areas. Of these, 21 ebb delta areas were

found to be temporally consistent with the tidal prisms from the database in the present study

(Appendix C). The surface area, Ap, characterized by spring tidal prism, P, was obtained from


A, (3.31)
2a,

The plot of Ap against AD is shown in Figure III-6.

45 -1 11 1 1 1+111 1 I I III 1 I'' "I I I I III + '1 + -
w| 3
S2 -
+
1000000 ................ ................. .... ..
S6 +

I 4 -



S 100000 ... ........................









Ebb Delta Area, Ap (m2) Tidal Prism Method



Figure III-6. Ebb delta area, AD, versus tidal prism based area, Ap, for twenty-one inlets based
on data of Davis and Gibeaut (1990).
100000 2 3 4 1000000 2 3 4 le+007 2 3 4
Ebb Delta Area, Ap (m2) Tidal Prism Method



Figure III-6. Ebb delta area, AD, versus tidal prism based area, Ap, for twenty-one inlets based
on data of Davis and Gibeaut (1990).








41

Regression analysis resulted in r2 = 0.65 indicating a reasonable correlation between the AD and

Ap. The equation of the regression line relating the Ap and AD is


A = 2.34AO.8 (3.32)

Equations 3.31 and 3.32 were used in the model to determine AD from P and ao,,

assuming their applicability to the inlets considered.



3.3.2.2 Suspended sediment concentration

Downing (1984) presented a time-series of sediment concentrations at three locations

across the surf zone at Twin Harbor Beach, Washington. The investigator found two distinct

types of vertical concentration profiles. The first occurred between resuspension events, when

the sediment concentration had vertical uniformity, while during resuspension events a significant

concentration gradient occurred within approximately 0.10 m height above the bed in a total

water column depth of 0.25 m. The uniform concentration between resuspension events ranged

from 0.0002 to 0.0004 kg/m3 and approximately 0.0015 to 0.0100 kg/m3 during resuspension

events. In the present study, the influence of depth-averaged concentration, C,, ranging from

0.00005 and 0.00020 kg/m3 will be examined.



3.3.2.3 Friction factors

The friction factor due to current (f) is proportional to the square of Manning's n and

inversely proportional to the cubic root of the water depth, h (Mehta, 1978):


S- 8gn2 (3.33)
c h

As mentioned, Mehta and Ozsoy (1978) noted that a typical mean Manning's n value of 0.028








42

can be used for sandy inlets since the mean grain size at most inlets range between 0.2 and 0.4

mm. The initial water depth used to model the evolution of the ebb deltas in Chapter IV

averaged 4 m, resulting in a characteristic friction factor due to current of 0.039. It should be

noted that Mehta (1978) determined friction factors for three inlets on the Gulf Coast of Florida

ranging between 0.021 to 0.050.

The friction factor due to waves (f,) was obtained from the wave friction factor diagram

developed by Jonsson (1965) which plots the friction factor against the wave Reynolds number

defined as


R U, b (3.34)


where Ub = maximum near-bed orbital velocity due to waves, = maximum near-bed

horizontal excursion and v = kinematic viscosity of seawater. The maximum orbital velocity,

Uwb, and maximum horizontal excursion, b,, are obtained from the linear wave theory for shallow

water waves (Dean and Dalrymple, 1984b):


SH (3.35)
Uwb 2 h



H (3.36)
2kh

Given the typical initial water depth of 4 m, deep water wave height equal to 0.4 m, and wave

period of 8 seconds, R, = 1.7 x 104. From Figure 6 in Jonsson (1966), this wave Reynolds

number corresponds to the fully turbulent flow range. Given the typical variation of Re in the

present study, a representative value off, = 0.005 in the fully turbulent flow range was chosen.

It should be noted that bothfc andf, are water depth dependent, however, for simplicity,

both friction factors will be held constant (0.039 and 0.005, respectively) in this study.










3.3.2.4 Sediment grain size

Mehta and Ozsoy (1978) noted that for sandy inlets the median grain size at most inlets

range between 0.2 and 0.4 mm. This range will be considered in the present study.



3.3.2.5 Deep water height and period

As described in Section 3.4, the deep water wave height has a significant effect on the

growth rate of the ebb delta and its equilibrium volume. By adjusting the wave height, the delta

volume-time curve can be made to pass through the appropriate smallest and largest measured

delta volumes at a given inlet. Deep water wave heights obtained in this way are given in Table

IV-4. A characteristic wave period of 8 seconds will be used for all model runs.



3.3.2.6 Tidal inlet characteristics

The tidal inlet characteristics utilized in the analysis are derived from the database in

Appendix A. Specifically, the characteristics include: inlet throat width, throat depth, tidal

prism, and spring tidal range.



3.4 Effects of Important Parameters on Delta Growth

The effects of important parameters on the rate of delta formation at coastal inlets is

examined. The three selected parameters are 1) suspended sediment concentration, C,; 2) median

sediment grain size, d5o; and 3) deep water wave height, Ho. The influence of varying these

parameters on the volume growth curves are next shown in plots of ebb delta volume versus time,

beginning with a new inlet with no delta. The range of values of these three parameters are given

in Table III-1. Also given are other model input parameters including wave period T, spring tidal

prism P, spring tidal range 2a,, inlet throat width w, and water depth ho, current friction factor

f,, and wave friction factorf.








44

3.4.1 Variation in Suspended Sediment Concentration

In the Eqn. 3.22 for the rate of water depth change, dh/dt, is proportional to the

suspended sediment concentration, C,. Figure III-7 plots the ebb delta volume, V = AD(ho-h),

versus time (years) for three suspended sediment concentrations.

The first characteristic that is evident from the growth curves is that the equilibrium ebb

delta volumes are the equal (1.4 x 106 m3) for the three concentrations. However, it is evident

that as C, increases the rate of deposition becomes more rapid. For a concentration of 0.00005

kg/m3, the equilibrium volume is reached in approximately 60 years from the initial formation

of the inlet. By doubling this concentration to 0.00010 kg/m3, the deposition rate is increased,

achieving equilibrium in 25 years. If the concentration is doubled again, to 0.00020 kg/m3, the

time for the delta to achieve equilibrium is reduced to 15 years.



3.4.2 Variation in Sediment Grain Size

Two physical parameters are dependent on the median grain size diameter, dso, the

settling velocity (Eqn. 3.6) and the critical shear stress for sediment transport (Eqn. 3.11). The

ebb delta volume versus time plot for varying sediment diameters (Figure III-8) is characterized

by three different growth rates and equilibrium volumes. For a dso of 0.2 mm, the ebb delta

achieves equilibrium in approximately 50 years as compared to 40 years for a dso equal to 0.3

mm, and 30 years for dso equal to 0.4 mm. The increase in the sediment diameter increases the

rate of deposition, due to the dependence of particle fall velocity on sediment size. An increase

in the sediment size also increases the critical shear stress, allowing the sediment bed to remain

more stable as compared to a bed composed of smaller grain size under the same flow conditions.

This effect results in an increase in the equilibrium volume for increasing grain diameters.



















Cs =i0.000 0 kg/m3
. ..... ........ ............. .............. ... ....... ..... .. .. ............. .......... ...






) 10' I 0 0 40 50 00010 0 80 0 1
........ ...... ...... ... .. ......... .............. ............. ............ ...... ... .. .... .. ..... .. .......

.... .. ............. ............... I ............. ............. ............. ............. .............
S/ Cs= 0.00005 kg/Mn3
S........... ............. ........................... ............. ........... .............


IF I /

4 1 ... .... .. ..... ...... .


) 10 20 30 40 50 60 70 80 90 100
Years


Figure III-7.


Ebb delta volume versus time comparing the effects of three suspended sediment
concentrations, Cs, 0.00005, 0.00010, and 0.00020 kg/m3. Runs 1, 2 and 3.


2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0


Figure HI-8.


0


10 20


40
Years


50 60 70 80


Ebb delta volume versus time comparing the effects of three grain size diameters,
dso, 0.2, 0.3 and 0.4 mm. Runs 4, 5 and 6.


............. ... ... 4 n.....
............... ........... /.';. .............. i............... ..................................................................
Si d5o= 0.3mmr


I :
......... ....... ................ ..... .................. .... ................ .. .............. i ......... .....

" i : :

!, ...... ...... ............ .. ".............. ............... ................ ....... ......... .............. ...................
I ..


















Initial input parameters for examining the effects of variations in suspended sediment concentration, C,,


grain size diameter, ds, and deep water wave height, Ho on ebb delta growth.

Run C, dso Ho T P 2a, w h, fc /f
(kg/m3) (mm) (m) (s) (x106 m3) (m) (m) (m)

1 0.0002 0.35 0.4 8.0 6.50 1.00 109 4.0 0.039 0.005
2 0.0001 0.35 0.4 8.0 6.50 1.00 109 4.0 0.039 0.005
3 0.00005 0.35 0.4 8.0 6.50 1.00 109 4.0 0.039 0.005
4 0.0001 0.20 0.4 8.0 6.50 1.00 109 4.0 0.039 0.005
5 0.0001 0.30 0.4 8.0 6.50 1.00 109 4.0 0.039 0.005
6 0.0001 0.40 0.4 8.0 6.50 1.00 109 4.0 0.039 0.005
7 0.0001 0.35 0.0 8.0 6.50 1.00 109 4.0 0.039 0.005
8 0.0001 0.35 0.4 8.0 6.50 1.00 109 4.0 0.039 0.005
9 0.0001 0.35 0.8 8.0 6.50 1.00 109 4.0 0.039 0.005


Table III-1.











