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DOCUMENT
COLLECTION

Estimation of Flow Through
Offshore Breakwater Gaps Generated
by Wave Overtopping

by
William N. Seelig and Todd L. Walton, Jr.

COASTAL ENGINEERING TECHNICAL AID NO. 80-8
DECEMBER 1980

Approved for public release;
distribution unlimited.

aa U.S. ARMY, CORPS OF ENGINEERS
ae. COASTAL ENGINEERING)
ee | RESEARCH CENTER

Kingman Building
no, 0-F Fort Belvoir, Va. 22060

Reprint or republication of any of this material
shall give appropriate credit to the U.S. Army Coastal
Engineering Research Center.

Limited free distribution within the United States
of single copies of this publication has been made by
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The findings in this report are not to be construed
as an official Department of the Army position unless so
designated by other authorized documents.

UNCLASSIFIED
SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

READ INSTRUCTIONS
REPORT DOCUMENTATION PAGE BEPREAD INSTRUCTIONS
1. REPORT NUMBER 2. GOVT ACCESSION NO.| 3. RECIPIENT'S CATALOG NUMBER
CETA 80-8

4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED

ESTIMATION OF FLOW THROUGH OFFSHORE BREAKWATER
GAPS GENERATED BY WAVE OVERTOPPING

Coastal Engineering

Technical Aid
6. PERFORMING ORG. REPORT NUMBER

8. CONTRACT OR GRANT NUMBER(s)

7. AUTHOR(s)

William N. Seelig
Todd L. Walton, Jr.

10. PROGRAM ELEM
AREA & WORK U

NT, PROJECT, TASK
IT NUMBERS

9. PERFORMING ORGANIZATION NAME AND ADDRESS
Department of the Army

Coastal Engineering Research Center (CERRE-CS)

Kingman Building, Fort Belvoir, Virginia 22060

CONTROLLING OFFICE NAME AND ADDRESS

Department of the Army

Coastal Engineering Research Center

Kingman Building, Fort Belvoir, Virginia 22060
14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office)

=
N

F31538

12. REPORT DATE
December 1980
13. NUMBER OF PAGES

21

15. SECURITY CLASS. (of this report)

UNCLASSIFIED

DECL ASSIFICATION/ DOWNGRADING
SCHEDULE

15a,

16. DISTRIBUTION STATEMENT (of this Report)

Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, if different from Report)

18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side if necessary and identify by block number)

‘Breakwaters Wave height Wave period
Offshore breakwaters Wave overtopping Waves

20. ABSTRACT (Continue on reverse side if necesaary and identify by block number) } 2
This report presents a method for estimating the net flow through the gaps of

offshore segmented breakwaters caused by wave overtopping of the breakwaters.
The method was developed so that either monochromatic or irregular waves can be
specified. Example problems illustrate the effects of wave height and period,
breakwater freeboard, spacing between breakwaters, and shore attachment on the
flow rate. Computations may be done manually or by using the computer program,
BWFLOW2, available from the Corps of Engineers Computer Library, U.S. Army
Engineer Waterways Experiment Station, Vicksburg, Mississippi.

DD , FORM 1473 EDITIow OF 1 Nov 65 IS OBSOLETE

TAN 72 UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

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PREFACE

This report describes a method for estimating the flow rate through the gaps
of offshore segmented breakwaters caused by wave overtopping. Factors that can
be investigated using this method are the influence of breakwater freeboard,
wave height and period, breakwater length and spacing, number of breakwaters,
distance offshore, water depth at the breakwater, and shore attachment on the
flow rate. Other wave effects on hydraulics, such as diffraction, refraction,
reflection, and wave-current interactions, have not been considered. The work
was carried out under the offshore breakwaters for shore stabilization and
evaluation of shore protection structures programs of the U.S. Army Coastal
Engineering Research Center (CERC).

The report was prepared by William N. Seelig and Dr. Todd L. Walton, Jr.,
Hydraulic Engineers, under the general supervision of Dr. R.M. Sorensen, Chief,
Coastal Processes and Structures Branch and Dr. J.R. Weggel, Chief, Evaluation
Branch.

Comments on this publication are invited.

