Citation
Shoreline modeling at Holly Beach, LA

Material Information

Title:
Shoreline modeling at Holly Beach, LA
Series Title:
Shoreline modeling at Holly Beach, LA
Creator:
Dean, Robert G.
Place of Publication:
Gainesville, Fla.
Publisher:
Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
Language:
English

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.

Full Text
UFL/COEL -2001/010

SHORELINE MODELING AT HOLLY BEACH, LA by
Robert G. Dean

June 19, 2001
Prepared for: Coastal Planning and Engineering, Inc. 2841 N.W. Boca Raton Blvd. Boca Raton, FL 33431




SHORELINE MODELING AT HOLLY BEACH, LA
June 19, 2001
Prepared for: Coastal Planning and Engineering, Inc.
2841 M W. Boca Raton Blvd.
Boca Raton, FL 33431
Prepared by: Robert G. Dean Civil and Coastal Engineering Department
University of Florida
Gainesville, FL 32611-6590




TABLE OF CONTENTS
LIST OF FIGURES ......................................................1
LIST OF TABLES.......................................................11
1.0 INTRODUCTION .................................................. 1
2.0 THE MODEL "HOLLY.FOR" ........................................ 1
2.1 General Description ................................................ 1
2.2 Breakwater and Wave Representation ................................... 1
3.0 ILLUSTRATION OF THE APPLICATION OF HOLLY.FOR TO THE
HOLLY BEACH SYSTEM........................................... 2
3.1 Shoreline and Breakwater Representation ............................... 2
3.2 Cases 1 a 1 e. Normally Incident Waves, Breakwaters a Uniform Distance Offshore 3 3.3 Case 2. Oblique Waves, Breakwaters a Uniform Distance Offshore .............3
3.4 Case 3. Normally Incident Waves, Actual Distances of Breakwaters Offshore ..... 3 3.5 Case 4. Oblique Waves, Actual Distances of Breakwaters Offshore .............8
3.6 Cases 5a 5d. Normally Incident Waves, Actual Distances of Breakwaters Offshore,
Overtopping Represented......................................... 8
4.0 SUMMARY ...................................................... 11
5.0 REFERENCES....................................................11
APPENDICES
A CHARACTERISTICS OF PROGRAM: HOLLY.FOR ...................A-1
B LISTING OF PROGRAM: HOLLY.FOR.............................. B-i
C LISTING OF ANNOTATED INPUT FILE: HOLLY.INP .................C-i




FIGURE PAGE
I Definition Sketch of Breakwater Units and Shoreline ............................ 2
2 Case Ia. Shoreline Response to 85 Breakwaters Located a Uniform Distance of 300
feet From the Shoreline. One Year of Waves Represented ....................... 5
3 Case lb. Shoreline Response to 85 Breakwaters Located a Uniform Distance of 400
feet From the Shoreline. One Year of Waves Represented ....................... 5
4 Case 1c. Shoreline Response to 85 Breakwaters Located a Uniform Distance of 500
feet From the Shoreline. One Year of Waves Represented ....................... 6
5 Case I d. Shoreline Response to 85 Breakwaters Located a Uniform Distance of 600
feet From the Shoreline. One Year of Waves Represented ....................... 6
6 Case le. Shoreline Response to 85 Breakwaters Located a Uniform Distance of 600
feet From the Shoreline. Two Years of Waves Represented ...................... 7
7 Case 2. Shoreline Response to 85 Breakwaters Located a Uniform Distance of 400
feet From the Shoreline. One Year of Oblique (-300) Waves Represented ............ 7
8 Case 3. Shoreline Response to 85 Breakwaters Located at Actual Distances From the
Shoreline. One Year of Normally Incident Waves Represented .................... 8
9 Case 4. Shoreline Response to 85 Breakwaters Located at Actual Distances From the
Shoreline. One Year of Oblique (-30') Waves Represented ....................... 9
10 Case 5a. Shoreline Response to 85 Breakwaters Located at Actual Distances From
the Shoreline. One Year of Normally Incident Waves Represented. Overtopping of
25% in Region Indicated ................................................... 9
11 Case 5b. Shoreline Response to 85 Breakwaters Located at Actual Distances From
the Shoreline. One Year of Normally Incident Waves Represented. Overtopping of
50% in Region Indicated ................................................. 10
12 Case 5c. Shoreline Response to 85 Breakwaters Located at Actual Distances From
the Shoreline. One Year of Normally Incident Waves Represented. Overtopping of
75% in Region Indicated ................................................. 10

LIST OF FIGURES




13 Case 5d. Shoreline Response to 85 Breakwaters Located at Actual Distances From
the Shoreline. One Year of Normally Incident Waves Represented. Overtopping of
100% in Region Indicated............................................. 11
TABLES