3.4.3 Variation in Deep Water Wave Height

As the waves approach the shoreline, its height increases as the water depth decreases

(Eqn. 3.15). This increase in wave height in turn increases the near-bed orbital velocity, Uwb,

hence reduces the rate of deposition. Figure III-9 plots the ebb delta volume versus time

illustrating delta growth due to current alone, i.e. 0.0 m wave height, and two additional deep

water waves heights of 0.4 and 0.8 m.

During sea conditions when the deep water wave height is equal to 0.0 m, the rate of

deposition is observed to be relatively rapid compared to the other two wave conditions. For a

wave height of 0.0 m the equilibrium volume is reached in 20 years and the time is doubled to

40 years to achieve equilibrium for a 0.4 m wave. Equilibrium requires an additional 10 years

when the wave height increases from 0.4 to 0.8 m. Note also the drastic decrease in the

equilibrium volume with increasing Ho.



2.5H OOm

3.0 . I .

S 1 .5 .............. .. ............................... .............. ...................
0 .o





0.0
0 10 20 30 40 50 60 70
Years

Figure III-9. Ebb delta volume versus time comparing the effects of three deep water waves
heights, Ho, 0.0, 0.4, and 0.8 m. Runs 7, 8 and 9.














CHAPTER IV

RESULTS



4.1 Ebb Deltas

4.1.1 Estimated Delta Volumes

Seven surveys from a total of four inlets were found to have adequate bathymetric data

to estimate ebb tidal delta volumes by the Dean and Walton (1973) method noted in Section

2.2.1. Each survey had a "best-fit", "no-inlet" contours (contour B in Figure III-1) and a grid

system superimposed on the bathymetry (Figure III-2). The grid cell size was determined

subjectively to provide a tight coverage of the seafloor undulations in order to obtain an

appropriate estimate of the delta volume, as described in Section 3.2. Table IV-1 presents the

size of the grid cells and the estimated delta volumes for each of the seven surveys.



Table IV-1. Ebb delta volume for the "best-fit", "no-inlet" contours.

Inlet Year Grid size (m) Delta volume (x106 m3)

Ponce de Leon 1944 152 2.91
Jupiter 1957 76 0.38
1979 152 0.68
1993 76 0.74
South Lake Worth 1968 61 0.67
Clearwater 1972 122 2.03
1976 122 1.29










4.1.2 Delta Volume Sensitivity Analysis

The ebb delta volume estimates due to the imposed change in the "no-inlet" contour

positions are given in Table IV-2, and due to change in the grid cell size in Table IV-3. The

contours A, B, and C, are described in Section 3.2.1 (Figure III-1), and the change in the grid

cell size in Section 3.2.2 (Figure 111-2). The results in Table IV-2 include the location of the

survey, the year of the survey, and the grid cell size for which the volume was estimated in

columns one, two and three, respectively. The forth column, with the heading "contour A" is

the delta volume obtained using the smallest grid cell size and the "no-inlet" bathymetry for the

seaward exaggerated contour position. The same column contains the percent difference in the

volume estimated from contour A to that of the delta volume resulting from the "best-fit", "no-

inlet", contour B. The ebb volume estimated from the position of contour B and is given in the

fifth column. The sixth column, "Contour C", contains the volume resulting from the landward

exaggerated "no-inlet" bathymetric condition, and the percent difference between volumes

estimated from contour positions B and C. Finally, the last column contains the percent

difference in estimated ebb delta volumes between contour positions A and C.


Table IV-2. Delta volumes and percent differences due to changes in the "no-inlet" contours.
Delta Volume (x106 m3)
Inlet Year Grid Size Contours A Contours B Contours C Contours
(m) A-C
Ponce de Leon 1944 152 2.60 (-11%) 2.91 3.38 (+14%) +23%
Jupiter 1957 76 0.25 (-34%) 0.38 0.45 (+16%) +44%
Jupiter 1979 152 0.63 (-7%) 0.68 0.78 (+13%) +19%
Jupiter 1993 76 0.71 (-4%) 0.74 0.87 (+15%) +18%
South Lake Worth 1968 61 0.55 (-17%) 0.67 0.83 (+20%) +34%
Clearwater 1972 122 1.91 (-6%) 2.03 2.29 (+11%) +17%
Clearwater 1976 122 1.11 (-14%) 1.29 1.43 (+10%) +22%








50

The percent difference of the volume estimates between the three contour positions range

from -34% for Jupiter Inlet, 1957, between contours A and B to +44% for Jupiter, 1957,

between contours A and C. Note that the highest percent difference can be expected to occur

between the two surveys with the greatest horizontal change (landward versus seaward) in the

contour positions. By moving the "no-inlet" contour positions landward (C) would result in a

comparatively thicker lens of sand and therefore a larger ebb tidal delta volume. Conversely,

moving the contour positions seaward has the opposite effect by reducing the sand lens thickness,

thus resulting in a comparatively smaller delta volume. The percent differences corresponding

to the "best-fit" delta volume show that the minimum and the maximum percent change between

A and B, and B and C are -34% and +16%, respectively.

Using the same contour configurations described above and doubling the size of the grid

cells from the initial grid pattern, the delta volume were re-estimated. The results of this exercise

are given in Table IV-3, where the forth, fifth and sixth columns respectively give the estimated

ebb delta volumes using the larger grid cells for the same contours A, B, and C. Also included

in each of the columns containing the delta volumes is the percent difference of volumes resulting

from the change in grid cell size for that particular contour position.

The volume percent difference were found to be dependent on the complexity of the

bathymetry. Comparatively straight, widely spaced contours have a tendency of resulting in

smaller percent differences. By having a constant (or near constant) slope between intersecting

corners, the volume of the enlarged grid is close in value to that of the volume of the four initial

smaller grid cells covering the same surface area. Where if the contours were irregularly spaced,

so that the omitted intersections caused a number of small shoals or depressions to be missed, the

change in volume between the grid cell sizes was relatively large. The percent differences for

changing the grid cell size ranged between -22% and +9%.








51

Table IV-3. Ebb delta volumes and percent differences due to changes in the grid cell size.
Delta Volume (x106 m3)
Inlet Year Grid Size (m) Contours A Contours B Contours C
Ponce de Leon 1944 305 2.82 (+8%) 3.28 (+11%) 3.66 (+8%)
Jupiter 1957 152 0.21 (-19%) 0.34 (-12%) 0.40 (-13%)
Jupiter 1979 305 0.56 (-13%) 0.58 (-17%) 0.64 (-22%)
Jupiter 1993 152 0.56 (-27%) 0.63 (-18%) 0.77 (-13%)
South Lake Worth 1968 122 0.57 (+3%) 0.68 (+2%) 0.82 (-2%)
Clearwater 1972 224 2.01 (+5%) 2.14 (+5%) 2.35 (+3%)
Clearwater 1976 244 1.22 (+9%) 1.31 (+2%) 1.49 (+4%)


The cumulative effect of the interpretation of the bathymetric conditions in selecting the

"no-inlet" contours and grid cell size is varied. For example, the 1979 Jupiter Inlet survey had

a relatively smooth, gradual change in the bathymetry. The estimated ebb volume for the "no-

inlet" seaward contours (A) with a small grid size (152m x 152m) was equal to 0.63 x106 m3,

and for a larger grid size (305 m x 305 m) with a "no-inlet" landward contours (C) the delta

volume was estimated to be 0.64 x106 m3, thus resulting in a relatively small change.

Conversely, the 1944 Ponce de Leon survey was more complex with large undulations including

small shoals. As a result, the difference in volume for the two contour and grid cell size

conditions was estimated to be 3.66 x106 m3 2.60 x106 m3 = 1.06 x106 m3.



4.1.3 Delta Volumes versus Tidal Prism

The ebb delta volume versus spring tidal prism relationship presented by Walton and

Adams (1976) and Hayter et al. (1988) found a significant relationship between the volume and

the spring tidal prism categorized by three wave energy levels (Section 2.2.2). This relationship

is re-examined here using delta volumes, tidal prisms, and synchronous wave data in an effort

to clarify the issue of the dependence of the volume-tidal prism relationship on wave energy.








52

The need for synchronous wave information limits the quantity of data available for

analysis. The tidal prism and ebb delta volume must be measured during the same year, and

these data must fall between 1956 and 1975, so as to be able to use the hindcast wave data

obtained from Hubertz and Brooks (1989), Hubertz, et al. (1993) and Brooks (1993a,b).

Twenty-eight sets of data met this criterion, of which twenty fell within the range characterized

by Walton and Adams (1976) as a mild energy coast (0-30 m2s2) and eight data as moderate

energy coast (30-300 m2s2). Note that the wave energy is characterized by the parameter, Ho2T~.