Approved for publication in accordance with Public Law 166, 79th Congress,
approved 31 July 1945, as supplemented by Public Law 172, 88th Congress,
approved 7 November 1963.

ED E. BFSHOP
Colonel, Corps of Engineers
Commander and Director

IIL

10

CONTENTS

CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI) .
SMMIBOLES ANNO) DIIMIMERONS, 56 6 6 69 6 60500 0000
IGNALOWDIOKCTEWOW 5 95 a 6 Go Oo oO O 0 0 ONG 0 0 0 GO 6 0
HYDRAULICS OF DETACHED BREAKWATERS. . ...-.. . -»

1. Enclosed Breakwater Systems ........ .-

2. Offshore Breakwaters with Gaps. ...... -
ID VAMP, TROIS 5 5 6 06 590 6 5 6 Oo Go 0 060 oO DIO
SUMMARY AND CONCLUSIONS . . ....-:....4.c4 ©

TAI VOI (IMDS 6 6 6 60000000 OOo OO 8

TABLES
Computer program input for example problem 2... .

Computer program output for example problem 2... .
FIGURES
Definition sketch. . ~~... +--+ «© + s+ s+ 2 ee eee

Overtopping parameters, oa and Qs > riprapped 1:1.5 structure

slope on a 1:10 nearshore slope ........ . -
Ponding levels for porous multilayered breakwaters .
An offshore breakwater system. . . . . « « » «= «= « «
Dimensionless velocity as a function of K.....
Design conditions for example problem 1. ..... .
Effect of breakwater freeboard and gap spacing on V.
Effect of incident wave height and gap spacing on V.
Effect of wave period and PapEspacine mon ViEem iment

Effect of shore attachment and gap spacing @m Woo 6

Page

iL7/

18

20

20

CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI) UNITS OF MEASUREMENT

U.S. customary units of measurement used in this report can be converted to
metric (SI) units as follows:

Multiply ; by To obtain
inches 25.4 millimeters
2.54 centimeters
square inches 6-452 square centimeters
cubic inches 16.39 cubic centimeters
feet 30.48 centimeters
0.3048 meters
Square feet 0.0929 square meters
cubic feet 0.0283 cubic meters
yards 0.9144 meters
Square yards 0.836 square meters
cubic yards 0.7646 cubic meters
miles 1.6093 kilometers
Square miles 259.0 hectares
knots 1.852 kilometers per hour
acres 0.4047 hectares
foot-pounds 1.3558 newton meters
millibars 1.0197 x 10 3 kilograms per square centimeter
ounces 28.35 grams
pounds 453.6 grams
0.4536 kilograms
ton, long 1.0160 metric tons
ton, short 0.9072 metric tons
degrees (angel) 0.01745 radians
Fahrenheit degrees 5/9 Celsius degrees or Kelvins!

1To obtain Celsius (C) temperature readings from Fahrenheit (F) readings,
use formula: C = (5/9) (F -32).

To obtain Kelvin (K) readings, use formula: K = (5/9) (F -32) + 273.15.

Qn

ZA

td

O Ol
t=)

SYMBOLS AND DEFINITIONS
cross-sectional flow area of gap between breakwaters
cross-sectional flow area between breakwaters and shoreline
empirical runup coefficients
breakwater gap width

discharge coefficient for breakwater gaps

discharge coefficient for space between breakwaters and shoreline

water depth at the toe of the structure
breakwater freeboard = h - ds
acceleration due to gravity

wave height at the structure

equivalent deepwater wave height
significant wave height at the structure

structure height

difference in mean water levels inside and outside of breakwaters

a dimensionless parameter
deepwater wavelength
breakwater length

log e

number of breakwaters

_ ponding level

mean net flow rate through a breakwater gap or inlet

net inflow by overtopping of a breakwater

empirical overtopping parameter

net inflow by overtopping per unit length of a breakwater
overtopping per unit length of breakwater with no return flow

runup

SYMBOLS AND DEFINITIONS——Continued
wave period
mean net water velocity for flow through a gap = V/A,
dimensionless velocity
empirical overtopping parameter
breakwater seaward-face slope angle

surf similarity parameter

Fy pasttid deve sn wl : re : i.
4 shen wc Diese tenia»: re ie a . oe
QR, aet. Lot low he eimanepning | ofa eal ine , 7 +

w soap ixtenl overtopping parnnst ex
a = ast intice uy eer vogtitng tend Hott seat af 4 ae | en oor m
iv : ty ieréontng, par wrod | oak of brava = he atiiiaty fm ei