TABLE

PAGE

1 Characteristics of Case Examples to Illustrate Program HOLLY.FOR ..............4




SHORELINE MODELING AT HOLLY BEACH, LA

1.0 INTRODUCTION
The interaction of a series of detached breakwaters with the shoreline represents a complex hydrodynamics and sediment transport problem that is not well understood quantitatively in coastal engineering and for which only limited empirical relationships are available. Interaction components include sheltering, overtopping, diffraction, differential wave set-up leading to longshore currents etc. Key concerns of the coastal engineer can include the shoreline response to design parameters for the case of a new breakwater system and the shoreline response to modifications of an existing breakwater system. The breakwater distance offshore and the breakwater length are primary factors for the determination of whether a tombolo or salient will form for a single breakwater. Additionally, the availability of sediment affect shoreline response. The Holly Beach, LA system consists of 85 detached breakwaters located at varying distances from shore and of varying heights and conditions of repair. This report describes and illustrates with examples, the computer program HOLLYFOR which was developed specifically to represent the response of the Holly Beach shoreline to this system of detached breakwaters and to provide guidance for considerations of nourishment and modification or repair of this system.
2.0 THLE MODEL "HOLLY.FOR"
2.1 General Description
The numerical model HOLLY.FOR includes the capability to account for: (1) Variable distances of individual breakwater units from the shoreline, (2) Overtopping due to combinations of high waves and elevated water levels, and (3) Forcing which includes time varying tides and wave conditions. The main effort directed to the development of this model has been to establish a general framework which is amenable to further additions rather than to provide easily used features. That is, the model allows a user with reasonable skills to add features which, in the present version, are not provided directly. The chief merits of this model are its general versatility. As examples, the present version does not include a recommended overtopping relationship or module nor does it include an easily represented time varying wave climate and water level history; however, these can be readily incorporated.
2.2 Breakwater and Wave Representation
The breakwater and wave representation is based on the concepts presented by Dean (1978) in which gaps in breakwaters are represented as a series of wave sources, each emanating a wavelet with a circular front. If the gap is long consisting of a large number of sources, the wave front in the lee of the breakwater system is straight and travelling in the direction of the incident wave. For gaps that are small compared to the wavelength, the wave front emanates as a circular segment, consistent with the planforms of pocket beaches. The wider the gap, the more




alongshore elongate the pocket beach which is formed. The emanating wave height can be limited by a "sill" over which the wave propagates providing a basis for representing -wave overtopping of low breakwaters. Figure 1 illustrates the breakwaters and gaps.The source elements which represent the breakwater and gap elements can be either active or inactive in the generation of waves on the downwave side of the breakwater.
Breakwater Units
Shoreline
Figure 1. Definition Sketch of Breakwater Units and Shoreline
3.0 ILLUSTRATION OF THE APPLICATION OF HOLLY.FOR TO THE HOLLY BEACH SYSTEM
This section provides examples of the application of the program HOLLY.FOR to the Holly Beach, LA nearshore system.
3.1 Shoreline and Breakwater Representation
Because of the rather short lengths of the individual breakwaters and the associated shoreline response characteristics, small alongshore elements are required. For purposes here, each element was selected to be 5 0 feet in length and the entire shoreline length of 90,000 feet (17' miles) was represented, resulting in a total of 1,800 elements. Because an explicit method of solution is employed for this finite difference model, the time step must be selected in accordance with the shoreline element length and the wave height. For purposes here in which wave heights are on the order of 1 foot and the element length of 50 feet, a time step, At, of 3,600 sec (1 hour) is appropriate.




The breakwater and shoreline system were defined relative to the y axis which was positioned at an arbitrary distance of 800 feet from the nominal 1995 shoreline. The position of the ith element of the breakwater is defined as (XBL iand YBL~) and the coordinates of each shoreline position are defined as (XSL i and YSL i ). In this report, the breakwater lengths and gaps have all been taken as 150 ft and 300 ft, respectively.
Unless noted differently, the results presented in the following cases will represent a shoreline response time of one year to a deep water wave height of one foot, conditions which will be shown to be generally sufficient for the shoreline to respond to the breakwater system. The cases examined are discussed below and summarized in Table 1.
3.2 Cases la le. Normally Incident Waves, Breakwaters a Uniform Distance Offshore
The results for this case are presented in Figures 2 through 5 for breakwater distances from the shore of 300 ft, 400 ft, 500 ft and 600 ft, respectively. Inspection of these figures demonstrates that the breakwater ends sequester sand from the adjacent beaches and thus advance more that the shoreline in the lee of the breakwaters at some distance from the breakwater ends. Additionally, the alongshore oscillations decrease rapidly with offshore distance of the breakwaters. The offshore breakwater distances selected for this example span the actual approximate range of 400 to 650 feet from the 1995 shoreline for the Holly Beach breakwaters.
Figure 6 illustrates the effect of a total run time of two years for the case of the breakwaters located an offshore distance of 400 feet where comparison with Figure 3 shows that with a wave height of one foot, the shoreline response was generally complete after a period of one year.
3.3 Case 2. Oblique Waves, Breakwaters a Uniform Distance Offshore
The deep water wave direction for this case is -30' which results in a westward longshore sediment transport of approximately 58,000 cubic yards per year along the unaffected shoreline. The results for this case are presented in Figure 7 for the breakwaters located a uniform offshore distance of 400 feet. Comparison of these results with those in Figure 3 for normally incident waves shows that the main difference, as expected, is the accumulation of sediment on the updrift side of the breakwater system and erosion on the downdrift side.
3.4 Case 3. Normally Incident Waves, Actual Distances of Breakwaters Offshore
These results are presented in Figure 8 with the primary difference from the normally incident case (Case 1) being the variation in local salient response as a function of breakwater distance offshore.




Table 1

Characteristics of Case Examples to Illustrate Program HOLLY.FOR

Deep Water Wave Breakwater Unit Locations Time Overtopping
Case Direction (0) and Other Information Represented I Represented
la Normally Incident Uniform, 300 ft Gulfward One Year No
lb Normally Incident Uniform, 400 ft Gulfward One Year No
lc Normally Incident Uniform, 500 ft Gulfward One Year No
ld Normally Incident Uniform, 600 ft Gulfward One Year No
le Normally Incident Uniform, 400 ft Gulfward Two Years No
2 -300 Uniform, 400 ft Gulfward One Year No
3 Normally Incident Actual Distribution Relative to One Year No
1995 Shoreline
4 -30 0 Actual Distribution Relative to One Year No
1995 Shoreline
5a Normally Incident Actual Distribution Relative to One Year Yes, 25% of 1995 Shoreline Incident
Wave Height
5b Normally Incident Actual Distribution Relative to One Year Yes, 50% of 1995 Shoreline Incident
Wave Height
5c Normally Incident Actual Distribution Relative to One Year Yes, 75% of 1995 Shoreline Incident
Wave Height
5d Normally Incident Actual Distribution Relative to One Year Yes, 100% of 1995 Shoreline Incident
I__I ___Wave Height




4 5 6 7 8 9 10 11 12
AJongshore Distance (Miles)

Figure 2. Case 1 a. Shoreline Response to 85 Breakwaters Located a Uniform Distance of 300 feet From the Shoreline. One Year of Waves Represented.

4 5 6 7 8 9 10 11
Alongshore Distance (Miles)

12 13 14

Figure 3. Case l b. Shoreline Response to 85 Breakwaters Located a Uniform Distance of 400 feet From the Shoreline. One Year of Waves Represented.

100
..................... ............... ...... ..................... .......... .......... ..........
8 0 ...... ........ ..................... ......... ....... ........
....... ... .......... .......... .................... ......... .......... ..........
---------- ..........
6 0 ..... ...... .......... ....................
....... .......... ...... .......... ..................... ................... .......... ..........
4 0 ..... ............... .......... .......... ........... ................. .......... ..........
(D ...... ......... .......... .......... .......... .......... .. ....... .......... ..........
E 20 ....... ..........
..........
ca 0
Noma
-2 ......... .......................... ..........
a 0 : : .
.......... .... ..... ......... .......... ..........
a) VT
4 0 .... .. .......
..................... .............. ... .......... ........
.. ........
................... .
-60 ....... .......
.8 0 ......... .......... ....... .......... .......... .......... ........... .......... .......... ..........

-ion

13 14

100 80 60 C40 E 20
0
0 -20 =-40
0 = .60 U)
-80

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

-10




100
80 60
Mo
0 -20
_40
0
-0

.inn I .r. I l.r I I l

4 5 6 7 8 9 10 11
Alongshore Distance (Miles)

12 13 14

Figure 4. Case 1 c. Shoreline Response to 85 Breakwaters Located a Uniform Distance of 500 feet From the Shoreline. One Year of Waves Represented.

inn

80
60
0 E 20
8
co
-aa0
.
0' -20 40
0 60
-80

4 5 6 7 8 9 10 11
Alongshore Distance (Miles)

13 14

Figure 5. Case Id. Shoreline Response to 85 Breakwaters Located a Uniform Distance of 600 feet From the Shoreline. One Year of Waves Represented.

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

... ...........;..........
. . . . .. . . . . .
.. .......... .. .......

................................ .......... .........................................
. ........ .......... .. ...............
........................ ........ .......... ...... .......... ...........
....... .. ..................... .......... .......... .......... ....... ..........
.......... .......... .......... .......... .......... .......... .......
.......... .......... ...... ..........
..........
.......... ....... .......... ........
--! .......... ...............

..... ... .. :.. ... .. :.......... ;. . .
- : .......... :. ......... . . .i. . .

. . . . . .!. . . .. . . i . . . . .... .. . .. J ... . .. i ... .. . .. . .. .
. . .......... .......... .......... .... . :.......... ........... .......... . .. . .
......... ; .......... ...........i .......... i.......... :,.......... :.......... .......... .......... ........... . .. ......... I ......... .......... i.......... ...... ....... ... .. .. ..... . ...... .........
. . . : .......... ::.......... i....... .......... .......... i... .... ......... .......... ..........
...... ..........,..... .. ............




-40
* 2 0 . . .. . . . . .
~0
-2 0 . . . -- - . . . .. . . . .
4 ......9.0.1.1.1 1
-20~ ~ ~ ~ lnghr Distance. (Miles)..................

Figure 6. Case l b. Shoreline Response to 85 Breakwaters Located a Uniform Distance of 400 feet From the Shoreline. Two Years of Waves Represented.

120
100
80
- 60
C 01) E 40 aC 20
0 O~-20
C
~j-40
0
-C-60
.80

4 5 6 7 8 9 10 11 12 13 14
Aongshore Distance (Miles)

Figure 7. Case 2. Shoreline Response to 85 Breakwaters Located a, Uniform Distance of 400 feet From the Shoreline. One Year of Oblique (-3 0') Waves Represented
7

.......... .......... ....... .. ........ ......... .. ....
.. ........ ......
..................... .......... .......... .......... ........... .......... .......... ..........
.. .. ........... ...... .... ...... ..........
..........
....... ...................... .......... .......... ...... ................ ..........
. ...... .... ...... ......... :. ..........
....... .. ............. .......... .......... .......... ...................... .......... ..........
........... ..........
flifl
U111 I mqj Jm ...
...... .... ........ ............
.................. .... ..... ..........
. ......... .......... .......... .......... .......... .......... ...................... ... ...... ......
.......... .......... .......... .......... .......... .......... ...................... .. ....... ..........
. .................... .......... .......... .......... ...... .......... .... ........ ..........
........... I .......... .... .... ..................... .......... .......... ........ .......
. ............. ....... ........... ............ .........
.......... ........ ....... .. ........ ... .......... ............ ..........
.......... .......... .......... .......... .......... .......... .......... .......... .......... ..........

-IVU




80 70 60
50
E
0 40
30
20 10
0
0
-10 -20

-.0
4 5 6 7 8 9 10 11 12 13
Longshore Distance (miles)
Figure 8. Case 3. Shoreline Response to 85 Breakwaters Located at
Actual Distances From the Shoreline. One Year of Normally
Incident Waves Represented
3.5 Case 4. Oblique Waves, Actual Distances of Breakwaters Offshore
These results are presented in Figure 9 for a deep water wave obliquity of 100 such that a westward longshore sediment transport of approximately 58,000 cubic yards per year occurs. As anticipated from previous cases, the primary difference between this result and that for normally incident waves is the accumulation and erosion on the updrift and downdrift sides, respectively.
3.6 Cases 5a 5d. Normally Incident Waves, Actual Distances of Breakwaters Offshore, Overtopping Represented
For this case, three different levels of overtopping are represented for breakwaters 39 through 44 (This numbering system starts with Breakwater 1, the easternmost breakwater and increases sequentially toward the west). All other conditions are maintained the same as in Case 3. Results are presented in Figures 10, 11, 12, and 13 for wave overtopping of 25%, 50%, 75% and 100%, respectively. Figure 8 can be considered as the case for 0% overtopping. The rather small effect on the shoreline due to 25% overtopping is explained as due to the 2.5 exponent in the transport equation which results in a very small relative transport (0.25025 = 0.031)!
8

...._ Breakwater Distance From 1995 Shorelirne/1 0.0 ft)
. . . . .. .... ....... ............ .. . ...... . .........
: . . .i. . .... .i ...... ... ............. . ."- --- ....... -...




-:Breakwater Distance From 199 he~ineli 0.0 (ft)
. .... .... ... ..... . ........... L .... ... .......-...... ....... ........
A i] iiiiiiiiiiiiiii~iL Z il,, ....

4 5 6 7 8 9 10
Longshore Distance (miles)

11 12 13

Figure 9. Case 4. Shoreline Response to 85 Breakwaters Located at Actual Distances From the Shoreline. One Year of Oblique (-300) Waves Represented

, E ast ......... .......W e t ........W .............. ... ........... W est
BrBreakwat.rDistance From Shore11O.O .
2., .... .-R..... .... e... ,:=giondo~ ,e *n ......
o
...... . ......... ......... .......... i.... ..... .......... ........... ......... .......... i.........
-20 .. .. ..... . . . .
. o ........ ....... ... .......... .......... . . Lo ........ .......... .. . .......... i .........
40 ............
-0

4 5 6 7 8 9 10 11
Alongshore Distance (Mles)

12 13 14

Figure 10. Case 5a. Shoreline Response to 85 Breakwaters Located at Actual Distances From the Shoreline. One Year of Normally Incident Waves Represented. Overtopping of 25% in Region Indicated.

..........

M M.. M M A A VVVVVVVVVVV ....... A V..........




100 80 60 40
20
0
~-40
-80

-100

4 5

7 8 9 10 11
Alcngshxoe Distance (Mies)

12 13 14

Figure 11. Case 5b. Shoreline Response to 85 Breakwaters Located at Actual Distances From the Shoreline. One Year of Normally Incident Waves Represented. Overtopping of 50% in Region Indicated.

100 80 60 S40
20
-20
~-40
-60 U)
-80
-100

4 5 6 7 8 9 10 11
Alongshore Distance (Miles)

12 13 14

Figure 12. Case 5c. Shoreline Response to 85 Breakwaters Located at Actual Distances From the Shoreline. One Year of Normally Incident Waves Represented. Overtopping of 75% in Region Indicated.
10

.. a t.. .. i. ... ........ .:... ....... i.... ..i.......... ...... W e s t ..
-. --i--Breat'-er bh-.Frbm.S aO-------.
::::::::: :::::..........: . ... .. ........... : : : : : : : : : : :
. . .

....... s ......... .... ..... ...... .. __.....
.. .. . . .. .i. . . .. . i . .. .. ...... i.......... ; .. ....... ..... ....
... .. ... .. ... .... ... .. ;... .. .. i .. .. ...? .. ............... . . . ....... .. .. .
.. . .............. ........ i ........ .. .. ..... i .................... ..... . ....... i .........
.......... / i i ; : ; i ,..




100
.... East Breakwater Distance From Shore/ I0.0 ..
80 -.
.......... i................ .. .
-80.
" ~ ~ ~ --- -4 ..................... .......... .. ..........................
0 0 .... .. .. . .i. . . . . i. . . . . .i. . . . . . . . .
2 0 . . .:. . . .: .... . . i... . . . . . . i.. . . .:.. . . .. . :.. . . .. . . . . . . . . .
-2 0 . . ... ......... .......... .......... .... ...... ........... ........... ......... ......... ..........
Q . . . . . :. . . . . . . . . . ... . . . .. . . . . . I . . . . . !. . . . . . :.. . . . . . ... . . .
-10O0 i r I I I i I r
4 5 6 7 8 9 10 11 12 13 14
Alongshore Distance (Miles)
Figure 13. Case 5d. Shoreline Response to 85 Breakwaters Located at Actual Distances From the Shoreline. One Year of Normally Incident
Waves Represented. Overtopping of 100% in Region Indicated.
4.0 SUMMARY
A program has been developed for the representation of the Holly Beach, LA system of breakwaters and the associated shoreline response. Examples have been presented illustrating the capabilities of the model which include: (1) Variable distances of individual breakwater units from the shoreline, (2) Overtopping due to combinations of high waves and elevated water levels, (3) The presence of a non-erodible shoreline along selected portions of the shoreline, and
(4) Forcing which includes time varying tides and wave conditions. Although the latter capability has not been incorporated into the model; the model framework allows its ready inclusion. The model could also be easily adapted to account for the effects of beach nourishment. The model, employed in conjunction with engineering judgement, should provide a useful basis for design of beach nourishment and/or breakwater modifications in the Holly Beach, LA area.
5.0 REFERENCE
Dean, R. G. (1978) "Diffraction Calculation of Shoreline Planforms", Proceedings, Sixteenth Conference on Coastal Engineering, ASCE, New York, pp. 1903-19 14.
11




APPENDIX A
CHARACTERISTICS OF PROGRAM: HOLLY.FOR




APPENDIX A

CHARACTERISTICS OF PROGRAM: HOLLY.FOR
1.0 INTRODUCTION
The following sections describe the various characteristics of the Program HOLLY.FOR including the methods of representing the wave interactions with the breakwater elements, and transformation, sediment transport and required input. Figure A-i presents the system of interest, defines the coordinate system and provides definitions for the wave and shoreline orientations.

BP, reakwater Units I' Typical Source

-Waves Radiating Out From Source

Figure A-1. Definition Sketch, Showing Waves Radiating From a Typical Source and Wave and Shoreline Angle Definitions.

A




2.0 PROGRAM BASIS

2.1 Wave Transformation From Gulfward Source Elements to Breaking Location.
Considering a particular grid line at the shoreline where sediment transport is to be calculated, the wave height and direction associated with a particular source element are represented as described below.
2.1.1 Wave Height and Wave Direction
The total wave height and direction at a shoreline position of interest are based on the sums of wave components originating from 10 source elements on either side of position of interest.
The wave height and direction are calculated at a distance midway between the breakwater and the shoreline with the direction being composed of the weighted sum of the radially propagating circular wave fronts and the refraction and the wave height being the product of the effects of shoaling and spreading of the circular wave front such that total energy is conserved gulfward of the breaking location.
3.0 SEDIMENT TRANSPORT
The longshore sediment transport, Q, is calculated according to the usual equation
Q 1K (1p) (S 1)
where K is the so-called sediment transport coefficient (here taken as 0.77), Hb is the breaking wave height, g is the gravitational constant, ic is the retio of breaking wave height to breaking water depth (here taken as 0.78), p is porosity, S is the specific gravity of sediment relative to that of water in which the sediment is immersed, f3 is the orientation of the local shoreline and ab is the breaking wave direction (See Figure A-i for definitions of 03 and Cb).
Representation of Overtopping
The result of breakwater elements being overtopped by a particular combination of wave and water level conditions is simply to "activate" these elements which then are treated as described above for a normally active element. The program included with this report has the following very simple algorithm for the wave transmission coefficient, Kr,, by first defining a quantity, BB




BB = ii+ H/2-z

where rI is the tide elevation, H is the wave height at the breakwater and z is the breakwater crest elevation. With BB quantified, the overtopping coefficient is defined as K,=0, BB<0 K, = BB/2.0, 0 < BB < 2.0 K, = 1.0, BB > 2.0




APPENDIX B
LISTING OF PROGRAM: HOLLY.FOR




$LARGE
C HOLLY.FOR
C
C ********************************************************************* C THIS PROGRAM DEVELOPED FOR APPLICATION TO HOLLY BEACH, LOUISIANA C FOR PREDICTION OF EFFECTS OF BREAKWATERS AND BEACH NOURISHMENT *
C THIS IS FINAL VERSION OF HOLLY.FOR **
C THIS VERSION USES ORIGINAL COORDINATE SYSTEM *
C
C *********************************************************************
C
DIMENSION XSL(2000),YSL(2000),XBL(2000),YBL(2000),JB(2000),
1 ELEV(2000),WORD(20),Q(2000),XBLV(100),YBLV(100)
OPEN(UNIT=6,FILE='HOLLY.OUT')
OPEN(UNIT=5,FILE='HOLLY.INP',STATUS='OLD')
OPEN(UNIT=7,FILE='HOLLYC1 .OUT') OPEN(UNIT=8,FILE='HOLLYC2.OUT')
120 FORMAT(5E12.4) 121 FORMAT(8F10.2)
122 FORMAT(//)
123 FORMAT(5F8.2,416)
124 FORMAT(8F8.2)
125 FORMAT(4(E8.2,F8.2))
126 FORMAT(20A4)
127 FORMAT(20A4,/)
128 FORMAT(216,F8.2)
129 FORMAT(214,8E9.3)
130 FORMAT(' BETA = 'F8.2,' DEGREES',/)
160 FORMAT(816)
162 FORMAT(F8.2,316,2F8.2)
164 FORMAT(816)
165 FORMAT(/)
166 FORMAT(I6,3F12.3)
167 FORMAT(' INITIAL SHORELINE (INCL. NOURISHMENT) POSITION',/)
168 FORMAT(I6,F8.1,2E12.4,F8.3)
169 FORMAT(I6,3E12.4) 449 FORMAT(216,8F8.3) 450 FORMAT(216,2F8.3)
451 FORMAT(216,3F10.2)
READ(5,126)(WORD(I),I=1,20)
READ(5,124)HO,T,ALPO,BTAO,XMU2,DY,DT,XSLC
WRITE(*,*)HO,T
READ(5,123)HSTR,B,XK,VFACT,QBKREF,IREF,JMAX,NTIMES,NBREAK C READ(5,124)(YBLV(K),XBLV(K),K=1,NBLOC)
WRITE(*,*)NBREAK,HSTR,B,VFACT
C WRITE(6,170)HO,T,ALPO,BTAO,XMU,DY,DT
C WRITE(6,172)HSTR,B,XK,VFACT,QBKREF
C WRITE(6,173)IREF,IMAX,NTIMES,NS
WRITE(6,165)
PI=3.14159
GRAV=32.2 XKAP=0.78
HSTRB=HSTR+B
HTBL=HO TIDE=0.0
FACTD=PI/180.0
XMU2=FACTD*XMU2 BBTAO = FACTD*BTAO ALPO=FACTD*ALPO THTAO=BTAO-ALPO




C READ(5,128)(I,JB(J),XBL(J),J=1,JMAX)
DO 700 J=1,JMAX
JB(J)=0
XSL(J)=XSLC
YSL (J) = (J-1) *DY YBL (J) = (J-1) *DY
700 XBL(J)=0.0
C THIS PART READS IN BREAKWATER LOCATIONS AND ELEVATIONS
KK=1
DO 702 J=1,NBREAK
READ(5,450)IB,IJ,XA,XB
JB(IJ) =1
XBL(IJ)=800.0-3.28*XA
ELEV(IJ)=XB
KK=KK+1
YBLV(KK)=YBL(IJ+1)
XBLV(KK)=XBL(IJ)
DO 701 JJ=IJ+1,IJ+2
XBL(JJ) =XBL(IJ) YBL(JJ)=YBL(JJ)
ELEV(JJ)=ELEV(IJ)
JB(JJ)=JB(IJ)
701 CONTINUE 702 continue 704 CONTINUE
YBLV(1)=0.0
YBLV(KK+1)=YBL(JMAX)
XBLV(1) =XBLV(2)
XBLV(KK+1)=XBLV(KK)
KK=KK+1
C WRITE(7,451)(J,JB(J),YBL(J),XBL(J),ELEV(J),J=1,JMAX)
C INTERPOLATE TO DETERMINE BREAKWATER LOCATION LINE
CALL INTERP(JMAX,KK,XBL,YBL,XBLV,YBLV) C do 333 j=1,jmax
C 333 WRITE(6,166)J,YBL(J),XBL(J)
DO 345 j=1,jmax
XBL (J) =400.0
aa=800.0-xbl(j)
345 IF(jb(j).eq.1)write(7,451)j,jb(j),ybl(j),aa
c WRITE(7,451)(J,JB(J),YBL(J),XBL(J),ELEV(J),J=1,JMAX)
C WRITE(6,121)(YBL(I),XBL(I),I=560,660)
C JJ=1
C IF(JJ.EQ.1)GO TO 600
C CALL WVNUM(HSTR,T,CC)
CO=GRAV*T/(2.0*PI) C CGO=CO/2.0
HTBL=1.0
CBL=SQRT(GRAV*HTBL/XKAP)
THTA=ASIN(CBL/CO*SIN(ALPO))
WRITE(6,*)THTA
DPTBL=4.0
C ***** FOLLOWING IS TIME LOOP
DO 300 NT=1,NTIMES
C WRITE(*,*)NT,NT
IF(MOD(NT,50).EQ.0)WRITE(*,*)NT,NTIMES,XSLC
C DETERMINE WAVE HEIGHTS AND DIRECTIONS AT LOCATIONS MIDWAY C BETWEEN BREAKWATER LINE AND SHORELINE
JBS=J1
JBE=J2 B-2
CEL=8.0




SIG=1.0
KMAX=1
DO 1800 I=2,jmax
C FIND COORDINATES OF GRIDLINE FOR WHICH TRANSPORT IS TO BE CALCULATED
XC=0.25*(XSL(I)+XSL(I-1)+XBL(I)+XBL(I-1))
YC=0.5*(YSL(I)+ysl(I-1))
220 CONTINUE
CALL PHASE(I,XC,YC,XK,ELEV,TIDE,
1 CEL,DY,SIG,HTBL,DPTBL,J1,J2,
2 JB,XBL,YBL,XSL,YSL,Q,JMAX,THTA)
IF(NT.EQ.50.AND.I.EQ.100)WRITE(*,*)NT,I,Q(I)
C WRITE(7,129)I,K,DYDX(I,K),XC,YC,XEPS(I),YEPS(I)
C WRITE(7,120)ALPHA(I),XEPS(I),YEPS(I),XMU2(I)
1800 CONTINUE 1802 CONTINUE 1700 CONTINUE C WRITE(7,120)(DYDX(I,K),XEPS(I),YEPS(I),I=1,IMAX
CALL CONT(Q,XSL,DT,DY,HSTRB,JMAX,XSLC)
IF(MOD(NT,394).NE.0.AND.NT.NE.1)GO TO 300
TY=DT*NT/(31.536E06)
YMAX=XSLC-XSL(202)
YMIN=XSLC-0.5*(XSL(198)+XSL(206))
YBAR=0.5* (YMAX+YMIN)
YSAL=YMAX-YMIN
WRITE(6,120)TY,YMIN,YMAX,YBAR,YSAL
300 CONTINUE
DO 302 I=1,JMAX DYC=XSLC-XSL(I)
CC=YSL(I)/5280.0
AA=800-XBL(I)
302 WRITE(8,166)I,CC,AA,DYC
304 CONTINUE
DO 340 J=1,jmax
IF(JB(J).EQ.0)GO TO 340
AA=800.0-XBL(J)
BB=YBL(J)/5280.0
WRITE(6,121)BB,AA
340 CONTINUE 600 CONTINUE
STOP
END
C ************************************* C *************************************
SUBROUTINE PHASE(I,XC,YC,XK,ELEV,TIDE,
1 CEL,DY,SIG,HTBL,DPTBL,J1,J2,
2 JB,XBL,YBL,XSL,YSL,Q,JMAX,THTA)
DIMENSION XSL(2000),YSL(2000),ELEV(2000),
1 JB(2000),XBL(2000),YBL(2000),Q(2000)
128 FORMAT(I6,8E9.3)
129 FORMAT(214,4F6.1,3F8.3,4F6.3)
130 FORMAT(516,3F10.4,2F10.2)
pi=3.14159265
QSUM=0.0
HSM=0.0
S1=0.0 S2=0.0 S3=0.0
DXSL=(XSL(I)-XSL(I-1))
DYSL=YSL(I)-YSL(I-1) B-3
BETAS=ATAN2(DXSL,DYSL)




C WRITE(*,*)BETAS
CC=0.5*CEL
J1=I-10 J2=I+9
IF(J1.LT.1)J1=1
IF(J2.GT.JMAX)J2=JMAX
DO 1600 J=J1,J2
FACT1=1.0
IF(JB(J).EQ.1) CALL OTOP(J,ELEV,HTBL,TIDE,FACT1) C WRITE(*,*)J,J1,J2,JB(J),FACT1
IF(FACT1.EQ.0.0)GO TO 1600 1500 DXC=XC-XBL(I) DYC=(YC-YBL(J))
ALPHA=ATAN2(DYC,DXC)
ALPHA=-ALPHA+THTA
RC=SQRT(DXC**2+DYC**2)
C WRITE(*,*)DXC,XSL(JBS),XBL(JBS),DYC,YC,Y(J),RC
HTC=SQRT(DY/RC)*HTBL
HTCS=HTC
C NEXT FEW STATEMENTS ARE FOR OVERTOPPING OF BREAKWATER
HTC=factl*HTCS
IF(JB(J).NE.1)HTC=HTCS
c if(j.eq.201)write(*,*)j,jb(j),factl,htcl28
XX=HTC
AA=XX**2*SQRT(DPTBL)
ab=sig*RC/cel
AC=SIG/(CEL*RC)
C WRITE(*,*)I,DXC,XMU
HMAX=SQRT(AA)
BMA=BETAS-ALPHA
IF(BMA.GT.PI/4.0)BMA=PI/4.0
IF(BMA.LT.-PI/4.0)BMA=-PI/4.0
S1=S1+HMAX**2.5*SIN(2.0*BMA)
S2=S2+HMAX**2.5
S3=S3+HMAX
c WRITE(6,129)I,J,DXC,DXC,DYC,RC,HTC,XMU,BETAS,ALPHA,HMAX,QCUR,QSUM
1600 CONTINUE C if(i.eq.2)write(*,*)I,BETAS,ALPHA,HMAX,QSUM,DXSL,DYSL
202 CONTINUE 600 CONTINUE
S3=S3/7.69
Q(I)=0.374*XK*S3**2.5*S1/S2
RETURN
END
C ***************************************************
SUBROUTINE CONT(Q,XSL,DT,DY,HSTRB,JMAX,XSLC)
DIMENSION Q(2000),XSL(2000)
XSL(11)=XSLC
XSL(JMAX-11)=XSLC
DO 100 J=11,JMAX-11
XSL(J)=XSL(J)+DT/(DY*HSTRB) (Q(J+1)-Q(J))
100 CONTINUE
XSL(1)=XSLC
XSL(JMAX)=XSLC
RETURN
END
C
C B-4
SUBROUTINE INTERP(JMAX,NBLOC,XBL,YBL,XBLV,YBLV)




DIMENSION XBL(2000),YBL(2000),XBLV(1000),YBLV(1000)
DO 100 J=1,JMAX
YC=YBL(J)
DO 80 N=2,NBLOC
IF(YC.GE.YBLV(N-1).AND.YC.LE.YBLV(N))GO TO 60
GO TO 80
C START INTERPOLATION HERE
60 AA=YC-YBLV(N-1)
AB=YBLV(N)-YBLV(N-1) AC=XBLV(N)-XBLV(N-1)
XBL(J)=XBLV(N-i) +AA/AB*AC
GO TO 100
80 CONTINUE
100 CONTINUE
RETURN
END
C
C
SUBROUTINE OTOP(J,ELEV,HTBL,TIDE,FACT1)
DIMENSION ELEV(2000)
FACT1=0.0
AA=TIDE+HTBL/2.0-ELEV(J)
IF(AA.LE.0.0)GO TO 200
FACT1=AA/2.0
IF(FACT1.GT.1.0)FACT1=1.0
200 CONTINUE
RETURN
END

B-5




APPENDIX C
LISTING OF INPUT FILE: HOLLY.INP




Tes< N1 ,re Piob 5T
/PC. &\I/CI r Ivt~ VI ALs~ 5#4C,' RE~ 1, 1 I
1.00 6.8 0.0 0.0 180.0 50.0 3600.0 800.0
8.0 4.0 0.78 1.48 0.0 1 1799 8760 85 V RA4n gn f
___ __ __ ___ __ __~ v i.u~op p R .b- 6 p 8
1 507 200.0 4.0 o \ F ost 94 swe Iou (A)
2 516 200.0 4.0
3 525 200.0 4.0
4 534 195.0 4.0

5 543 200.0
6 552 197.0
7 561 195.0
8 570 190.0
9 579 188.0
10 588 195.0 11 597 195.0 12 606 188.0 13 615 180.0 14 624 170.0 15 633 165.0 16 642 165.0 17 651 163.0 18 660 163.0 19 669 160.0 20 678 176.0 21 687 160.0 22 696 130.0 23 705 130.0 24 714 130.0 25 723 130.0 26 732 130.0 27 741 130.0 28 750 130.0 29 759 126.0 30 768 126.0 31 777 126.0 32 786 126.0 33 795 126.0 34 804 126.0 35 813 126.0 36 822 120.0 37 831 120.0 38 840 120.0 39 849 120.0 40 858 120.0 41 867 120.0 42 876 120.0 43 885 120.0 44 894 120.0

4.0
4.0
4.0
4.0
4.0
4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0
4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0

"b R O TaTl




45 903 120.0 4.0 46 912 120.0 4.0 47 921 120.0 4.0 48 930 120.0 4.0 49 939 120.0 4.0 50 948 125.0 4.0
51 957 120.0 4.0
52 966 120.0 4.0
53 975 150.0 4.0 54 984 152.0 4.0 55 993 149.0 4.0
56 1002 152.0 4.0 57 1011 150.0 4.0 58 1020 152.0 4.0 59 1029 152.0 4.0 60 1038 177.0 4.0
61 1047 194.0 4.0
62 1056 194.0 4.0
63 1065 188.0 4.0
64 1074 188.0 4.0
65 1083 188.0 4.0
66 1092 197.0 4.0
67 1101 197.0 4.0
68 1110 200.0 4.0
69 1119 200.0 4.0
70 1128 202.0 4.0
71 1137 192.0 4.0
72 1146 190.0 4.0
73 1155 190.0 4.0
74 1164 190.0 4.0
75 1173 192.0 4.0
76 1182 190.0 4.0
77 1191 188.0 4.0
78 1200 151.0 4.0
79 1209 125.0 4.0
80 1218 130.0 4.0
81 1227 130.0 4.0
82 1236 130.0 4.0
83 1245 125.0 4.0
84 1254 138.0 4.0
85 1263 148.0 4.0

C-2