The regression plot of the tidal prism against the ebb delta volume characterized by mild

wave energy shows a fairly good correlation (Figure IV-1), yielding a regression line with r2 =

0.80. The equation of the regression line for mild energy coasts was found to be


V = 1.86x10-3P1.3 (4.1)

The data set for moderate energy coasts has more scatter around the regression line

(Figure IV-2) than seen for the case for mild coasts. The r2 = 0.45 indicates a poor correlation

of tidal prism against delta volume which may be due to the small data set used in this analysis.

Note also that the data scatter may also be due to the divergence of the V versus P values from

equilibrium. The regression line equation for moderate energy coasts was found to be


V = 5.49x10-P-3-2 (4.2)

Figures IV-1 and IV-2, show that the ebb delta volume does increase with increasing tidal

prism which is in agreement with the observations made by Walton and Adams (1976).

However, due to the small sizes of the data sets, it is inconclusive as to the precise influence of

wave energy on the tidal prism to delta volume relationship. Additional data within both wave

energy regimes are necessary to clarify this issue.

















le+008

+ +



0

+
le+007 "" ...................



+ +



1000000
le+007 le+008
Tidal Prism, P (m3)

Figure IV-1. Ebb delta volume versus tidal prism for mild energy coasts (0-30 m2s2).








S l e + 0 0 8 ....... ............... ................................................... ---- -- ...................





V le + 0 0 7 ................................ .... ......... ........... .....................................-
le+le+00 7 O




*0 V









Tidal Prism, P (m3)

Figure IV-2. Ebb delta volume versus tidal prism for moderate energy coasts (30-300
2s ).
mV)2.










4.1.4 Time-Evolution of Delta Volume

The following analysis presents the time-evolution of sand volumes of four selected deltas

along the east coast of Florida including those at 1) Jupiter Inlet; 2) South Lake Worth Inlet; 3)

Boca Raton Inlet; and 4) Bakers Haulover Inlet. These inlets were chosen because 1) the date

when each inlet was opened were available, and 2) four or more data points were available per

inlet to represent the time-variation of ebb delta volumes. For each inlet, a plot of the measured

delta volumes versus date of survey with the corresponding volume ranges obtained from the

model is presented.

The theoretical volume curves were derived from the model using the specific

characteristics of the respective inlet. These data including 1) spring tidal prism, P; 2) inlet

throat width, w; 3) inlet depth, ho; and 4) spring tidal range, 2aos, along with other necessary

data presented in Section 3.3.2 are summarized in Table IV-4. By adjusting the deep water wave

height, Ho, and the suspended sediment concentration, Cs, the delta volume-time curves were

made to pass through the appropriate smallest and largest measured delta volumes.

The inlet stability parameter, a, introduced by O'Brien (1971) and defined in Section

2.4.1 (Eqn. 2.18) was later expanded by Mehta and Hou (1974) to provide an indicator of the

stability of inlets on the south shore of Long Island, New York. For the present study, a will

be used to provide an indication of the relative effect of waves and tidal current in governing the

rate of growth of the ebb delta. As the deep water wave height is increased at a given inlet, a

increases and reflects a tendency to drive material toward the inlet and the nearshore area, thus

limiting the delta volume. Conversely, if the deep water wave was set to zero, the corresponding

a would equal zero indicating a current-determined delta. This condition results in a larger ebb

delta volume as compared to a higher a-value for the same inlet when waves are present.






















Table IV-4. Initial input parameters and resulting wave to tidal energy ratio, a.

Inlet Cs dso H, T P 2a, w h, f fw a
(kg/m3) (mm) (m) (s) (x106 m3) (m) (m) (m)


Jupiter 0.00015

Jupiter 0.00015

South Lake Worth 0.00006

South Lake Worth 0.00006
Boca Raton 0.00010

Boca Raton 0.00010

Bakers Haulover 0.00020

Bakers Haulover 0.00012


0.35

0.35

0.35

0.35

0.35

0.35

0.35
0.35


0.54 8.0

0.68 8.0

0.19 8.0

0.28 8.0

0.39 8.0

0.46 8.0

0.62 8.0

0.63 8.0


6.46

6.46

1.59

1.59

5.50

5.50

10.20
10.20


1.00 109 4.2 0.039 0.005

1.00 109 4.2 0.039 0.005

0.94 30 3.3 0.039 0.005

0.94 30 3.3 0.039 0.005

0.90 50 3.6 0.039 0.005

0.90 50 3.6 0.039 0.005

0.82 110 3.7 0.039 0.005
0.82 110 3.7 0.039 0.005


0.17

0.27

0.03

0.06
0.05

0.07

0.17

0.18











4.1.4.1 Jupiter Inlet

Nine delta volumes were available for Jupiter Inlet since this entrance was re-opened for

navigation in 1947 (Figure IV-3). The non-zero delta volumes range between 0.23 x106 m3 and

0.77 x106 m3, for the years 1981 and 1993, respectively. The model was used to simulate the

growth curves matching this volume range. The a-value of 0.17 resulting from a Ho = 0.54 m

yielded a volume of 0.77 x106 m3 in 1993. The higher a-value of 0.27 was calculated for a Ho

= 0.68 m to modify the growth curve to achieve a volume of 0.23 x106 m3 in 1981. It is

therefore surmised that the relative wide range in the delta volumes between the two curves is

the result of waves relative to current. Larger delta volumes correspond to lower values of a and

vice versa. The maximum range of a being 0.17 to 0.27 for this inlet.

I I

0 .7 ...................... .............. ....... ................... .................... ............. ........ .......................

0 .6 -... -..... .. ..- -............ .... ....... ........... ......

0 .5 ....................... ....................... ........................ ........................ ........................ .......................
a = 0.17 [..-' i !
0



> 0 .4 ..................... ... ...................................................................................... ......................
0.6



-- -- 0 .5 -- - -
s ,'
S 0 .42 ...................- .... .................... ................. .................................. .............
S0.3 --------------------
S0..2" a =0.27
0 ,,.-...... ... .... '.................. ...............................................................................................
5,,
0 .0 ...... ........................ ................................................ ........................ .......................
1940 1950 1960 1970 1980 1990 2000
Year


Figure IV-3. Ebb delta volume versus year with model-calculated volume ranges for
Jupiter Inlet.




4.1.4.2 South Lake Worth Inlet

Six delta volumes for South Lake Worth Inlet were obtained since the entrance was

artificially opened in 1927 (Figure IV-4). A growth curve was passed through the lower ebb









57

volume of 0.54 x106 m3 with a Ho = 0.28 m resulting in an a-value of 0.06. Conversely, a

curve was unable to be passed through the largest volume of 2.27 x106 m3 estimated from a 1990

bathymetric survey because to achieve this volume would have required a larger delta area, AD,

than obtained from Eqn. 3.32. It was decided to consider the next highest volume of 1.07 x106

m3 (1969, 1979) for this analysis. To accomplish this, Ho = 0.19 m was used, which resulted

in an a-value of 0.03. Thus, with the exception of 2.27 x106 m3 the other volumes are contained

within the a range of 0.03 to 0.06.

2.4
S 2 .2 ................... .......................................... .................... ......................................... ........... ....


.o ................. ..................... .................... ...................... .................... ................... ..................... .... .
X 1 ...................................... .................... .................... .................... .................... ......................
1.6 ---.-



a = 0.03
S 0 ...................... ..........................
0.6



aa 01 ..--~~--~;-.-----------------
0 1 .................. .............. ............. .:. .............................. ..............


0 10-" a = 0.06"
0 .2 ...... 0 .8. .. ....- .. .................................. .... .... ..... .. ...................... .........
0.8 *. i

0 .0 ...... .. ............. .......... ..................... ....................-.................... ..................... .....

1920 1930 1940 1950 1960 1970 1980 1990
Year

Figure IV-4. Ebb delta volume versus year with model-calculated volume ranges for
South Lake Worth Inlet.


4.1.4.3 Boca Raton Inlet

Four ebb delta volumes were obtained for Boca Raton Inlet after the inlet was opened in

1925 (Figure IV-5). Two of the surveys resulted in a volume of 0.61 x106 m3 (1978,1983), and

the third was 0.84 x106 m3 (1981). Ho = 0.39 m resulting in an a-value of 0.05 passed through

the upper volume and Ho = 0.46 m (a-value of 0.07) through the lower volume.












0.9
0.9 ...... .......-----------------------
0 .8 ................... ....... .. .
:a = 0.05 :
0 .7 ................................... ............................................. .................... .............. ... .................
/7


0.5 ............. --....
S0.4 -
"- 0 .4 . .................... ..................... ................... ..0.0 7


0
0 .2 .............. .......................................... ..................... .................... ..................... ..................
o



S 0 1 ...... .......................... ........................................................................................
0.3 1

t 0.2

P 0.1
P 1:
0 .0 ........ .............................................................................................................................-
0.0 *
1920 1930 1940 1950 1960 1970 1980 1990
Year


Figure IV-5. Ebb delta volume versus year with model-calculated volume ranges for
Boca Raton Inlet.



4.1.4.4 Bakers Haulover Inlet

Four delta volumes were available for Bakers Haulover Inlet, including zero volume when

the entrance was artificially created in 1925 (Figure IV-6). A curve was passed through a point



S0.17 ----- -----
S 0.5
> 0 .3 ............... ... ........ ............................. ................................. ............... ..................
0 .............. .................... ...... ........................................-- -............................................

a 0.18
> 0 3 . . . .. . .. . .. . ... .. . . . .. . . . . . . . . . . .