‘ESTIMATION OF FLOW THROUGH OFFSHORE BREAKWATER
GAPS GENERATED BY WAVE OVERTOPPING

by
William N. Seeltg and Todd L. Walton, Jr.

I. INTRODUCTION

Offshore breakwaters are often constructed to protect harbors or eroding
coasts from wave action. Wave overtopping of segmented breakwaters generates
a seaward flow through breakwater gaps. Low discharges and low water velocities
are usually desirable in gaps between breakwaters. High velocities may be a
hazard to navigation or swimmers, and large net exit flows through the gaps
May transport sediment out of the breakwater area. This report illustrates a
technique for predicting the net discharges and mean velocity through breakwater
gaps caused by overtopping.

II. HYDRAULICS OF DETACHED BREAKWATERS

Since the cost of a breakwater increases with the height of the structure,
it may be necessary to build the structure to allow some wave overtopping (Fig.
1). A moderate overtopping rate, which helps maintain water quality by encour-
aging circulation, may also be desirable. If the breakwater is impermeable the
volumetric rate of overtopping per unit length by breakwater, q, (assuming
mo return flow over the breakwater), may be predicted (Weggel, 1976; U.S. Army,
Corps of Engineers, Coastal Engineering Research Center, 1977) by

(1)
PROTECTED
REGION
Np = P= ponding level for an
enclosed system
SWL

Figure 1. Definition sketch.

where

g = the acceleration due to gravity

H5 = the equivalent unrefracted deepwater wave height

R = the vertical: height of runup on the structure if the breakwater
were high enough so that no overtopping occurred

F = breakwater freeboard = h - d,

h = the structure crest elevation

ch ae the water depth at the toe of the structure.

Qs and a are empirical overtopping coefficients found in the Shore Protection
Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering Research Center,
1977, Ch. 7). Sample values of the empirical coefficients for an impermeable
riprap structure with a 1 on 1.5 seaward slope are shown in Figure 2.

A first approximation of the wave runup on rubble-mound breakwaters may be
estimated using the equation of Ahrens and McCartney (1975):

nS Re ge aca
Lo

where Ly is deepwater wavelength, and 6 is the slope angle of the seaward
face of the breakwater; the empirical coefficients a = 0.692 and b = 0.504 are
recommended. Note.--Other methods for estimating runup on various structures
may be found in the SPM (U.S. Army, Corps of Engineers, Coastal Engineering
Research Center, 1977) and Stoa (1979).

Equations (1) and (2) were developed using monochromatic wave tests, so
they should be used for swell wave conditions where the wave height and period
from one wave to the next is approximately constant. The method of Ahrens
(1977) for modifying equations (1) and (2) for irregular waves is recommended
for irregular waves generated by nearby storms. The irregular wave overtopping
prediction procedure is rather complicated, so the computer program BWFLOW2
(CERC program number 752X6R1ANC) is recommended for irregular waves. This pro-
gram is available in the Corps of Engineers Computer Library at U.S. Army
Waterways Experiment Station, Vicksburg, Mississippi. Note that the irregular
wave overtopping method tends to be conservative because a Rayleigh wave height
distribution is assumed, while the actual distribution may be truncated due to
depth or steepness limited breaking.