I
S 0 ...... ........ ... .................. .............................................................. ..................... ................... .
0.0 "

a :


1920 1930 1940 1950 1960 1970 1980 1990
Year


Figure IV-6. Ebb delta volumes versus year with model-calculated volume ranges for
Bakers Haulover.









59

occurring three years after the inlet was opened (0.23 x106 m3) and the largest available volume

of 0.46 x106 m3. This was accomplished with He = 0.62 m resulting in the a-value equal to

0.17. For the lower curve He = 0.63 m had an a-value equal to 0.18, thus defining an a range

of 0.17 to 0.18.



4.1.4.5 Influence of a on delta growth

Table IV-5 presents a comparison of the ebb delta volume ranges and the corresponding

wave to tidal energy ratio, a, for each of the four inlets. As a increases, the ebb delta volume

has a tendency to decrease, and vise versa. Figure IV-7 further illustrates this trend. Although

there is data scatter and a r-value of 0.60, which is low, the regression line does show that there

in an inverse relationship between the delta volume to a. The equation of the regression line

relating a and V is


V = 0.17a-050 (4.3)

Note that V in this case may not represent the actual equilibrium value, but may be close to it,

given the manner in which the curve fitting was conducted.


Table IV-5. Comparison of wave to tidal energy, a, and the corresponding delta volumes.

Inlet a V (x106 m3)
Jupiter 0.17 0.77
Jupiter 0.27 0.23
South Lake Worth 0.03 1.07
South Lake Worth 0.06 0.54
Boca Raton 0.05 0.84
Boca Raton 0.07 0.61
Bakers Haulover 0.17 0.46
Bakers Haulover 0.18 0.38











60


S1 I : : I; '. I I I I I I '. 'I' 1. I I I !

100 .
0 ...... ,.- -... ... .. -. -- b -.- ; . : .i ... ... -.....i.i.i. .... .... .......... -.. -
9-



5 ... .-.- ......- ....... ...-.----. ..-.... .. -.. ..-...... ..... .... .. ....... ...... .... ..... .... ..-..
S: /..:. ...... ....... ......
.-.-i --' .. .. ..i-- ". ..... .. .. .

!'"!"'": ".'": ":": "!'.'! . """ "" ":: ':::'" ...... ........ : -- .......

i .;" !'"~i \ ". .. "............ .... ". ..'.....L ..I..+ ...
a a






F E

"4 i i ;4 i A, .














ba
2~~~~~ mi:Ip ii:ii iiii:i iii
2 3 4 .... a 7 8 --O- 2 3-
J '''''"""a
Figure I-7. Ebbdelta voume aganst waveto tida energy atio, a














CHAPTER V

CONCLUSIONS



5.1 Estimated Ebb Delta Volumes

Personnel interpretation of the bathymetric condition at an inlet measurably influences the

estimated delta volume based on the method of Dean and Walton (1973). The percent difference

due to a change in the "no-inlet" contour positions from the a "best-fit" contour positions ranged

between -34% and +20%, and as much as 44% between the landward and seaward exaggerated

"no-inlet" contours. The choice of grid size also effected the estimated volumes, ranging between

-22% and +9%. In general, the percent volume difference appears to be dependent on the

complexity of the bathymetry. Straight, widely spaced contours have a tendency of resulting in

smaller percent differences as compared to irregularly spaced contours where small shoals or

depressions may be missed, thus resulting in comparatively larger volume differences.



5.2 Ebb Delta Volume versus Tidal Prism

The ebb delta volume versus tidal prism relationship presented by Walton and Adams

(1976) was re-examined in an effort to clarify the issue of the dependence of this relationship on

the wave energy. It was confirmed that the delta volume does increase with increasing tidal

prism; however, the precise influence of wave energy on this relationship could not be examined

conclusively due to the small number of data points. Note, however, that the exponential

correlation coefficient for Eqns. 4.1 (1.30) and 4.2 (1.25) found in this analysis are close to those








62

given by Walton and Adams (1976) for mildly exposed coasts (1.24) and highly exposed coasts

(1.23).



5.3 Effects of Significant Physical Parameters on Delta Growth

Three parameters, namely the suspended sediment concentration, sediment grain size, and

the deep water wave height, were varied in the diagnostic model developed for delta growth to

determined their effects on the rate of delta formation at coastal inlets. It was found that an

increase in the suspended sediment concentration increases the rate of approach to equilibrium,

but does not result in a change in the equilibrium volume. On the other hand, a change in the

sediment grain size and the deep water wave height effect both the rate of growth and the

equilibrium volume. Thus, an increase in the sediment diameter increases the rate of growth due

to the dependence of the particle fall velocity on sediment size, and increases the critical shear

stress resulting in an increase in the equilibrium volume. An increase in the deep water wave

height increases the near-bed orbital velocity at the site of the delta, hence decreases the rate of

growth. The equilibrium delta volume likewise decreases.



5.4 Effects of a on Equilibrium Delta Volumes

It was shown through the application of the model to four Florida inlets that there is a

dependence between the ebb delta volume and the wave to tidal energy ratio, a. An increasing

a-value decreases the accumulated ebb delta volume, and vice versa. This dependence of delta

volume on a partly explains the observed fluctuations in the delta volume at many inlets, since

a tends to vary seasonally as well as annually. Another cause of variation of the delta volume

at a given inlet is that even under constant sea conditions, the equilibrium volume often occurs

after several decades following the opening of an inlet. Thus the delta volumes measured during

the early years of evolution will be lower than the equilibrium volume.








63

5.5 Influence of a on Navigability

As noted in Section 2.4.1, Bruun and Gerritsen (1960) proposed a stability criterion in

which the condition for the inlet to remain open, and therefore the condition for navigation, are

shown to be dependent on the ability of the tidal current to remove the wave-driven littoral drift

deposited at the entrance. O'Brien (1971) and later Mehta and Hou (1974) noted that inlet

stability is governed by the relative dominance of wave energy and tidal energy defined by the

parameter a. In this study it was found that as a-values increased the corresponding delta

volume decreased, thus confirming the work of Walton and Adams (1976) whereby they found

the delta volume to be dependent on the tidal prism and on wave energy. Decreasing the delta

volume increases the controlling depth, thus providing additional underkeel clearance for a vessel

to navigate the entrance. By providing an understanding of the mechanism by which delta growth

is controlled by the prevailing physical parameters, this investigation also provides a potential

means to design safer navigation channels at coastal inlets.



5.6 Future Investigations

If future studies of the ebb delta rate of growth and equilibrium volume are to be

undertaken using the model developed in this study, it is recommended that one important change

be instituted. In nature, the combination of the ebb and flood flows causes the tidal current to

transport sediment toward the inlet from the adjacent shoreline during all tidal stages. It was also

noted that the forces acting to transport sediment are not only dependent upon the effects of ebb

and flood currents, but also on wave refraction which tends to transport sediment toward the inlet

from the adjacent shoreline. Modeling wave refraction and the resulting sediment transport in

the vicinity of an ebb delta was disregarded in the development of this model due to the

complexity of the process. In future studies, it would be a more realistic model to include








64

sediment transport in evaluating the effects of littoral drift on the rate of deposition and

equilibrium volume.



5.7 Note of Caution

The model presented in this thesis is preliminary and conceptual in nature. Many

simplying assumptions have been made with varing levels of justification. This effort is intended

to be a first attempt at understanding and estimating the dynamic nature of ebb tidal deltas.

Therefore attempts to apply the model to actual inlet conditions should be done with caution.














APPENDIX A

DATABASE





Key To Symbols



V ebb delta volume

w width at the inlet throat

ho water depth at the inlet throat

Ac cross-sectional area at the inlet throat

P spring tidal prism

H, significant deep water wave height

T 20-yr average wave period

2aos spring tidal range












8) 09'OZ tI) o0t'I tI) S'Z vI) 085 VC6I
8) L8"11 l) VZ8 I) L9"91T S6T plui uoa-
01) ES', 1 tZ6I op oouod

6) 99 I S) Z'L t) I'I i-OZ
8) II'T EI) SI6 I) O' ET) SOE 9) Z8t' 8L61
8) SO'1 El) 016 I) L'Z SI) OL LL61
8) LL'II I) L18 9L61
S) 6"9 0) 6"0 I) OZt'I CI) L06 tL61
S) 8"9 t) O'1 8) 21 I) t'Z9 EL61
S) L'9 t) o' 8) W96 tI) Z99 ZL61
S) 1L t) iI Z 8) 5r9T l) 191'I I) 9c V961 uI
8) EE'6 li) Oi9 t'6I SzUt Iri

6) Lg'1 S) I'L 0) 0I A-Og
) It,'8 6L61
) L'L t,) O'I I) 0918 I) 019'ti I) L'TI I) Ot' 9L61
5) O'L 0) I'1 tZ ZI) 0518 ZI) OE8't, 5L6I
z) 60'L Z) z g9' Z) o0* 8 5.6i luI
I) L1'09 VtZ6 oau.snnv "1S

6) Z81 5) I'L 0) 0oI 1J-OZ
II) 96"0 EL61
) 9"9 ') 6"0 LZ 01) L90t' V61i
01) 90'It M'6T
01) LL'LE ILSI puno" nfSSvN

6) 68T1 S) T'L t) 0OI Jx-oz
S) L'L i') 60 8) 09'6ZI L) OZ9'01 L) O'ZI L) S88 9) 01f'6 SL61
5) L'9 ') 8'0 LZ ) ijZ'LI )S gL'ZI I) 0E'96 tL61
z) LO'SEI Z) 8LE'I Z) 86'EOI S6IT auarvug
I) LV'06 OL81 sIAIAI -IS

(m) (s) (mi) UOTS Qm 901x) (m) (Um) (m) (Eu 90ox)
I'O I H ISOpu-IH rd v J/ M A aeAx WTI

Is oo ppolj aip SuoIe saoijua u Iisoo joj saiuolr-d paplaj ell-p qqa "I-V alcql
















IZ) 9"Z TZ) ool


OZ) S'Z
OZ) '*
OZ) 'Z
oz) S',
oz) 5';


oz) w'I
OZ) Z9
OZ) Ot'1
oz) tz
OZ) tcI


IC-oz
8861
ZZ) SI'I L861
9L61
ZZ) 08'0 tL61
961
Z961
1961
8561
6V61
8t'61
OZ) 000' Lt61
oz) oo00 t'Z61
OZ) 00'0 9881


6) OZ' 5) SL t') I'

9) Z't' 6L61
5) L I,) 1't 8) L'Z 60 OSL'I 61) 96"5 961
5) 9"L 0) Z'I 6I) SZ 8561
S) V/L V,) ZI 81 61) O'I 6I) 019'1 L561 oouluI
9) 00'0 1561 IJA~VUD VZ od

6) 'eI 5) )'L V) I'I is-Oz
tI) o0'9 9IT) 08Z'I tT) I' t'I) ZI fI) 9'' 9L61
5) O'L ,) 6'0 8) tO'SI 8)0 OO'I 81) S't' 81) tl 9) OV'LI L61
5) 69 t')I' LI) Z5L1 rT) 6L"' EL61
5) V'L 1) 1'1 IZ tI) LV'91 t') 586 L961
8) g'91 t') 80'I1 91) v' 91) 99 ZS61
8) 8t'ZI ,I) t)06 91) 8" 91) 8Z S ) 167Z "61 (ponmuuoo)
8) "O'L fr) 5z''I 1I) fl) 089 t'61 PIUI
8) L'ET VI) 00'1 tI) O'Z tI) 005 661 uoa oap ?ouod

(m) (s) (U) UOI.S (gI 90IX) (zUI) (um) (1U) (m 90Ix)
'Z J. H sopuTH J V M A X8&A 9Itrli

(panu!uoo) "I-V olq L


S) S"L
S) E'L
5) Z'S
S) 1.
S) 'L


t') o'I
') z'\
t,) vI
0) v I


ZZ) ZL'VI
8) oz'S
TZ) 05'8
ZZ) oL'1H
8) OZ'S
8) o0'
8) 89',
8) 85'0
8) 66'Z
8) 05'0


ZZ) Z9g
ZZ) 09
TZ) j9
oz) Z9
oz) 09
oz) voz
OZ) ZZ
oz) 9
oz) IOZ
OZ) 0


aluI uqilsuqas


6) ZI'I S) 9'L 0) Z'l












6) 00I1 S)L'9 0')'I


5) j'9
5) O'L
S) V'9


V) 6'0
t') O'
t) O'T


6) 0'T ), )v'L ')0 'I


s) O'L
S) 9'L
) V'L
5) VL
) I'L
5) 'L
S) 8'9


0) 6'0
V) 6'0

t') o'
t') o'
,) i-i
t') o'T


6) 90'1 S) 9,L t) I'T 'x'-OZ
9) O'LI 9) 086 9) Zt' 9) OLZ 9L6I
) '8 t) I' SI 8) L'eI 9) 086 9) 8i'ZZ 5L6I luI
9) 00"0 IZ61 QrOJTo ,oI

(Ti) (S) (T) UOPis (cm 90ix) (Zm) (m) () ( U) 9wT0ix)
1SH IseopnH J V M1 A M)L aIqI

(panupuoo) 'I-V alqoL


6Z) S'I
91) t,.'O
6Z) 69'0
9) z'o
8z) TE'O
SI) 89'0
1) 1-0

01) 9L'O
1I) 8'0
) o00'0
1) 69'0


8) Z0'9
z) v'


8) 55'61
LZ) 00L1
8) 89'61
SZ) 0OZ91
8) 6Z'61
8) 50'91
8) 88'LI


8) 16'81
8) IZ'T
8) LL'OZ


9) oz'
1) get


9z) OSt' I
/Z) OOt'I
9z) 09V'I
SZ) stVI
tz) OE' I
i ) 8LI'I
tz) OZ'T


Z) 00O'
1z) 096
Z) 9t'S'T


.Am


IA-OZ
661
661
9861
1861
0861
6L6I1
8L61
EL61
L961
L961
LtZ61
881


JA-fJZ


JA-OZ
Z861
0861
61.61
9L61
VL6I
8961
9961
961
'961
961
0961
LW6I
Z681


~z) 9'Z
tZ) 'Z
,Z) O'


Z) L'Z
t,) 8'1
EZ) 67


,z) o55
tz) Z15
t') Ott


z) s81
tZ) CE;
Z) S


jlUI zjz.dnf


WoluI
aoonq "is


9) 0O'9I
I) 09'9I



1) 00'0


0) Z', I) ,OI













6) Z8o0 Is-oz
8) 96"' c) SIt C) 9"t' ) 06 Z861
9) 8'0 8.L6I
9) OZ'OI 9) LOt' 9) L' 9) Oil 9L61
S) 1'9 ) 6"0 6 1) 9'"0 6961 louI
Z) E-'0 8Z61 JTAOIInH
I) 00"0 SZ6I sZa O

6) 06'0 ) 0'9 t') 60 01 i,--o
Z) OS'S ze) 08T ZE) 9" ze) O0 9) 19"0 861
I) tWO 1861
ze) 19'0 8L61 IolUI
I) 00'0 5Z61 uojIH ool

6) t*'I S) Z'9 ') 6"0 i4(-OZ
8) 88s' 1) 1 I) 0' T1) It 1) LZ'Z 0661
I) L0'I 6L61
9) tw8' 8L61
1) LO'I 6961
5) 9"9 t,) OI 1) IL'0 8961
S) 99 t) 8"0 1) 00"1 8961
S) 9"9 t) 60 I) t5'0 961
) T'9 t) 6-0 8) t,'WI 9)001 9) v' 9) o0 t961
S) 9"9 0) 8,0 11 9) OI' Z961 aluWI ITOM
I) 00"0 LZ61 o6I tl noS

6) L.60 S) v'9 t') 60 I(-OZ
S) 19 ') 6'0 0) 01W'8Z 9) 091'1 9) O't 9) 06Z EL61
S) 8'9 ) 60 z1 LI) 86" L961
I) 0S'9 6Z61 louI
1) 000 8161 qIoM OqI

(Ta) (s) (uK) uo.IS (X 90Ix) (Iu) (Qt) (um) (gi 90ox)
*uZ 1 'H Isopnui d M V 0V if A ax lU I
(panupluoo) 'I-V alqtL












Ot) 88'0 9) 61 S) 6"0 J-OZ
8) 18'l 6) O7O'I 9861
6e) S8'6 6e) Z99 6) I'Z 6) OZZ ie) 80'0 t861
8) t'8SI 6) Zt'I 6) 0"' 6) 6SZ LL6I
9e) 8"t SE) 80 6 6) 09'6 6) 008 6) 6' 6) 60Z SL61 SSvd
t) 00'0 IZ61 OarOULnH

LE) 09"0 9) S'5 S) S'1 se V--OZ aoDIua
E') LI'Z '861 JOqzvH
') SL'g Z881 aaoqBAJUD

LE) Lg'O 9) S'S S) IT'l IX-O
9) vS S) S 8) 'O w0L61
v) 00'0 tS6T 3no sa3.S

LE) LS'0 9) t'S S) 11' VT JX-O-
v) Or'Lt, V86T SSBd saOM

LE) I,'0 9) V'S S) 6"0 Z .X-0Z aoouu ua Avg
t) 98'01T Pt861 qdasof is

LE) TI'0 9) S't SO) 8'0 I )A-OZ
n) IT'Z 861 aommuJug A v
t) 00'0 K61 smIxpuv 'IS

L) E 0 9) S S) 80 0 JX-OZ
8) L'ST L) 00'I L) O' L) SEE t) LZ'9 1861
8) 6'9Z 01) 009' 01) SL' 5,61 TlsaI
t) 00'0 86T 'SSud IsvH

LE) 'O 9) t'S SO) O' 6Z 8) I'ELE L) 0Z8'tI L) Z'S~ L) SL6 is-OZ
V) 8L'T t86
0I) 6S'L9Z 01) SOt'OI 01) LV6 06T1 ssud
t') 61 8 LL81 UlOOVSUOd
(uI) (s) (uI) UOIBS (i9ox) (u) (u) (uI) (iw goix)
BZ I 'H ISVOPUIH d Vy OV Mm A JWA TIUI

(pnuipuoo) .I-V alqqL












Ot) L9"0 90) L/. S) 8"0 O, JCI-OZ
8) I'uI 6E) SLL 66) tl' 60) 8ZZ v) Zz'9 Z861
8) 81f61 Z) On,'0 I Z) 56"5 t561 sseI
60) 6 Z1 8881 lvoqguo"

0F) 1L'O 90) L,' g) 8"0 O I,-OZ
V) 88'7 6L6I
01) I Z'O 01) Zsz'c 00) L6'LI ZS61 Ff.D-V-ss~ed

W) SL'O 9) L't S) 8"0 017 IX-O
8) 9t,'z 6) 8IZ 6S) V'I 6S) Z81 t,) 9g'I V861 (uno"Z
8) L9'I 6) LST 6E) '0 Z561 Sul aud
60) L8'0 S88T SSJd puI.