1. Enclosed Breakwater Systems.

If the breakwater system is enclosed on either end by impermeable groins
and the breakwater has no gaps, water overtopping the breakwater would cause
the water level landward of the breakwater, hp, to rise. Eventually, the
zone landward of the breakwater would fill up to a ponding level where the sea-
ward flow of water over the breakwater would equal inflow and the net flow, Shas
would be zero. Diskin, Vajda, and Amir (1970) tested a number-of breakwaters

10

Bs Appr imate Breaking! Limi 1
ee (110 Nearshore slope),

or ie x nei Feat | RE main pa ne - = 0.8
Non=Breaking}—|—|_|- Hi i
ie eect att :

S

{ Riprop roughly , !
Papal 3 ft. in diameter ah 0.08

sw.

fe
o
[-2)
4
*& (ft/sec®)

| 0048 @-
; + (0.1600)

Figure 2. Overtopping parameters, a and Q&, riprapped 1:1.5 structure
slope on a 1:10 nearshore slope (from U.S. Army, Corps of
Engineers, Coastal Engineering Research Center, 1977).

at various water depths, wave heights, and wave periods and found that the
ponding level (Fig. 3) may be estimated from

F
= 0.6e -(-0.7 ‘ a)

aie”

(3)

0.1 for ae 2.05

where F is the breakwater freeboard defined as (h-d,). The maximum ponding
level occurs at F/Hg = 0.7 because this is the point just before the seaward
flow over the top of the breakwater occurs. Note that there is scatter in the
data used to develop equation (3) with approximately 90 percent of all data
points falling within 20 percent of the equation. A sensitivity analysis shows
that this scatter is not important for this report, because flow rates are
weakly influenced by the value of P.

Note that the laboratory tests used to develop equation (2) show some
ponding for high breakwaters not overtopped and submerged breakwaters. This
ponding occurs because the breakwater reduces the wave height landward of the
structure and the change in wave height causes wave setup (Longuet—Higgins,
1967).

Overtopping tests by Diskin, Vajda, and Amir (1970) show that the net over-
topping rate, q,, for breakwaters may be estimated from

an = a (1 - 32) (4)

P/Ho

F/Ho

Figure 3. Ponding levels for porous multilayered breakwaters (after
Diskin, Vajda, and Amir, 1970).

I2

2. Offshore Breakwaters with Gaps.

Overtopping of breakwaters causes a buildup of water in the zone landward
of the structure. If there are gaps between the breakwaters and the breakwaters
are not connected to shore, the butldup of water landward of the breakwaters
causes flow through the openings (Fig. 4). Ome method of estimating the exit
flow through breakwater gaps or inlets is to use a combined continuity-—energy
equation for discharge.

Q = VAc = Cq 28h, A, (5)

where Cg is a discharge coefficient, A, is cross-sectional flow area at
the water level of interest, and V is the mean velocity of water flowing
through the gaps. Many factors may influence the magnitude of Cy but, as
a first estimate, Cq = 0.8 is recommended for gaps. The discharge coefficient
for spaces between breakwaters and the pee Cge>, has a recommended

value of Cg, = 1.0.

Breakwater

Ace = Cross-
Sectional Area

=f

Gap b >— Gap Flow

Q
>—__:—SasV
hp = Difference
in Mean Water Overtopping
Levels
N=3

End Flow

Shoreline

Figure 4. An offshore breakwater system.

Note that in this first approximation of breakwater gap flow that the waves.
are assumed to approach approximately normal to the breakwaters and shoreline,
so the longshore current can be neglected. Other effects such as diffraction,
refraction, reflection, and wave-current interactions have not been considered.

If incident wave conditions do not vary rapidly with time, a condition will
be reached where water flowing into the zone protected by the breakwaters will
equal the exit flow through breakwater gaps or inlets. The equation describing
this condition is

hy
do (1 = ne) Ne = 2ehp (CqgBdg(N - 1) + 2CacAce) (6)

where N is the number of breakwaters, Aca is the cross-sectional flow area
between the breakwaters and shoreline at the end of the system, and B is the
gap width between breakwaters (Fig. 4). Solving equation (6) and putting into
dimensionless form, the dimensionless velocity,

becomes a function of a single coefficient, K, where

2g P |cgBa,(N - 1) + 2c Ne
N28 F [cabs - D+ 2achee] (7)

qo LN

Figure 5, which gives the relation between dimensionless velocity and K, shows
that any combination of factors causing K to increase will produce a smaller
dimensionless velocity. For example, keeping all other factors constant, if the
gap spacing B is increased, K will increase and V will be reduced.