O) LL'O 9E) 6'1 S) 6'0 Ji-OZ
t) E8' V861
9E) 8,t' S) 8'0 6c 8) 66'1Z 6E) Z88 6C) 61' 66) 081 t'L61
01) Z'Il 01) Z8", ZS61
8) 6'I Z ) Ot'Z Z) IL'E 0561
8) L8l ; Z) 096'Z Z) 8*Z 9Z61 ssvd s,UqOr

Ot) t'8'0 9E) 61' 5C) 6"0 I'-OZ
8) 0'LI 6) EE'I 9861
t,) gi'*g V861
Sg) LZ'I 9L61
90) 8t' S) 8"0 6E SI) LO'z ZL61
8) 68"S 01) ZLO'Z 01) 6Z'Z 0S61 ssud
8) 8t'g ) 856'Z Z) 8Z 9Z61 JBM'ai.lD

t0) LT'O 90) 61' 5E) 60 6 JA-Z0
8) 8Z'I 6E) 9ZI 6) 8'I 6E) OL 1E) 9'E V861
6E) S0 6E) 05'9 0561
8) 19,0Z 6C) 00'I 6) IL'9 g8-0881 ssid uipauna

(mu) (s) (m) no.pis (im 90ix) (im) (N) (m) (cm 9OIx)
le SH IsVopUnH Jd V0 "t M A MQAU 12Io'
(ponuIIuoo) 'I-V glqL










Ot) L'0 9E) O S) 6"0 1-0
8) E'S 6) IZS'Z 6) 9"t' 60) M8t'S f) 51'6 Z861
9) 0"5 S) 60 t 8) St'8,' Z) 999'Z Z) Wt'6 9561
6e) LW'9 88i
8) 90"o8 Z) 8t9'z Z) Z9,8 6L81 SSed A! id~o

ot) IL'O 9) 05 S) 6"0 JI-OZ0
8) 6"'OZ 6) L56'8 6E) 8"6 6e) t'16 vt') OIZZI S861
9) o0S S) 60 zt 8) t'S9e Z) ooS'tI Z) 08"I 9S61 ssd
6) 60'98 88T apup D TOOg

0F) OL'O 9) 0S S) 60 sIJ-O)
8) 8'8 6) Z61'Z 6) O't 6) tS t'E) 99'Z Z861
90) 05 E) 60 zt 8)) 6E'61 01) Sa'I 6) 67Z 60) 90t 1) 825 9S61 SSvd
60) 9t' 881 IauudsvD

OF) IS'0 9) 0oS S) 80 IV J-0oz
tv) wT'0 Z861
Z) LS'I Z) 6tI' Z) IL'0 Pt61 SScd 00n!A

0F) 59"0 9E) 05 S) 80 it' s-oz
6E) SVO 6) 81 6E) Z'1 6) SI 6) ZVO Z861
60) 06L. 6E) 66Z 6E) 'Z 6) 07'T 5561 SSed
60) 8t'0 tV561 qIg!uP .

ot) S9,0 9) Lt, S) 8"0 at is-oz
8) I*'L 60) Z90' 6) L'9 6) LSgt' t) L'OT Z861
8) t'ZS 6) St8'Z 6) Z' 6) 688 6) 0'1 t'S61 SSvd
6) S8'9 8881 mBOSmBS Sig

a0) 99"0 9) L. S) 8)0 0t IA-aZ
8) 0.'8 6) 09 6) 9"' 6) LEI ') 9'c Z861 AunoOD
Z) Z6S5 tV61 o6 SoiBS
6) 00I1 8881 SSed MaN

(n) (s) (m) uo!Wi (m I90ox) () (a) () (Ea 9A1x)
,oB 'H IsROpniTH d 0 v 0 y A vA JltI


(pTnuIluo0) *I-V 9olqeL










0W) L6'0 90) r'4 S) 8'0 g-OZ sstvd
9E) 9't Sq) 8,0 o Zt) It'8 tL61 sqiuvexvD

OV) 56'0 90 )'t S) 8'0 Ji-Oz
8) Z8'I 60) Io)'I 66) O'* 6C) LV t'V) OL'II Z861
9g) 9't S) 8'0 f ZV) IT'61 tL6T ssud
60) L9'S1 6881 ootaI 21a

0) I6'0 90) r't S) 8"0 IS-OZ
90) 9' Sg) 80 E1 8) L611 60) t6E 6) V'Z 60) t91 t') WO' Z861
Zv) w'0O tL61 Sstd uopJOD

W) 88'0 90) r't gc) 8"0 Az-OZ
90) 9' S) 8'0 D Z1) Oo'0 'L61 Ssvd UIID

o0) 98'0 9) O*'S S) 6'0 -OZ
9E) 6'1 S) 6'0 zt 8) 5L'I v) t9 1 ) 8'I VC) 16 t) 09'0 Z861
Zv) 9f'0 tL6I SSBd stUIn2A

Ov) 8'"0 9) 0'S S) 6'0 -OZ
8) IO'L 6E) ZS 60) I'7 60) OSZ n) Z'0 Z861 XIunoo a"I
90) 61' S) 6'0 ZF 60) I'O 5961 SSvd MON
Ot) 8'0 9) O'S S) 6'0 JA-OZ
8) L0 6) 6'I 60) 60 60) 011' t) 51'9 Z861
9) O'S S) 6'0 ZV 8) tS'Z 60) 806'1 68) L6"' 0961 Ssud
60) 89' 6881 SoliBo g!g

o0) 08'0 90) 0' S) 60 ZVr aL-OZ Av
VC) V6'61 Z861 SolJBo uns

0') Lo'0 9e) 0'S S) 6'0 .a-Oz
8) IZ\'I 6) LE8 60 91' 60) Z81 v) tI'Z Z861
9) 0'S S) 6'0 Zt IT) 90'91 Z) t6'I Z) 'Z 96I1
t7) 000 IZ61 SStd qsgpaI

(m) (S) (m) UOIToS ( l 90x) (gm) (m) (m) (Ul gOIx)
"oZ I H SMOpuiH J d'V 0 MA A nZea lam1

(panui uoo) 'I-V giquI













tS) t'*z S) O'L t) 6'0 A-OZ
S) 179 ') 8"0 6Z Sit) 00"081 rt) 00"L8 1tL6I punos
8) ZL'LS S) i7oL'9 tS) O't0 t1S) 9L9' E) 09"'81 uounS -is

iS) tP'z 9) O'L V) 6'0 Jl-OZ
S) 1'9 ') 8'0 6Z 5) 00'08Z 0t') 00"891 tL61 punoS
8) 9T'SLS L) 80oz'I ES) 0'8 U) 106'E C') 00'161 Mtipuv IS

ZS) wz't i) 9'9 1') 60 TA-OZ OArI
S) 0'9 ') 8'0 CE IS) IO' S IS) tlI't IS) 0'8 IS) 81S 0) 00'6S ,L61 T4BUUUls
60) 8E'Z 5) O'L 1) 6"0 JC-OZ
S) '9 ') 8'0 IT 8) 60'681 8') S08'SI 81) '9 8t') 16S'Z St) 00"S11 L61
Et') 08'*9I PUnos oIpdrs

Lit) 8'Z 5) 6"9 ') 6"0 Jx-OZ punos
) '9 t) 8'0 Z 8) IW'ZO0 LI) 016' Z LO) 0'S LO) Z8I'5 EO) 0o'I tL61 mAqvsso
L'V) 8'Z S) 6'9 ') 6"0 sc-OZ
S) '9 ') 8,0 Z S1') 00'861 L') 91E'51 L') L'9 LI) 98Z' t 5) 00'9II lL61 sOauPTUD
Lo') 01'5I "IS

tt) 8'Z 5) 0'L 0) 6"0 I)-oz
S) t'9 0) 8'0 6Z 50) LZ'*8 90) SVI'Z 91') O' 9t) LZt' t') 00*ZI ltL6 J .I
L't) OZ'v uoiduruH

,) 8'Z 5) 6'9 0) 0'I J-OZ
5) '9 ') 8'0 0 5t) 0001 I St') 00'Z9 VL61
8) 56'9 W,) 88t' t) 0'Z t') Z ') OO'EE punos ,oqna(

) 8E'Z 5) 6'9 t') 0I 0E ,A-OZ punoS
8) zS'iz tt) OZ6'I 1t') 0' t') 09 I) 0L'99 BqvUUiiv

(M) (s) () no iS (im 90Ix) H() (M) (J) (i 90iX)
"OZ .1 H IseopniH 1d V i M0 A seax lPIaI

sroo B Doo alp, UOlg soounuo l-U esoo jo0 sjaautrJeud polai Ellop qqg "Z-V alq l












825) 59'1I


LS) 98'I


SS) 9I'Z




LS) ETZ


95) 98'1


SS) It'Z


(m)
"eI


5) 6s'


S) 6'9


5) S'9
S) 0'9

) 6'5
S) 6'5

5) s'9


S) '9
S) 6'5
5) 9'9
S) 0'9
(s)
L


t6'0


) 6'0



t') 8'0

t')6'0
t') 80

t') 6'0



,) 8'0



(m)
'H


SE JX-OZ
Z) ZS5SS Z) ZOE'L z) Lz*9S


Z) 66"08 Z) SW'S o5 9Z')1L
JA-OZ
SE 8) S9'89t 55) 060'I' SS) 1'9 SS) 9EL'9 05) 00*81z tL6I Pu


S 8) E'IZZ SS) 069'8I 55) V'8 9S) SZZ'Z OS) 00'60Z tL61 pu
5IA-OZ
Z) 69'6ZI Z) Z'6 Z) 1I'59I


9E 05) 00"fSI 05) O'SZ tL61 ^
JA-OZ
E S) 00001 SS) LEI'OI s) r'6 sS) Z90'I S0t 00"09 'L61 pr

UoT.s (m g90ox) (W) (M) (m) (m o90IX)
Is9opuTH Jd 0V t M A aa

*IuSOo tullOuJo ipnos aitp uoj saomutlua jIsuoo joj sJ~iaurned pauiiJ lopp qqg


ZS) tt*' ) 99 ) 6"0 JP-OZ punos
S) 09 t) 8'0 EE S) 0oo0o zs) 8SL'sI zs) '5 zs) S98'Z st) 00011 L61 AMSSeMA

ZS) ,' S) 9"9 t) 6"0 IS-0Z 10o
S) 0'9 0) 80 C ) 00"TZ Sq) 00"c tL61 aql
(m) (s) (m) nopins (im 9Ox) (Q) (m) ( m) ( Oi 901x)
"Z S .H ISO3PU!H J "VO M A .max lalnI
(pNnup!uo) '*-V olqL


aUh qhUnI!


lalU oUnoI


noS ianO1H 'IS


noS Jeo-I t)Od


oIsipg qWON


uI uoIsaIJBaqD


inoS an~oq!uB3




*-V oalql















S~RL


It7) 8'W6V


Z) 0o'89I


Z) t','995


z) 00oo*'


Z) OZ'ETI


Z) L8g'


Z) OL0c


Z) e9,9S


Z) 18't.


Z) OL'.I


Z) 0'Lat


t9) LE'o


9) 91*1


Z9) EL'O


19) 86'0


09) ZS"1


09) o'I


09) s8'I


69) 91'1


65) LV I


9) 9*9





9) L'9


5) t'9


9) 9'9


5) 9'9


5) ,'9


S) '9


S) '9


t') IT


t,) v'i


t,) i


,) 0'I


t,) 0'


t') 1


1,) 1'



1,) '


It) 98t'I


Z) zoE'8s


Z) t9Z'6Z


z) .t0'8


Z) L,8'9


Z) L68


Z) 9I'


Z) E15'9


Z) I'I


z) 5LE'I


Z) 18s'5E


6t'





S9


L9


89


69


OL


It) 08"61


z) 01.L6


z) Z8'968


Z) IL1'C


Z) 6L'OZ


Z) S*Z


Z) 11'61


Z) E9'99


Z) ZV'T


z) ZO'io


z) tt'*


(mi) (s) (T) uo~,s (Em 9oTx) Qm) (im) (im) (Em 9ox)
"'R J 'H JsWopUIH d, Oi M A l IaI

Sugrooo 3!Pd pu 3plIUeV apv l 2UOl saouetjua ISeOa snoaullO3os!um oj sJaliaoeed poliai map qqH "'-V aiq l


'ssud Svsu.V

Stxaj, 'luoiua
UOISOAIVD

'uolA sqoj^

UIioJ3 qlyoN
*uI lojnvog

'lavUI uo aQO

ajmtUpaal 'PIUI


4as2af MaN
'PlUI pJOJOJOH


'joqivH 22a '"

OaSJf MON
'P31UI aQuiitB2ug




asjof MON
'3a3 oaN


.LC-OZ














JLC-0Z


.IA(-0Z
rA-OZ

























TUiOJI3
'oos1lu!iI "ES


'Aug S003

uogajo
'J2a.ra vnbdmfl


'Jaar I maliqaN


'JaA.d Bi!qmnlo3


':oonrnII!l

jnoq Iu slAi
'joq-tH sXjrf)


99) 91*'4"'I


59) 80'IL


99) 0c'Z9


59) W0'9T


59) O'I80s'I


99) 5L'6S


59) 6'8t,'


99) 'I'L8


59) osz'S


99) Z6Z't


S9) 968


59) 561'LZ,


99) S '"


S9) 9g0'LZ


99) 09'908


S9) 89'LZ


99) LL'S


S9) TZ'


S9) tI'69L


99) L8'9I


S9) 81'19Z


(m) (s) (ro) UoIMs ( 90oTix) (Q) (n) (M) (e 90ix)
oIZ s 'H ISBoPUTH d V "Z M A mlxrI

(panupTuoo) "'t- olqlj











References for Appendix A
1) Marino and Mehta (1986)
2) Walton and Adams (1976)
3) Hou (1974)
4) Hubertz et al. (1993)
5) Brooks (1994a)
6) Marino (1986)
7) USGS, Fernandina Beach (1975)
8) Eqn. 3.1, Section 3.1.2
9) Balsillie (1987a)
10) Dean and Walton (1973)
11) Work and Dean (1990)
12) Florida Coastal Engineers (1976)
13) Mehta and Jones (1977)
14) Jones and Mehta (1978)
15) Average of volumes, Section 4.1.2
16) Taylor Engineering (1992)
17) UFCOEL (1970)
18) USGS, New Smyrna Beach (1974)
19) Hunt (1980)
20) Mehta, Adams and Jones (1976)
21) Johnson (1976)
22) Coastal Technology (1988)
23) Walton (1974)
24) U.S. Army Corps of Engineers (1974)
25) Coastal Data & Engineering (1980)
26) Coastal Data & Engineering (1985)
27) Harris (1983)
28) Lee (1992)
29) Coastal Planning & Engineering (1993)
30) Jarrett (1976)
31) Olsen Associates (1990)
32) Strock and Associates (1983)
33) Van de Kreeke (1984)


Hine and Davis (1986)
Hubertz and Brooks (1989)
Brooks (1994b)
Basillie (1987c)
UFCOEL (1970)
Davis and Gibeaut (1990)
Basillie (1994c)
Bruun and Gerritsen (1966)
Coastal Engineering Consultants (1988)
Campbell et al. (1990)
NOS, Nautical Chart 11508 (1991)
Oertel (1988)
USGS, Sea Island (1974)
NOS, Nautical Chart 11511 (1974)
USGS, Sapelo Sound (1974)
NOS, Nautical Chart 11509 (1992)
Kraus et al. (1994, in press)
USGS, Savannah Beach North (1975)
Savannah Beach South (1977)
NOS, Nautical Chart 11512 (1974)
NOS, Nautical Chart 11504 (1991)
NOS, Nautical Chart 11506 (1992)
NOS, Nautical Chart 11513 (1974)
NOS, Nautical Chart 11523 (1992)
NOS, Nautical Chart 11521 (1992)
NOS, Nautical Chart 11532 (1992)
NOS, Nautical Chart 12323 (1993)
NOS, Nautical Chart 12318 (1991)
NOS, Nautical Chart 12216 (1994)
NOS, Nautical Chart 12204 (1994)
NOS, Nautical Chart 11547 (1992)
NOS, Nautical Chart 11376 (1993)
Johnson (1972)
O'Brien (1969)














APPENDIX B

FORTRAN MODEL AND INPUT FORMAT








B. I Input Parameter Format


The following is the format of the input parameter file 'I.INP' used with EBBSHOAL.FOR:

bed porosity/current friction/wave friction/median grain diameter/
+ suspended sediment concentration;
tidal prism/spring tidal range/tidal period (hr.)/inlet throat width
+ average inlet depth;
deepwater wave height/wave period/angle between currents and waves/
+ number of tidal steps;
initial output filename ('in quotes');
data output filename ('in quotes');
run date ('in quotes').