K and the resulting velocity may be easily solved using equation (7) and
Figure 5. The computer program BWFLOW2 can also be used to solve the velocity
and flow through breakwater gaps due to overtopping. This program is recom -
mended if a large number of calculations are needed. The program is also sug-
gested any time irregular wave conditions are assumed, because irregular wave
overtopping rates are a complex function of the overtopping rate given by equa-
tion (1). The cost of running BWFLOW2 is a few cents per condition of interest.

It is recommended that V be kept below 0.5 foot (0.15 meter) per second
for extreme design conditions. Velocities much higher than this value could
transport significant amounts of sediment out of the breakwater system and may
cause scour around the breakwaters. Recall that V is an average velocity
through the gap and that local velocities in breakwater vicinity may be con-
siderably higher.

See ee aaa

SECS Se
MESES eee Ee
SPEC ee
a a a
EEC U LIE SE eo
2
EEUU OSS
LLU PTET Pe a

0 pe —
0.1 0.2 0.4 0.60.8 | 4 6 810 20 40 6080
K

Figure 5. Dimensionless velocity as a function of K.

III. EXAMPLE PROBLEMS

Example problems are presented to illustrate the steps required for manual
or computer computation. The examples indicate the relative importance of the

breakwater design variables on the magnitude of V.
2

kk kK kK KK K KOK & OK & & EXAMPLE PROBLEM 1 * *& & ¥& & RR KKK KK KEE

GIVEN: Four rubble-mound offshore breakwaters have the design conditions
illustrated in Figure 6.

FIND: ve assuming a monochromatic wave height of 8.0 feet (2.44 meters) at
the structure.

SOLUTION: Manual computation is illustrated in this example.

Ho = 7.8 ft
T=7s

Monochromatic Wave

3 V
£=400ft ciate
d,=l2 ft
TID TD mr => EEE Het
Ace= 1,000 ft@ ema B= 125 ft tan 8 = 0.667
Cqe =!.0

Figure 6. Design conditions for example problem 1.

The first step in computations is to determine values for the dimensionless

parameters:
H!
) 7.8
= ———; = 0.0049
eT? 32.2(7)2
and
d
Sim eer
Hot ee bobs

From Figure 2, a and Q& are estimated as a = 0.053 and Q* = 0.019.

surf parameter and resulting runup are determined using equation (2):

= paORGG7alaD
r= : = 3.74
5.12(72)
and
0.692(8) (3.74) .

R= = 7.17 feet

(1 + 0.504[3.74])
The breakwater freeboard is F = h - dg = 13 - 12 = 1.0 foot.

The overtopping rate, q,, given by equation (1) is

0.1085
ge (4 = 1.) 0.053
fe) HER DOUG) Gees) 7 old ail.

9.53 cubic feet per second per foot of breakwater crest.

The

From equation (3) the ponding level is

a= 2s
P = 7.8(0.6)e7 0"? * 1-0/7.8)2 = 3.36 feet

From equation (7)

z= V64.4 3.36 [0.8(125) 12(4 - 1) + 2(1.0) 1,000]
- 9.53(400) 4

or

K = 5.4

The corresponding dimensionless velocity is

ee ee Ere -
cay2e P = 0.18 for K = 5.4 from Figure 5

and

V = 0.18(0.8) V64.6 3.36 = 2.11 feet per second.

kK kK RK KK Kk kK kk & OK ® ® EXAMPLE PROBLEM 2 * *% * RK RRR RK KKK KKK

GIVEN: The same breakwater system as in example 1.

FIND: V_ for irregular wave conditions with a significant wave height,
H, = 8.0 feet (2.44 meters).

SOLUTION: The computer solution is illustrated in this example with the
input shown in Table 1. Resulting computer output is given in Table 2.
The predicted velocity is V =_1.33 feet (0.14 meter) per second. This
velocity is lower than the V obtained for monochromatic waves in example 1
(2.11 feet per second), because irregular waves of a given significant wave
height have less overtopping than monochromatic waves.

Table 1. Computer program input for example problem 2.

iva.

GHCHHOCOHOHIND AHOHHHOOON OOLoIDOCHOHCHHOHHHH Boon0nnb8 OCDDKCHHOOHHHHODD0DDD0000

92245617868 91002 YW GH 19 20 21 2723 26 75 26 D 2875 $6 11 37 1) M4 46 37 35 4B 41 87 5 44 45 46 41 £2.49 90 51 5759 SE 55 SE ST SE S9EO G1 G7 694 ES ES 6/0869 N21 A) eo

FVUVTATTTTT TAT DATTA ATTA TATA 19079709T TTT TTA ata

Table 2. Computer program output for example problem 2.

hee IRREGULAR WAVES #888
N LCFT) 8CFT) HOCET) MCFT) TCSEC) OSCFT) HSCET) TANT O8 aLPHa
G@ 400000 125000 7.8 866 %0 1240 13560- e667 00190 .0536

Cp CDE ACECFT2) RUNUP(FT) G@O(CFS) PCFT) « WC(FPS)
B 400 1000.00 7,17 5e91 2,048 7,12 1.33

Kk KK kK Kk KOK KX & & ® EXAMPLE PROBLEM 3 * & & XK RK K RK KKK KK

GIVEN: Three rubble-mound offshore breakwaters are located with d, = 12 feet
(3.7 meters), 2 = 250 feet (76.2 meters), tan 9 = 0.667, and Ace = 1,440
square feet (134 square meters).

FIND: The influence of breakwater freeboard, incident wave height, wave period,
gap spacing, and shore attachment on V.

SOLUTION: The computer program was used to make these calculations and results
are given in Figures 7 to 10. Figure 7 shows that an increase in breakwater
freeboard or gap to length ratio causes V to decrease. An increase in in-
cident wave height and in wave period produces an increase in V as expected
(Figs. 8 and 9). Shore attachment with impermeable walls forces more flow
through breakwater gaps than for a detached system (Fig. 10). The most dra-
matic effect of shore attachment occurs for relatively small breakwater gaps.

kk ek AR ORK ROK KOR Rk OR RN Kk Oe KCRG CRA) KOR Re WOR * ke

IV. SUMMARY AND CONCLUSIONS

A method is presented for estimating the first approximation of the water
velocity and flow rate through breakwater gaps caused by wave overtopping.
Calculations can be performed either by hand, using a dimensionless curve, or
by a computer program, BWFLOW2, available in the Corps of Engineers Computer
Library. Examples of both calculation methods are given to illustrate the
relative influence of various design parameters on the magnitude of the gap
velocity, V. It is suggested that V not exceed 0.5 foot per second. High
values of V may produce scour around structures and transport sediment out
of the zone protected by the breakwaters.

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20

LITERATURE CITED

AHRENS, J.P., "Prediction of Irregular Wave Overtopping," CETA 77-7, U.S. Army,
Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va.,
Dec. 1977.

AHRENS, J.P., and McCARTNEY, B.L., "Wave Period Effect on the Stability of.
Riprap," Proceedings of Civil Engtneertng in the Oceans/III, American
Society of Civil Engineers, 1975, pp. 1019-1034 (also Reprint 76-2, U.S.
Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir,
Va., NTIS A029 726).

DISKIN, M., VAJDA, M., and AMIR, I., "Piling-Up Behind Low and Submerged
Permeable Breakwaters," Journal of Waterways and Harbors Divtston, No. WW 2,
May 1970, pp. 359-372.

LONGUET-HIGGINS, M.S., "On the Wave-Induced Difference in Mean Sea Level
Between the Two Sides of a Submerged Breakwater," Journal of Marine Research,
Vol. 25, No. 2, 1967, pp. 148-153.

U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore
Proteetton Manual, 3d ed., Vols. I, II, and III, Stock No. 008-022-00113-1,
U.S. Government Printing Office, Washington, D.C., 1977, 1,262 pp.

WEGGEL, J.R., "Wave Overtopping Equation," Proceedings of the 15th Coastal
Engineering Conference, American Society of Civil Engineers, 1976, pp.
2737-2755 (also Reprint 77-7, U.S. Army, Corps of Engineers, Coastal
Engineering Research Center, Fort Belvoir, Va., NTIS AO42 678).

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