B.2 EBBSHOAL.FOR Diagnostic Model
The following model was used to simulate and evaluate the growth of ebb delta volumes:
$LARGE
PROGRAM EBBSHOAL.FOR
C************** ********* ** *************
C Ebb Shoal Volume Model Program
C written in MS FORTRAN 5.0 by
C Michael R. Dombrowski
C Version 1.0
C July 1, 1994
C
C -------------- Variable Definitions --------------------------- ----
C
C Variable Description
C ------- -- ----
C AC Minimum cross-sectional area (m**2)
C ALPHA Wave to tidal power ratio
C AP Ebb shoal area calculated by tidal prism method (m**2)
C AD Ebb shoal area calculated from regression equation (m**2)
C CONC Sediment concentration (kg/m**3)
C D50 Median grain size diameter (in millimeters)
C D Depth of water array within deposition area (m)
C DO Initial depth of "no-delta" condition (m)
C F Friction due to both waves and currents
C FC Friction due to currents
C FW Friction due to waves
C HT Shoaled nearshore wave height array (m)
C HO Offshore wave height (m)
C N Bed porosity
C NN Number of tidal cycles
C RHOD Density of dry bed (kg/m**3)
C RHOS Density of water (kg/m**3)










C RHOW Density of sand (kg/m**3)
C TCR Critical shear stress (N/m**2)
C TB Shear stress due to currents and waves (N/m**2)
C TP Tidal prism (m**3)
C TPER Tidal period (s)
C TR Spring tidal range (m)
C TWAVE Wave period (s)
C UI Average current velocity over 1/2 tidal cycle (m/s)
C UO Current velocity over 1/2 radius ebb shoal (m/s)
C UMAX Maximum current velocity (m/s)
C VOL Ebb shoal volume array (m**3)
C W Width of inlet mouth and shoal (m)

C ---------------- Subroutine Definitions --- ----------------
C KUTTA Function for the calculation of change in depth (FF).
C SHEAR Calculates current and wave velocities and returns
C shear stresses due to both waves and currents (TB).
C SHOAL Calculates the nearshore shoaled wave height (HT) due to
C the change in the water depth of the ebb shoal.

C Declarations----
PARAMETER(IDIM= 15000)
CHARACTER*60 OUT1,DAT1,DATE
INTEGER J,DVOL,NPTS,VOL(IDIM),Z
REAL AC,AD,ALPHA,AP,CONC,C1,D(IDIM),D50,DO,DT,F,FC
REAL FF,FW,G,HO,HT(IDIM),K1,K2,K3,K4,L,N,NN,PHI,PI
REAL RHOD,RHOS,RHOW,T(IDIM),TB(IDIM),TCR,TP,TPER
REAL TR,TWAVE,UAVE,UI,UO,W,WS,X

C Open input file and read data -
OPEN(UNIT= 1,FILE= 'I.INP',STATUS = 'OLD')

C Parameters and filenames read in from I.INP
READ(1,*)N,FC,FW,D50,CONC
READ(1,*)TP,TR,TPER,W,DO
READ(1,*)HO,TWAVE,PHI,NN
READ(1,*)OUT1
READ(1,*)DAT1
READ(1,*)DATE
CLOSE(UNIT= 1)
OPEN(UNIT=2,FILE=OUT1,STATUS= 'UNKNOWN')
OPEN(UNIT= 3,FILE=DAT1,STATUS= 'UNKNOWN')

D50=D50/1000.0
G=9.81
PI=3.141593
PHI=PHI*(PI/180)
RHOD =2650.0*N










RHOS =2650.0
RHOW= 1030.0
TPER=TPER*3600
DT=TPER*NN
DVOL=1
D(1)=DO
J=1
T(1)=0
VOL(1)=0
Z=1

C Ebb shoal area and equivalent shoal length
AP=TP/TRS
AD=2.34*(AD**(0.81))

C Initial current velocity
AC=W*DO
UMAX= ((TP*PI*0.86)/(TPER*AC))
UI= (2.0*UMAX)/PI
RE= (SQRT(2.0*AREA/PI))
UO= (2.0*UI*W)/(PI*RE)

C Settling velocity and critical shear stress
WS = ((4.0/3.0)*((RHOS-RHOW)*G*D50)/(0.43*RHOW))**0.5
TCR=0.058*(RHOS-RHOW)*G*D50

C Do loop to calculate change in depth and volume with respect to
C changing conditions. The loop is completed when the absolute change,
C DVOL, between VOL(J+1) and VOL(J), is
DO WHILE (DVOL.GT.0.0)
CALL SHOAL(D(J),G,HO,TWAVE,HT(J))
CALL SHEAR(D(J),DO,F,FC,FW,G,HT(J),PHI,RHOW,TB(J),TWAVE,UO,L)
DO WHILE (Z.EQ.1)
PTIDE= (TR*TP*RHOW*G)
PWAVE= ((RHOW*(G**2)/(32.0*PI))*(HO**2)*TWAVE*W*TPER)
ALPHA =PWAVE/PTIDE
Z=Z+1
END DO
A= (WS*CONC)/RHOD
B = (RHOW*F)/(2.0*TCR)

C Solve dh/dt by 4th-order Runge-Kutta method
X=D(J)
CALL KUTTA(A,B,DO,HT(J),L,PHI,TWAVE,UO,X,FF)
K1 =DT*FF
X=(D(J)+(K1/2.0))
CALL KUTTA(A,B,DO,HT(J),L,PHI,TWAVE,UO,X,FF)










K2=DT*FF
X= (D(J)+(K2/2.0))
CALL KUTTA(A,B,DO,HT(J),L,PHI,TWAVE,UO,X,FF)
K3= DT*FF
X=(D(J)+K3)
CALL KUTTA(A,B,DO,HT(J),L,PHI,TWAVE,UO,X,FF)
K4=DT*FF
D(J+1)=D(J)+(1.0/6.0)*(K1 +2.0*K2+2.0*K3+K4)

VOL(J + 1)= (AD)*(DO-D(J + 1))
DVOL = (ABS(VOL(J + 1)-VOL(J)))
IF(VOL(J+ 1).LT.0.O) THEN
DVOL=0.0
ELSE
T(J+ 1)=T(J)+(DT/3.1557E+07)
ENDIF
IF(J.EQ. 15000) THEN
DVOL=0
ELSE
J=J+1
ENDIF
END DO
NPTS=J-1

C Write out ---
WRITE(2,19)OUT1,DATE
WRITE(2,20)RHOD
WRITE(2,21)D50
WRITE(2,22)WS
WRITE(2,23)CONC
WRITE(2,24)TCR
WRITE(2,25)FC
WRITE(2,26)FW
WRITE(2,27)HO
WRITE(2,28)TWAVE
WRITE(2,29)PHI
WRITE(2,30)TP
WRITE(2,31)TR
WRITE(2,32)AD
WRITE(2,33)W
WRITE(2,34)DO
WRITE(2,35)UMAX
WRITE(2,36)UO
WRITE(2,37)ALPHA
WRITE(2,38)NN
19 FORMAT(2X,'Output filename:',A14,'Run date:',A18)
20 FORMAT(2X,'Dry sediment density (kg/m**3) =', F15.5)
21 FORMAT(2X,'Mean grain size diameter (m) =', F15.5)










22 FORMAT(2X,'Settling velocity
23 FORMAT(2X,'Sediment concentration
24 FORMAT(2X,'Critical shear stress
25 FORMAT(2X,'Friction factor for currents
26 FORMAT(2X,'Friction factor for waves
27 FORMAT(2X,'Deep water wave height
28 FORMAT(2X,'Wave period
29 FORMAT(2X,'Angle between waves/currents
30 FORMAT(2X,'Tidal prism
31 FORMAT(2X,'Spring Tidal Range
32 FORMAT(2X,'Ebb shoal area
33 FORMAT(2X,'Minimum throat width
34 FORMAT(2X,'Initial inlet depth
35 FORMAT(2X,'Max throat velocity
36 FORMAT(2X,'Initial velocity over shoal
37 FORMAT(2X,'Wave/tide power ratio, ALPHA
38 FORMAT(2X,'Number of tidal steps, NN

CLOSE(UNIT=2)
WRITE(3,300)(T(K),VOL(K),K= 1,NPTS)
300 FORMAT(F8.4,I12)
CLOSE (UNIT=3)
STOP
END


(m/s)
(kg/m**3)
(N/m**2)


(m)
(s)

(m**3)
(m)
(m**2)
(m)
(m)
(m/s)
(m/s)


=', F15.5)
=', F15.6)
=', F15.5)
=', F15.5)
=', F15.5)
=',-F15.5)
=', F15.5)
=', F15.5)
=', E15.5)
=', F15.5)
=', F15.5)
=', F15.5)
=', F15.5)
=', F15.5)
', F15.5)
=', E15.5)
=', E15.5)


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


C
C
C
C-


This subroutine calculates the shoaled nearshore wave height due to
the change in the water depth of the ebb shoal assuming normal waves
with straight parallel contours resulting in Kr= 1.
--- --------- --- Variable Definitions -------------------


C
C Variable
C ---
C C
C CO
C HTWAV


IE


Description

Shallow water wave celerity
Deep water wave celerity
Shoaled nearshore wave height


SUBROUTINE SHOAL(D,G,HO,TWAVE,HTWAVE)

C Declarations---
REAL C,CO,D,G,HO,HTWAVE,TWAVE

C Calculate shoaled wave height ----
CO= (1.56*TWAVE)
C=(SQRT(G*ABS(D)))
HTWAVE= HO*(SQRT(CO/(2.0*C)))
RETURN
END




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs