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Coast.Eng Fes. Ctr.
MR 81-4
Movable-Bed Laboratory Experiments
Comparing Radiation Stress and
Energy Flux Factor as Predictors
of Longshore Transport Rate
by
Philip Vitale
MISCELLANEOUS REPORT NO. 81-4
APRIL 1981
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REPORT NUMBER 2. GOVT ACCESSION NO. RECIPIENT'S CATALOG NUMBER
“MR 81-4
4’. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED
MOVABLE-BED LABORATORY EXPERIMENTS COMPARING Miscellaneous Report
RADIATION STRESS AND ENERGY FLUX FACTOR AS
PREDICTORS OF LONGSHORE TRANSPORT RATE
PERFORMING ORG. REPORT NUMBER
6.
7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s)
Philip Vitale
10. PROGRAM ELEMENT, PROJECT, TASK
AREA & WORK UNIT NUMBERS
D31193
REPORT DATE
april 1981
Siusiee OF PAGES
PERFORMING ORGANIZATION NAME AND ADDRESS
Department of the Army
Coastal Engineering Reserch Center (CERRE-CS)
Kingman Building, Fort Belvoir, Virginia 22060
Gs
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Department of the Army
Coastal Engineering Research Center
Kingman Building, Fort Belvoir, Virginia 22060
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Energy flux Movable-bed experiments
Longshore transport rate Radiation stress
ABSTRACT (Continue on reverse side if necesaary and identify by block number)
The results of three-dimensional movable-bed laboratory tests are used
to empirically relate the longshore sediment transport rate to the radiation
stress and the longshore energy flux factor. Both correlate equally well
with the longshore transport rate, producing correlation coefficient squared
values of approximately 0.70. The surf similarity parameter also shows a
strong influence on the longshore transport rate.
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PREFACE
This report is published to provide coastal engineers insight into the
important coastal process of longshore transport along sandy beaches by pre-
senting the results of three-dimensional movable-bed laboratory tests. It is
hoped that future studies will expand on the analyses of the data in this
report. The report was prepared under the nearshore sediment transport
research program of the U.S. Army Coastal Engineering Research Center (CERC).
The report was written by Philip Vitale, Hydraulic Engineer, under the
general supervision of Dre ReM. Sorensen, Chief, Coastal Processes and
Structures Branch, Research Division.
The author acknowledges C. Galvin, RP. Savage, and RP. Stafford for their
assistance and advice in the design and operation of the experiment, and M.S.
Bartolomei, SL. Douglas, Be Keely, M. Koenig, MW. leffler, J.G. Tingler, J.
Sullivan, K.P. Zirkle, and, in particular, L.O. Tornese for their help in
collecting and analyzing the data.
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, ggth Congress,
approved 7 November 1963.
f/ :
ED E. WISHOP
Colonel, Corps of Engineers
Commander and Director
IV
VI
VIL
APPENDIX
A
B
C
D
E
F
CONTENTS
CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI)ececcsccccccces
SYMBOLS AND DEFINITIONS. ccccccccccc cc ccc ccc cc cre ceo cece cece cece
INTRODUCTLONec coccccccccec ccc ccc ccc ecco ces c cero ccc e ere eee oreo oeseee
EMPIRICAL RELATIONSccccccccccccccccccccevccc ccc ccc ccc ccc cer eccee
le Momentum Fluxccccceccccccccc cc ccc ce cccceccvccccvcc cece cceee
2. Energy Fluxccccccccccccccccccccccccccc ccc ccc coer eeecccce
3. Longshore Transport Rate€ecccccccccccccccccccccccccccceccccee
4. Empirical RelationSeccccccccccccccccccccccccccccvcccccsscee
5. Surf Similarity ParameteTrececcecccccccccecccccvccccccccccce
EXPERIMENTAL SETUPc cccccccccccc ccc ccc cccv ccc ccs ccccc ces ccc ccccee
1. Basin Layouteccccccccccccccccccccccccceccccccccccceccccccce
2. GENETACOLSecccceccecccccccccceccecvccccvccccv esse vcccecccccee
3. Sand—Moving SysteMeccccceccccccccsvccccccvccccecvccccccccce
Ae IMStrumMentSeccecceccccccccrcccccccceccccccccceseccccccevcccce
5e Dye Injectionecccccccccccccccccccccccccccccccccceevecccccce
66 Sand SUZCeccvccvccccccccecc ccc ec cece sce eee rece cee eee ee ele elec
EXPERIMENTAL PROCEDURE ccccccccccccccccccccrccc cc vcc cc cv ccc cc cecce
le Hourly Cyclecccccccccccccccccscvccccccccccsvccceersccccccee
2. Daily Cyclecocccccccccccccccccccscccccccccccccccccccecveccce
3. Test Cycleccccccccccccccceccccccccscccecccccccccveccccceece
4e Range of VariableSecccccccccccccccc cre cc vec c ccc eevcee ce ecce
DATAccccccccccccc ccc ccc cece cove eer eer eos eveeeseoooce core eeeeee
1. Hourly and Daily Data in Appendix Acccccccccccccccccccccccs
2. Summary Data Tablecccccccecccccccccccccccccccccccecccccccce
3. Survey Dataccocceccccccccccccccscccscscccccccccecccccccccece
4. Overhead PHOCOScecccceccccc ccc ccc cere esse sec er eereece eee leee®
DATA ANALYSIS cccccccccc ccc cc cccccccccccccscesccccscecceccccccces
1. Calculation of Sy wc c ccc cc cccccccccc cece ccc cccsccecccescces
2. Calculation of Poprrsescecrssccccccccccccecccccccccccccccccs
3. Calculation Of Ecccccccvcccccccvcccccccceccccccccevcccccvccs
4. Special TestScccccccccccccccccccccsccccccccccccccssecscecce
5. Daily Cycle GraphsSecccccccccccccccccccccccccceececsecreccce
6. Test Cycle GraphSecocccccscccccccccccccccccccccsscceccccces
7. Surf Similarity Relationeccccccccccccccccccccccccvceccccoece
8. Comparison to Past Datdcccccccccccccccccccccccccccvccceccce
SUMMARY AND CONCLUSIONS ec ccoccccccccc ccc ccc crc cc ccc eres ese c cee e eee
LITERATURE CITEDc ccc ccc cc ccc ccc creer sec ccc cere ere e eee core eo ene eee
HOURLY AND DAILY DATAcccccccccccccccvccccscvcececccccecesecveccce
BEACH SURVEY DATAcccoccccccccccccccevccccccccccccce sce sve seccnce
PLOTTED BEACH PROFILES. ccccccccccccccccccccvecccecececccesevcecce
SELECTED BREAKER BAR AND WATERLINE PHOTOS.ccccccccccccccccocccce
HOURLY CYCLE CALCULATIONS. ccccccccccccccecccccrcccvecevescseccce
DAILY CYCLE CALCULATIONS. cccccccccccccvcvcccccccccccccvesecesccce
Page
7
CONTENTS--—Continued
TABLES
Locations of overhead cameras mounted on the catwalkececccccccccccccce
Locations of dye injection by test numberececceccecccccccccccceccccccce
Test cycle variables and datacccecccccccccrcccscccccccccccccvsccccccce
Example of hourly and daily data tables in Appendix Acccecccccccccccce
Test cycle calculationSerccccccccccccccccccccccccccccccccc ccc cccvc0cvce
Comparisons of tests 1 and 2ecccccccccccccccccccccccvcccccccccecccccce
Daily cycle statisSticSecccccccccccccccccccccvecccscecccccccccccccccecce
Test cycle StatisSticSeccceccccccsccccccccrvcccccccccccccccceccccercccos
FIGURES
Coordinate system for momentum flux derivatioMmeccecccccccccccccceeccce
Diagram of test basin SetuPecccrccccccccccccccccccsceccccceccccccccccce
Photo of test baSin SeEtUPecccccccccccccccccccscccccccsccccccccccccceces
Photo Of Sand traPpoccccccccccecccrccccccccccerccccccccccccccc cc ccccccce
Diagram of diffraction analysis used to determine the alongshore
length of the test DEaACN ec cccccccccccccccocccccecoeeeeeeccocccceeeeeeceee
Shore-normal profile of the test beach, sand trap, concrete aprons,
and adjacent TuUbbillGlicccccccccccceee ccc ecececccceeeeeeececccccceeeceeee
Coordinate system used for test beach with locations of wave gageSece.
Diagram of EductOreccecccccccccccccccccccccccccceccccccccccccccsccccee
Photo of weighing StatioNececcccccccccrcccccccccvccveseescccssccccvcce
Diagram of sand feedereceeccccccccccccccccccccccccccccvcccccecececcces
Photo of sand feederececececccceccvevevcccccvevesccccccccccccccve cece
Diagram of complete sand-moving SySteMeccceecccsceccceecceecccecsccccce
Size distribution of sand used for all teStSececccccccccecccccscccccoce
Schematic diagram of the interrelationship of the three
experimental CYCLESecccccccccccccccccveccvccccesc veer ecveecs 2000000000
Example of overhead PHOCOccccccccecccccccccccccccecsveseccccccsccscccce
Page
24
25
32
34
36
38
38
4]
11
16
1L7/
18
19
19
20
22
(o>
23
23
24
25
26
27
16
17
18
19
20
ZA
22
23
24
25)
26
27
28
CONTENTS
F IGURES--Continued
Example of breaking Waveecccccecccccccccccccccccccccccecccccccceccccccce
Example of strip-chart wave recordecrceccccceccccccccccccccccccccccccsccce
Example of surf zone PphotOSececcccccccccccccccccccccccccccccccccccccece
Example series of drainage photOSecccccccecccrcccccccccccccccccceccccce
Example of bed-form photOcececccceccccccccccccceccccccccccccccecccccccce
Determination of beach slope used to calculate the surf
similarity PALTaAMETECTececeecceesccccrccceeescccvsecccsvrescssccescescecccccccce
Relation between longshore transport rate, lI», and radiation
stress, Sxy? using daily cycle dataccccccccccccccccccccccceccccccccce
Relation between longshore transport rate, I,, and longshore
energy flux factor, Py,, using daily cycle datacceocccccccccccccccccce
Relation between longshore transport rate, I,y, and radiation
stress, Sxy» using test cycle datacccccccccccccccccecsccccccvcccvcccce
Relation between longshore transport rate, I,, and longshore
energy flux factor, Pp,, using test cycle datacccccccccccccccccccccce
Relation between K, and the surf similarity parameter, €,
using test cycle iaitlaleticlctevel clelel clelelerelelel el cleteleleletelele/elellelel ele cjclcleloleleielelelorerelotolore
Relation between K. and the surf similarity parameter, €,
using test cycle ACLAcccc eve ccc eee vrec cesses LF2PFCFFECLFFFFFF2FFLOO OOO LOOOOe
Comparison of data in this report to past reports, using SPM
Figure Ly 33 Gicte: clelelolaleleleletelelele) cloleleveelelcioleieiclelelele clejsleleclelele ellelelecreielelelelelelelefelolelere
Page
27
27
29
30
B2
Sd
39
40
41
42
43
43
44
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 (SIL) units as follows:
inches Ti BSc hi a ae MLS
2054 centimeters
square inches 62452 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
aL esas We O97 1073 kilograms per square centimeter
ounces 28235 grams
pounds 453.6 grams
0.4536 kilograms
ton, long 1.0160 metric tons
ton, short 0.9072 metric tons
degrees (angle) 0.01745 radians
Fahrenheit degrees 5/9 Celsius degrees or Kelvins!
oo——eeeaeaeaSEaoamaoaoSaSoaoaoaoaoaoaoaaBa]aaEeEaEEEEeEEeEeEESESEESEeESSESESESESESESESESESESSESESEEEEEEESSESESSESSESESaEaSaESESESESEEESEESSaaSaaaEEEEEeE———
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.
SYMBOLS AND DEFINITIONS
ratio of sand volume to total volume of a sand deposit
subscript for breaker
wave phase velocity
wave group velocity
water depth
median sand size
energy density
flux of wave energy per alongshore distance
acceleration of gravity
wave height
average wave height
root-mean-square wave height
significant wave height
longshore transport rate in immersed weight per unit time
subscript for any point seaward of breaker zone
empirical coefficient relating Ip to Po)
empirical coefficient relation Ip to Sxy
wave number = 2n/L
wavelength
Latilowote Can tou
&
subscript for deepwater condition
energy flux term
longshore energy flux factor as used in this report
longshore energy flux factor as used in the SPM
longshore transport rate in volume per unit time
range of coordinate system defined in Figure 7
SYMBOLS AND DEFINITIONS--Continued
correlation coefficient
station of coordinate system defined in Figure 7
radiation stress component (flux of y-momentum in x-direction)
wave
time
period
onshore component of water particle velocity
alongshore component of water particle velocity
coordinate in onshore direction
coord
coord
angle
angle
angle
water
wave
surf
surf
mass
mass
inate in alongshore direction
inate in vertical direction
between wave crest and shoreline
between wave generator and shoreline
of beach slope with horizontal
surface elevation
phase
similarity
similarity
density of
density of
parameter as used in this report
parameter as used in Kamphuis and Readshaw (1978)
water
sand
angular frequency of wave = 2n/T
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MOVABLE-BED LABORATORY EXPERIMENTS COMPARING
RADIATION STRESS AND ENERGY FLUX FACTOR AS PREDICTORS
OF LONGSHORE TRANSPORT RATE
by
Phtltp Vitale
I. INTRODUCTION
Three-dimensional movable-bed laboratory tests were conducted to compare
radiation stress and energy flux factor as predictors of the longshore sedi-
ment transport rate. The tests were performed in the U.S. Army Coastal Engi-
neering Research Center's (CERC) Shore Processes Test Basin (SPTB). This
report presents derivations ‘of the radiation stress and the energy flux
factor, documents the experimental setup and procedure, tabulates most of the
data, and performs the data analyses. Many photos were taken during the
tests; however, only a few were used in the report. The complete set of test
photos is available from CERC's Coastal Engineering Information and Analysis
Center (CEIAC).
II. EMPIRICAL RELATIONS
The longshore transport data are related empirically to the two expres-
sions representing wave conditions. One, radiation stress, is based on momen-
tum flux, the other on energy flux. An important concept which is also used
in the data analyses is the surf similarity parameter.
1. Momentum Flux.
The dependent variable studied here is the longshore transport rate caused
by waves approaching the beach; therefore, the consequential momentum term is
the onshore flux of alongshore momentum. The derivation of the term follows
Longuet-Higgins (1970) which applies the concept of wave momentum flux to the
generation of longshore currents.
The coordinate system used is shown in Figure 1. The y-axis is along the
shoreline, the x-axis is normal to the shoreline and positive shoreward, and
the z-axis originates at the stillwater level and is positive upward. Using
this system, the onshore flux of alongshore momentum is the flux of y-momentum
in the x-direction, S,.. This term is one component of what is commonly
called the radiation stress tensor.
x Shoreline
Figure 1. Coordinate system for momentum
flux derivation.
ll
According to small-amplitude wave theory, the components of the water
particle velocity in the x- and y-directions for a wave traveling at an
angle, a, to the shoreline (Fig. 1) are, respectively,
_H gT cosh [k(z + d)]
WS a: —— meOSheaunmcon” cosa (1)
_H gT cosh [k(z + d)] ‘
Yay e EEE cos@ sina (2)
where
H = wave height
g = acceleration of gravity
T = wave period
L = wavelength
d = water depth
k = wave number
8 = wave phase.
The last two terms are defined as
27
Ge cli
and
6 = kx - ot
where t is time, and w the wave angular frequency
27
wo =—
Th
The y-momentum (alongshore momentum) per unit volume is pv where p is
the water mass densitye The flux of this momentum in the x-direction
(onshore) per unit alongshore distance and unit water depth is pvue Inte-
grating over the water column and averaging over time produce the mean along-
shore momentum flux in the x-direction per unit alongshore distance
n
oy = _ | dz (3)
where the overbar denotes the mean with respect to time and n the water
surface elevation. Substituting equations (1) and (2) into (3) and dropping
terms of higher than second order produce
sina (4)
S = CS cosa) C
xy
12
where C is the wave phase velocity, C the wave group velocity, and E
the wave energy density ©
2
pgH
= rms
Re (5)
where H is the root-mean-square (rms) wave height. The term in paren-
theses in equation (4) is the flux of wave energy per alongshore distance,
F,, assuming straight and parallel bathymetric contours. When zero wave
energy dissipation is assumed,
F = EC_ cosa = constant (6)
x &
In this report, dissipation is assumed to be zero up to the breaker zone;
therefore, F is constant from deep water to the breaker zone. Since the
ratio of sina to C is constant due to Snell's law, equation (4), which
represents the alongshore wave momentum entering the surf zone, is constant
seaward of the breaker zone.
Equation (4) can be revised for application of monochromatic waves, as in
this reporte For such wave conditions, the average wave height, H, measured
during the tests (and discussed later in Section IV) is equal to H.j.- By
rewriting equation (4),
og sina
Chey = 8 a cosa} ——— (7)
S is now defined for use with laboratory monochromatic wave data. Note
that equation (4) is valid for any wave condition; equation (7) is valid only
for conditions where H equals Hems*
2. Energy Flux.
In literature, the longshore transport rate has been empirically related
most frequently to a term found by multiplying both sides of equation (4) by
the wave phase velocity, C, to yield
Bye (EC, cosa) sina (8)
Unlike Sy. 5 Po is not constant seaward of the breaker line; therefore,
specifying where P, is being calculated is necessary. This report, follow-
ing convention, determines Pp at the breaker line,
Pie (EC, cosa), sina, (9)
representing the value of Pp, at the point closest to where the longshore
transport is occurring. The subscript b denotes breaker values. MThe term
13
in parentheses in equation (9) has been shown to be constant (see eq. 6)
seaward of the breaker line; therefore, subscript b may be replaced by i
which represents any point seaward of the breaker line. Making this change,
using. equation (5), and letting Hims equal H for monochromatic waves,
equation (9) becomes
2
= (2gH” We
Pop ( 8 oy cosa i sino, (10)
The Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal
Engineering Research Center, 1977) provides a term similar to Pe, except
that the wave height used is the significant height, H,- The term, called
the longshore energy flux factor, is defined as
ipa )
P = 3 C cosa sina b (11)
Pp, is derived in Galvin and Schweppe (1980). The relationship between
Here and H, has been shown in Longuet-Higgins (1952) to be
2 = 972
Hei yeh (12)
assuming a Rayleigh distribution of wave heights as well as a number of other
conditions. Therefore,
P
P
ns
Ni 2 aD (13)
Since Po, and P are essentially the same terms, this report uses the SPM
terminology and refers to Pp} as the longshore energy flux factor.
3. Longshore Transport Rate.
The longshore transport rate, Q, given in the SPM in units of volume per
unit time, is also commonly shown as_ I with units of immersed weight per
unit time. The relationship between the two is
Mn (Go) 119) E24 (14)
where p, is the mass density of sand and a" the ratio of sand volume to
total volume of a sand deposit, which takes into account the sand porosity.
For discussions of equation (14), see Komar and Inman (1970) and Galvin
(1979). Since the laboratory tests described here measured I, directly,
this term is used in most of the data analysis.
14
4. Empirical Relations.
The expressions derived in the preceding paragraphs are used to set up the
following empirical relations
Tp = KP eb (15)
and
iy = athe (16)
where K and K, are coefficients to be determined from the test data in
this report.
Equation (15) is based on the concept that the work done in moving the
sand alongshore is proportional to the energy which approaches the beach. The
units are consistent and K is dimensionless.
Equation (16) is based on the concept that the sand transported alongshore
depends on the alongshore force exerted by the wave motion on the bed inside
the surf zone. By the equation of motion, this force is related to the change
of momentum inside the surf zonee The alongshore momentum, S,., enters the
surf zone through the breaker line but cannot exit through ‘the shoreline
boundary. Therefore, the change in alongshore momentum is Sxy and equation
(16) results. K, has dimensions of length over time.
5- Surf Similarity Parameter.
Kamphuis and Readshaw (1978) showed that K and K, are dependent upon
the surf similarity parameter,
Boe _tan B (17)
1/2
(H,/L,)
in which tan 8 is the beach slope, Hp the breaker height, and Ly the
deepwater (d/L > 1/2) wavelength. Ep reflects variations in beach shape,
breaker type, and rate of energy dissipation. Using the results of laboratory
tests, the following relationships were found by Kamphuis and Readshaw
K
P
Ks OsO8Es foe Oath KB, < 1025 (19)
rd
0-7E, oie Wolk K BK hod (18)
For values of €&, higher than the upper limits, Kp and K, become inde-
pendent of €})-
The surf similarity parameter is evaluated in this report to determine its
effect on the longshore transport rate.
III. EXPERIMENTAL SETUP
This section discusses the setup in the SPTB (Figs. 2 and 3) and describes
the wave generators, wave gages, and cameras and their positions. Also dis-
cussed are the sand-moving system, the method for measuring the longshore
current velocity, and the size distribution of the sand used in the experi-
ment. The design of the setup was based in large part on Fairchild (1970).
15
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16
Wave Generafors
Figure 3. Photo of test basin setup.
1. Basin Layout.
A diagram of the basin setup is shown in Figure 2. The basin is 45.72
meters long, 30.48 meters wide, and 1.22 meters deep. The alongshore and the
shore-normal directions of the sand beach were 7.62 and 11.45 meters, respec
tively. The backbeach was 3.05 meters in the shore-normal direction, but it
was not part of the test beach.
Immediately downdrift of the beach was the sand trap, 0.91 meter wide and
12.7 centimeters deep (Fige 4), used to catch the longshore transporte
Concrete aprons, 4.57 meters in the alongshore direction, were located on
the downdrift side of the sand trap and on the updrift side of the beach. The
updrift apron provided enough distance for the longshore current to develop
between the updrift training wall and the beach. This phenomenon is discussed
in Galvin and Eagleson (1965). The downdrift apron served two purposes-——one
as a platform for depositing the longshore transport that escaped the trap,
the other as a surface on which the waves traveled to diminish diffraction
effects since no downdrift training walls were used.
The major limitation in the experimental planning was the size of the
SPTB, which permitted three wave generators, each 6.10 meters long, to be
linked together and leave enough room to be rotated through various angles to
the beach. The other limitation was the decision not to use downdrift train-
ing walls due to the wave reflection problem. When downdrift training walls
are used, the wave energy, which is reflected off the beach at an angle in the
downdrift direction, strikes the downdrift wall and is reflected back toward
the updrift direction. The energy is then reflected by the updrift wall and
the process repeats. The reflected wave energy is being trapped within the
17
’
Reference.
~~
Figure 4. Photo of sand trap.
two walls; this produces some complicated wave variability problems (eceg.,
see Fairchild, 1970). With no downdrift training walls, the reflected wave
energy moves away from the beach area into the outer parts of the test basin
where most of it is eventually dissipated by the rubble slope along the edge
of the basin (Fig. 2). This, however, creates a problem with wave diffrac-
tion. The energy of the wave leaving the generator spreads laterally into
still water and gradually decreases the wave height toward the updrift end of
the wave crest.
To minimize the decrease in wave height over the test beach, it was
designed using the diffraction diagram for a wave traveling past a semi-
infinite breakwater from Figure 2-33 of the SPM. The period and angle used in
the diffraction analysis were 3 seconds and 10°, respectively, since these
values produced the maximum diffraction closest to the beach. The spreading
of wave energy into the shadow of a breakwater is analogous to the spreading
of wave energy into the area of the test basin downdrift of the generators.
The diagram (Fig. 5) indicated that the alongshore length of the beach should
be 7.62 meters. Most of the diffraction-caused decrease in wave height occurs
over the downdrift concrete apron.
Rubble, ranging in size from 7.62 to 15.24 centimeters, was placed at
several locations in the basin to absorb wave energy and provide gradual
slopes between the concrete aprons and the basin floor. The beach, sand
traps, concrete aprons, and adjacent rubble were all built to the same shore-
normal profile (Fig. 6). This profile was based on Chesnutt's (1978) long-
term two-dimensional tests in which waves were run onto a sand beach to
determine profile response. After superposing several of Chesnutt's (1978)
18
Distance Below SWL (m)
Diffraction
Coefficient
Wave Used for Analysis
T=3.00s
L=7.50m Training Wall
Wave Generator
Figure 5. Diagram of diffraction analysis used to determine
the alongshore length of the test beach.
(0.00, 0.305 )
Qe A we Se oe UCROSOF0001) Ska EA hn Roa SWS Bee
(4.19,0.177)
(6.58, 0.253)
Backbeach
Test Beach
(11.46 ,0.710)
ESO Weal) O IeMiee wena S IGA ud Sa TG Weer Bk Oe chOy Niles ie
Station (m)
Figure 6. Shore-normal profile of the test beach, sand trap,
concrete aprons, and adjacent rubble.
19
profiles run for 80 hours or more with wave periods similar to those used in
this experiment, the shore-normal profile in Figure 6 was drawn as a compro-
mise or average through the superposed profiles. This profile was used to
lessen the onshore-offshore adjustment of the beach.
Figure 7 shows the coordinate system used for the test beache The origin
is at the updrift, shoreward corner of the beach. Ranges (in meters) are
along the alongshore axis, and stations (in meters) along the shore-normal
axis. Any point on the beach, or in the basin, can be described by a range-
station pair.
Range (m)
4
14 12 10 8 6 2 0 -2 -4 -6
Rubble Backbeach
Test Beach Updrift
Concrete
Apron
Station (m)
Downadrift
Concrete
Apron
| R 3.80, S Breaker Line)
Tests 12-15
@
Gage 4A
(R 3.80,5 6.00)
Tests 5-I1°
Sand Trap
Gage 3
(R 3.80, $9.00) MY
Tests 5-15
80 60 40 20 0 12
Water Depth (cm) ¢ A
Gage 2 Gage
(R 3.80, $12.50) (R0.00, $12.50)
All Tests All Tests
Figure 7. Coordinate system used for test beach with locations
of wave gages (R = range, S = station).
2. Generators.
The three piston-type 6-10 meter-long generators used in this experiment
produced only monochromatic waves and are discussed in Stafford and Chesnutt
(1977). The generators were set at four different angles--0°, 10°, 20°, and
30°--to the beach during the experimente For each setting, an updrift train-
ing wall was built from the generator to the 1-foot depth. This allowed
circulation past the wall to feed the longshore current. Figure 2 shows the
setup of the four generators and training wall.
For the 10° and 20° tests, the training wall was curved to allow for wave
refraction. However, since the wall stopped at the l-foot depth, the curves
20
were small and considered not worth the construction effort. Therefore, the
curve for the 30° tests was deleted and a straight training wall was used.
3. Sand-Moving System.
As the waves approached the beach at an angle, the sand moved in the
downdrift directione Most of it deposited in the sand trape The sand which
escaped the trap deposited either on the downdrift concrete apron or beyond
the apron and rubble (covered to keep sand from being lost within it) onto the
basin floor. This area is shown in Figure 2 as the supplementary deposition
area. Although separate measurements of the sand deposited in each area were
not taken, it is estimated that 80 to 95 percent of the longshore transport
fell into the trap. The greater the transport rate and the suspended sedi-
ment, the greater was the amount of sand escaping the sand trap.
The trap was cleaned continually during a test using an eductor attached
to a small centrifugal pump. Water was pumped through the eductor at high
speed, creating a suction to pick up the sand (Fig. 8). The sand was pumped
to the weighing station (Fig. 9), deposited in one of two bins, and weighed
submerged. When divided by the appropriate time period, the value became the
immersed weight longshore transport rate.
After the weighing, the sand was pumped, using another eductor, into a
sand feeder. The sand feeder is a vertical cylinder open at both ends in
which sand is introduced through the top and removed by waves through the
bottom. A diagram and a photo of the feeder are given in Figures 10 and ll.
The primary advantage of the feeder is that it permits waves to control the
amount of sand introduced onto the beach. Savage (1961) discusses the feeder
and its development.
In summary, the complete sand-moving system (Fig- 12) included the
following:
(a) A sand trap, a downdrift concrete apron, and a downdrift
deposition area which trapped the sand;
(b) a downdrift eductor-pump combination which moved the trapped
sand to the weighing station;
(c) a weighing station which weighed the amount of sand moved;
(d) an updrift eductor-pump combination which moved the sand from
the weighing station to the sand feeder; and
(e) a sand feeder which redeposited the sand onto the beach.
4. Instruments.
Wave heights were measured using parallel-wire wave gages (see Fig. 7).
Gages 1 and 2, located seaward of the toe of the beach, were used for all 15
tests. Gage 3, located over the beach, was used for tests 5 to 15. Gage 4A,
located close to the breaker line, was used for tests 5 to 1l. Beginning with
test 12 for the remainder of the tests, gage 4A was adjusted to measure the
breaker height and then renamed gage 4B.
21
@ Sand and Water Mixture from
Sand Trap or Weighing Station
Pulled in by Vacuum
@ OUTPUT: Sand and Water Mixture to
Weighing Station or Sand
Feeder () INPUT: Clear Water from
Centrifugal Pump
=—
---
=-=
eS ss
@) High-Speed vet S—-==/ }
Creates Vacuum <———| I.
&a— :
(I
= =.
=
=-—
>=
Figure 8. Diagram of eductor.
Figure 9. Photo of weighing station.
22
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23
® Sond is Moved to Weighing Station ~,
Sand Beach
Concrete
Apron
Concrete
Ol Sand is
Moved fo
Sand Feeder
Feeder Redeposits
Sand Onto Beach
@ Waves Breok and
Transport Sand
Alongshore
we
“aet
Sand Deposits
in Sond Trap
@ Wove Generators Drive Waves at Angle to Beach
Figure 12. Diagram of complete sand-moving system.
Two cameras were mounted over the beach on the catwalk of the SPTB. One
was a view camera with an adapter for taking 4- by 5-inch Polaroid black-and-
white photos, and the other a standard 35-millimeter camera. The locations of
the cameras are given in Table l.
Other instruments used in the tests include standard hydraulic scales for
weighing the sand, and a standard level and rod for surveying the beach after
each teste
Table 1. Locations of overhead cameras
mounted on the catwalk.
View 35-mm
(m) (m)
Range
Station
Elevation above SWL
laccurate only to + 0.1 meter.
24
5- Dye Injection.
Longshore current velocities for tests 5 to 15 were measured by injecting
dye into the surf zone through a hose which ran from the sand feeder to a
small stake in the surf zone. Dye was poured by hand into the top of the
hose. Table 2 gives the locations of the dye injection by test numbers. The
change in location of the stake in tests 7 to 10 was a procedural error and
not planned for a special purposee The dye injection procedure is discussed
in detail in the next section.
Table 2. Locations of dye injection by test number.
Test Nos. | Dye injected Dye timed Dye timed | Timed distance
at range from range traveled
(m)
Bistand 6 |
7 EO INO)
ll to 15
6. Sand Size.
Figure 13 shows the size distribution of the sand used for all 15 tests.
The median diameter was 0.22 millimeter. The geometric standard deviation is
defined as
d 1/2
“3 aa (20)
where djg and dg, are the sand sizes at which 16 and 84 percent, respec—
tively, of the sample is coarser. The value of for the sand used was
1.22. Figure 13 indicates that the sand was well ore
Screen Opening (mm)
0.1
0.0! 0.050102 05 § 2 5 10 30 40 50 60 70 00 ie 95 : 99 99.0 99.9
miert Coorser
Figure 13. Size distribution of sand used for all tests.
25
IVe EXPERIMENTAL PROCEDURE
Each test was composed of three major data collection cycles: an hourly
cycle, a daily cycle, and a test cycle. For example, wave heights were
measured every hour (hourly cycle), water temperature was measured twice a day
(daily cycle), and beach surveys were taken at the end of each test (test
cycle). The typical test schedule was 4 hourly cycles daily for 6 days for a
total of 24 run-hours per test. Tests 1 and 2, as discussed later, were
exceptions to this schedule. Figure 14 is a schematic diagram of the inter-
relationship of the three cycles. Since waves were run every other day, a
complete test took about 3 weeks.
24-HOUR COMPLETE TEST CYCLE
es oe ee Ol ee
7
S Depth Recorded.
1 HOUR CYCLE ~\.
—=——-Sand Continually Cleaned
Beoch Photo ol XX Out of Trap ond Weighed.
d.
Breaker Photo Wove Height Measur Longshore Current Measured.
Woter Depth Corrected
to 0.71 m,
7 SAX
7 ~
Beoch Regroded ees ES Basin Droined.
New Test Voriobles Set. Ba Sd Drainage and Bed-Form Photos Token.
a SS
Pe 4 HOUR DAILY CYCLE SK Beoch Surveyed.
eH RE ERcaaes ———_| mu an :
! YS All Remaining Sond Picked Up.
woter Temperoture ! Soy Surf Zone Photos ond Weighed.
Recorded. i SK Woter Temperature ond
1
!
Figure 14. Schematic diagram of the interrelationship
of the three experimental cycles.
1. Hourly Cycle.
The various types of data collected in a typical hourly cycle are shown in
Figure 14, along with an indication of time of collection. Before a new hour
of run-time was started, photos of the beach were taken from overhead with
both the 35-millimeter camera (Fig. 15) and the view camerae A reference rope
in the alongshore direction at station 5 and painted arrows on the concrete at
each station bordering the beach can be seen in Figure 15. Photos, such as
shown in Figure 15, provide a record of the change in waterline and breaker
bar throughout the tests. The waves were then turned on and usually, within 5
minutes of the start, an overhead photo of the breaking wave was taken with
the view camera. The angle between the breaking wave and the reference rope
was later measured from the photo to determine the breaking angle of the wave
(see Fig. 16). Note that this procedure assumes the alongshore direction
remained constant throughout the test. In actuality, however, the alongshore
contours are changing, as evidenced in Figure 15.
After a run-time of 30 minutes, wave data were collected for 2 minutes. A
sample strip-chart record is shown in Figure 17. The wave height was deter-
mined from this record. For a given length of wave record, a horizontal line
was drawn along what appeared to be the average wave-crest elevation. A
horizontal line was also drawn for the wave troughs. The distance between the
two lines was measured to determine the average wave height, H. This proce-
dure assumes that a nearly uniform distribution of wave heights is produced by
the monochromatic wave generators.
26
Figure 15. Example of overhead photo.
Downdrift ——>
~<@€— Onshore
Figure 16. Example of photo of breaking wave.
: Avg. Hgt. = 14.0¢m =Line established
ot Hf HH HB ; by eye
; EE erifits aii i faevaifitzee
Q EEE MEETHHEE
Figure 17. Example of strip-chart wave record.
27
Immediately after the wave data were collected, dye was injected into the
surf zone, as discussed in Section III, and the leading edge of the dye was
timed over a distance of approximately 4 meters (see Table 2) to determine the
longshore current velocity. Also recorded were the station at which the dye
left the downdrift edge of the beach and the station at which the waves were
breaking. Therefore, the determination of whether the dye moved offshore,
along the breaker line, or onshore could be madee Most of the dye injections
traveled along the breaker line.
During the hourly cycle, sand was continually picked up from the trap area
and weighed when a bin was full. A complete record of the amount of sand
moved in a given time period existed only at the end of the day after the
waves had been stopped and all the remaining sand had been picked up and
weighed. Therefore, the longshore transport rate can be given for a daily
cycle or a test cycle only.
2. Daily Cycle.
At the start of every test day (see Fig. 14), the water temperature was
recorded, the water level was corrected to 0./10 meter, the wave gages were
calibrated, and a check of all equipment was made. The hourly cycles were
then started. Four hourly cycles were usually completed each day.
Shortly before the waves were turned off at the end of the day, photos of
the surf zone were taken from the side (see Fig. 18 for examples). After the
waves were stopped, all the sand in the sand trap, on the downdrift concrete
apron, and in the downdrift deposition area was moved to the weighing station
and weighed. The day's longshore transport movement was then determined after
the final weighing. This quantity, divided by the total number of run-hours,
provided the immersed weight longshore transport rate for the day.
3. Test Cycle.
At the beginning of each test, new test values for the wave period, T,
the generator angle, a,, and the generator eccentricity, Ecc, were
selected and set (Fig. 14). Ecc is half the distance the generator bulkhead
movese The combination of period and eccentricity produced a predicted wave
height, using the calibration curve of the generators (see Fige 2 in
Fairchild, 1970). This guided the selection of T and Ecc but was not used
for wave height determination.
The beach was regraded to the shore-normal profile (see Fig. 6) before
each new teste This included raking the beach to remove all traces of ripples
from the prior test. The basin was usually flooded to cover the entire beach
and left over a weekend to allow the new beach to stabilize before the new
test cycle began.
After the test was completed, the basin was drained in 10-centimeter
increments, producing depth contours of 0, 10, 20, 30, 40, 50, and 60
centimeters. An overhead photo of the waterline was taken at each
increment. An example series is shown in Figure 19. Surveys of the beach
were then taken, using a standard level and rod, along ranges 1.5, 2, 3, 4, 5,
6, 7, and 7.6 meters. The elevation on each range was read at all major
breaks in slope.
28
Reference Rope
_ (Station 5)
Te PS
Figure 18. Example of surf zone photos.
29
esojoyd o8euteip jo
softies o[duexy
61 ean8Ty
30
cs \\
META
)
Led I fe gfe 3
hag ZA LZ
Sete,
\ MAUR |
yA wily
\
rie
NAS
~
we
Ba,
Ay ‘
ae)
TNR
AAI
Ce LEED .
Se thy
nr
Example series of drainage photos.--Continued
Figure 19.
Finally, photos of the beach were taken at close range to document impor-
tant bed forms, such as ripples and bars (Fig. 20).
4. Range of Variables.
Table 3 gives the test variables for all 15 tests. Note that the 0.710-
meter water depth and the sand were the same for all tests. The wave heights
listed are the average of all the hourly measurements of gages 1 and 2 for
each teste
Table 3. Test cycle variables and data.
Total 4 Breaker | Longshore
run-time angle current
(degrees)
1Not available.
Sy?
Ve DATA
The data collected during the experiments are provided in Appendixes A to
D. Appendix A contains the hourly and daily data for each test. Appendix B
lists the beach survey data, which are plotted in Appendix C, taken after each
test. Appendix D provides 35-millimeter photos of the beach taken during a
test with the waves stopped.
1. Hourly and Daily Data in Appendix A.
Table 4 is an example of how the daily and hourly data are tabulated in
Appendix A. Column 1 lists the run-time over which the data were collected.
Run-time is defined as the cumulative time of wave operation from the begin-
ning of the test. A run-time of 05 10 means that up to that point, waves had
been run at the beach for a cumulative total of 5 hours and 10 minutes. This
would be the case even if the first wave had been run 2 days before.
Column 2 lists the length of time (in minutes) waves were stopped to take
overhead photos of the beach. The letters CFD or TC indicate that the testing
was completed for the day or the test was completed. Between any two entries
in column 2, the waves were run continuously.e For example, from the beginning
of the test at run-time 00 00 to run-time 01 00 (see Table 4), the waves were
continuously run. At that point the waves were stopped for 5 minutes to take
overhead photos of the beach. The waves were then restarted and run continu-
ously until run-time 02 00.
Columns 3 and 4 list the water temperature and the water depth, respec-
tively. These measurements were taken in the morning before the testing
started and in the afternoon after the testing stopped.
Column 5 lists the immersed weight of sand moved during testing from the
previous entry in the column. A value is always listed with a CFD or TC entry
since it was only at the end of the day that the balance of sand not weighed
during the time the waves were running could be picked up and weighed. In
Table 4, the value of 4,227 immersed pounds of sand is the quantity of sand
transported from run-hour 04 00 to 08 00. This column is not a cumulative
listing of sand transported.
Columns 6, 7, 8, and 9 list the wave heights measured by gages l, 2, 3,
and 4A or 4B, respectively. Section III discusses the locations of these
gages, which are shown in Figure 7. Column 10 lists the breaker angles meas—
ured from the Polaroid 4- by 5-inch photos of the breaking waves (see Fig.
16). Column 11 lists the longshore current velocity measured by dye injec-—
tions, as discussed in Section III. Column 12 lists the breaker type, using
the following code: sg, surging; p, plunging; c, collapsing; and sp, spill-
inge A double entry indicates both types of breakers were evident with the
first type predominant.
2. Summary Data Table.
For a comparison of test conditions, Table 3 provides the average values
of water temperature, wave height, wave breaker angle, longshore current
velocity, and average longshore transport rate in immersed pounds per second
for each teste Also included are the wave period and generator angle.
33
Table 4. Example of hourly and daily data tables in Appendix A.
TEST 13
PERIOD 3,00 StCONDS GENERATOR ANGLE 30 DEGREES
RUN TIME MINUTES ostee @ATER IMMERSED WAVE HEIGHT BREAKER LONGSRORE BREAKER
STOPPED TEED DEPTH wEIGHT : cH ANGLE - CURRENT TYPE
HR HN CeLG sus cH LBs GaGE 1 GAGE 2 GAGE $ GAGE 4A/4R DEGREES CM/S
o 0 2@07 71,0
0 4 1s
0 3o 606 7.6 Tel Tol 6 8G
0) +)
16 1S
1 3o 60? 8,0 7.3 604 c) 3G
2 0 10
2 oy 16
2 43 oot 7.6 7,0 %ok 6 86
30 s
3 16
3 30 602 7,8 607 9.0 6 3G
ao cro 2301 70,48 4239
Coa) 22.9 71,0
ag 19
3a 30 Vo2 7,0 5.9 11.9 8 SG
$ 0 lo
Sips 19
53 30 607 6.8 bo! 1106 7 8G
6 0 1o
6 Ss 1a
6 3a 608 659 6,0 11.9 8 8G
7.0 to
7 4 13
? 30 Tol 6.8 604 tol 9 86
@o0 co 23.1 71,0 4227
8 0 23.6 71,0
ay 1S
G30 603 7.3 7.0 1107 9 8G
9 0 1s
9 2 15
9 30 bo2 7,0 7.0 1202 8 SG
10 0 CFO 23.8 70,9 1861
10 0 23.7 71,0
10 2 20
10 30 Cr 6.6 bo2 1006 o 86
110 10
41 2 14
11 30 To2 6.5 008 909 9 8G
12 0 to
12.5 16
12 3o Fol @,4 6,9 904 10 SG
13 0 10
13 4 lo
13 30 7.0 6,6 6.0 Fol 8 SG
1a 0 CeO 2305 71.0 3506
10 0 23.5 71,0
19 8 18
12 30 Tot 6.6 6,5 Cr 9 SG
190 10
Ses) 16
1S 3o 6.8 o.8 604 06 1 8G
16 0 10
16 @ 18
16 30 605 6.7 3,6 8.6 7 86
17 0 1o
17 © 12
17 30 bod O07 6.8 1009 7 8G
18 0 (400) 22,0 71,0 3633
18 0 22.8 1,
16 =6$ 16
18 30 6.8 7.0 bo! 604 5 SG
19 0 20
NO 18
19 30 6.3 Tol 602 605 5 86
20 0 60
20 $ 14
20 30 5.9 7,8 763 7.8 8 8G
21 0 10
21 $ 12
21 30 5.8 8.2 7.2 8.0 ry 8G
22 0 CFO 2301 71,0 3769
22 06 71,0
22 5 13
22 30 3,7 7.0 6.5 608 5 8G
23 0 s
23.63 i
23 30 b02 7.9 7.7 703 8 8G
23 55 11
24 0 Te 2301 71,0 1680
eee
1¢FD = testing completed for day;TC = testing completed.
34
3. Survey Data.
After each test, the SPTB was drained and the beach was surveyed. The
distance and elevation pairs are listed in Appendix B and plotted in Appendix
C. The elevation datum is the stillwater level (SWL), which corresponded to a
0.710-meter water depth.
4. Overhead Photos.
Every hour during testing, the waves were stopped to take an overhead 35-
millimeter photo of the beach (see Fige 15). The photos show the waterline,
the longshore bar, and the swash zone. They are useful for a qualitative
description of how the beach responded to the waves. Appendix D contains a
series of photos for run-times 01 00, 08 00, 16 00, and 24 00.
VI. DATA ANALYSIS
This section includes the data analysis to determine the relations between
Ip and S,, and I, and Po,e The empirical coefficients found from these
relations are then, in turn, related to the surf similarity parameter, €,
which is adapted to the data collected. Also included is an explanation of
the calculations of S,., Ppp, &, and I,, along with plots of the various rela-
tionships. The wave Benet used in the calculations is that measured at the
toe of the beach (average of gages 1 and 2 wave heights). The breaker wave
height, which would have been a better value, was not used for the following
reasons. The wave height at the toe of the beach was measured for all 15
tests; the breaker height was not. Also, only one gage was used to measure
breaker height, while two were used at the beach toe. The significant differ-
ence in height between waves measured at the two beach toe gages (see App. A)
indicates that some wave height variability existed along the wave crest.
Therefore, the average of the measurements at the two beach toe gages is
probably a more reliable estimate of the entire wave passing the toe than the
one gage measurement at the breaker is of the entire breaker waves A compar-
ison of the data in this report with past studies is shown in a Q _ versus
Pop graph.
1. Calculation of Sxy?
Equation (7)
2 A
xy 8 g C
was used to calculate Sxy* Rearranging the equation,
Sg = ao an sin 2a @2i15)
where n is the ratio C,/C and a function of the water depth and wave
period or length. Sx was calculated at the toe of the beach by using the
average of the wave heights measured at that location (see Fig. 7), and by
using the generator angle for a. This was calculated for each set of wave
data. Thus, for the standard 24-hour test, 24 values of 5S, were calculated
(see Appe E)- The average of Sxy for each test is listed in Table 5.
35
Table 5. Test cycle calculations.
Pop Ip Ks Kp E
(J/m/s) | (N/s) | (m/s)
2-201 | 0.6116] 0.5190] 0.2779 | 0.6604 |
2-043 0.6889] 0.6058] 0.3373} 0.6686
35232 0.8396} 0.3682 | 0.2598 | 0.3374
3.615 0.6188) 0.2868; 0.1712} 0.4508
0.789 0.7544; 0.7640 |} 0.9557 | 0.8997
2-144 | 0.9966} 0.5042] 0.4648] 0.6815
4.158 O23 IN Oe23.037 | Oli Sle | Onavisi
3.918 0.3446} 0.1142) 0.0880] 0.4835
4.286 Os 227 1 Ool8o2) | Ost 2 20 Oe SoM
14.761 1.0605} 0.1285} 0.0718] 0.3764
4.839 1.6328) 0.5550 | 0.3374] 0.6644
2-948 1.1941} 0.5328}; 0.4051] 0.9190
14 24 11.578 | 28.802 3.2938! 0.2845} 0.1144] 0.6112
15 24 OG ARS) UG HSS 225502} 0.2756; 0.1884! 0.3934
2e Calculation of Pope
Equation (10)
—2
a pg fe
Pop ( 8 c,cosa), sind,
was used to calculate P,,;.- The term in the parentheses, like Sy >» was
calculated at the toe of the beach. However, the sine term used the beesiker
angle as measured from the photos of the breaking waves. The breaker angle
used in the calculation was the average of the breaker angles collected 30
minutes before and after the wave data were collected (see Fig. 14). Pep was
calculated for each set of wave data, 24 values of P were calculated for
the standard 24-hour test (see Appe E). The average of Pep for each test is
listed in Table 5.
3. Calculation of &.
The surf similarity parameter of Kamphuis and Readshaw (1978) was
presented in equation (17) as
tan B
(#4, / Lai
For the data in this report, a different surf similarity parameter is needed
since H will be substituted for Hp» as discussed at the beginning of this
section. Therefore, the surf similarity parameter in the following analysis is
noe
g = tans (22)
(H/ OO he
36
The same beach slope was used for all 15 tests and was determined as shown in
Figure 21. A value of &€ was calculated for each test using the average
H for the entire test. These values are listed in Table 5.
-0.4
-0.3
-0.2
_-0.1
= (2.65 ,0.000) SWL
a] (0) ase he ee 5 SS SS SSI Se
a SS. Slope Used in Surf Similarity Parameter
0.1 S 0.253- 0.000 |
é Si tan B: 658-265 = 0.0644
mo 0.2 \
e (6.58, 0.253)
= 0.3
2
S 0.4
Backbeach Test Beach
0.5
0.6
0.7
-3 -2 -l 0 | 2 3. 4 5 6 7 #8 Qs 107 alee We
Station (m)
Figure 21. Determination of beach slope used to calculate
the surf similarity parameter.
4. Special Tests.
Three tests were performed under special circumstances. Test 2 was a
repeat of test 1; test 8 was a repeat of test 7, except the sand feeder was
moved shoreward; and test 11 was done with a generator angle of Zero.
Tests 1 and 2 were both run with a period of 2.35 seconds, a generator
angle of 10°, and a generator eccentricity of 5.9/7 centimeters. Test 1 ran
for 25 hours, test 2 for 50 hours. A twofold comparison of the two tests was
originally planned. The first 25 hours of test 2 data was to be compared to
the test 1 data, and then, both sets of data were to be compared to the last
25 hours of test 2. Unfortunately, due to an experimental error, only the
first 30 hours of the test 2 longshore transport data was collected accu-
rately. Therefore, the only comparison made was test 1 to the first 30 hours
of test 2. Reference to test 2 in the remainder of the report refers to the
first 30 hours only. Appendix A contains all 50 hours of test 2 data.
Table 6 compares the results of the two tests. The differences listed
give an indication of the repeatability of the data collection. The longshore
transport rate changed by 12.6 percent, which is a significant variation. This
is an inherent problem of longshore transport tests, indicating that some
important unknown factors are at work.
3ii/
Table 6. Comparison of tests 1 and 2.
Total Avg Avg Ip Sxy Pop
run-time H Oh,
‘ (cm) aria (N/s) | (N/m) | (J/m/s)
8.17 0.612 1.18 2.20
ea 03 0.689 eee 14 eal 04
[stem] =125 | +12.6 7) 53-4 730)
‘(Test l= est Dy, 100 _
Test 1
eo difference =
Tests 7 and 8 were both run with a period of 1.90 seconds, a generator
angle of 20°, and a generator eccentricity of 5.9/7 centimeters. The only
difference was that the sand feeder, which was located at the SWL for all
other tests, was moved shoreward 1.4 meters for test 8. The feeder was moved
because the shoreline at the end of test 7 significantly angled shoreward
toward the downdrift side of the beach. This can be seen in the test 7 photos
in Appendix D. The feeder was moved shoreward to see if a straight shoreline
resulted. It did, as the photos in Appendix D for test 8 show. Another major
effect was the change in I, from 0./28 newton per second for test 7 to 0.345
newton per second for test 8, a decrease of 53 percent. Test 8 is excluded
from the remaining data analyses.
Test 11 was run with a period of 2.35 seconds, a generator angle of 0°,
and a generator eccentricity of 5.97 centimeters. The test was meant as a
control to determine the amount of sand moved by the diffusion caused by
breaking wavese This value of I, for test 11 was 0.089 newton per second.
A comparable quantity of sand, 0.059 newton per second, also moved updrift.
Test 11 is also excluded from the remaining data analyses.
5. Daily Cycle Graphs.
As discussed previously, longshore transport could be measured only on a
daily cycle or test cycle basis. For the typical 24-hour test, six values of
longshore transport rate were calculated. Each rate covered a period of 4
run-hourse During this time period, four values of 5 anda were
calculated, averaged, and related to the corresponding value of I,. These
values are listed in Appendix F and plotted in Figures 22 and 23. Table 7
lists the important statistical parameters.
Table 7. Daily cycle statistics.
Relation ‘Least squares lines
ee Y-intercept | Through origin
| slope _ slope _
pe versus us), "|
I, versus Be
The square of the correlation coefficients, r2, represents the fraction
of the variation of I, about its mean which is explained by the abscissa
eepailg i62 \se@ne 1) and P are 0./4 and 0.73, respectively. These numbers
show that Ip) correlates well with both terms to approximately equal
degrees. The least squares lines listed in Table 7 are in Figures 22 and 23,
which also include the least squares lines calculated with the limitation that
the lines pass through the origin. The slopes of these lines are 0.28 for
the I, versus S xy graph and 0.13 for the I, versus Pop graph.
38
M4aADD ABOVHWZDA[AA MBODHOZOE
V2
Oo
2
Oo Oo
ae Oo
2?
8 7
7
2
-
eG
? Go
2?
go a
2?
7
?
7?
2
Z| 0 ly
wm = A
? Oo
2 o
fa =] ee 7
281 eae Ue
0,’ Oos
y
?
e 4 6 8 10 ie
RADIATION STRESS N/M
Figure 22. Relation between longshore transport rate, lI),
and radiation stress, S,., using daily cycle
data (tests 8 and 11 excluded).
39
14
MADD ADOVWVIZDAA MBOTBZ®HOOZOEP”
NN Z
a
“0 ai
7G
% 5a
Oo uaa
o Nae
a) 2?
G MZ
@ oo oo"
a oO ee
ogee 9
O°
ap -TE)
5 1@ 15 28 25 38
LONGSHORE ENERGY FLUX FACTOR J/M/S
Figure 23. Relation between longshore transport rate, I,,
and longshore energy flux factor, Pop» using
daily cycle data (tests 8 and 11 excluded).
40
35
6. Test Cycle Graphs.
The average longshore transport rate for each test was calculated and
compared with the test average of Sxy and P,,. These values are listed in
Table 5 and plotted in Figures 24 and 25. Statistical values are in Table
SoZ Lon. Lj versus S,, and I, versus Pp), are 0.72 and 0.74, respec-
tively. As with the daily cycle calculations, Ip is shown to correlate well
with both terms to approximately equal degrees. Figures 24 and 25 include
both the standard least squares line and the least squares line forced through
the origin. The slopes of the latter lines are 0.26 for the Ip, versus Sxy
graph and 0.13 for the Ip versus Py, graphe
Table 8. Text cycle statistics.
Relation Figure Least squares lines
No. Standard i Y-intercept | Through origin
slope | slope
versus
versus
versus
versus
&
Ww
MADD ADOVNSDVA MBOTNOZOSe
wu
@ e 4 6 8 10 ie 14
RADIATION STRESS N/A
Figure 24. Relation between longshore transport rate, I
and radiation stress, S.., using test cycle
data (tests 8 and 11 excluded).
41
an
eS
MADD ADOVHWIDAA MBOTHHOZOP
[s¥) Ww
WN
As)
@ 5 10 15 28 es 38 35
LONGSHORE ENERGY FLUX FACTOR J/M/S
Figure 25. Relation between longshore transport rate, Ip),
and longshore energy flux factor, P»,, using
test cycle data (tests 8 and 11 excluded).
7. Surf Similarity Relation.
Figures 26 and 27 were drawn to test the dependence of K, and on &.
Test numbers are indicated in the figures. Table 8 lists the statistics.
The K terms were calculated using equations (15) and (16). These graphs
show that K is far from being constant, as is commonly assumed, and that it~
is strongly related to €.
8. Comparison to Past Data.
They units of el and Py, were converted to those used in the SPM and
plotted in Figure 28, which is taken from Figure 4-36 of the SPM. The SPM
figure was modified by shifting the x-axis to convert from P to Pope
Equation (13) shows the relation between P and Pose Test numbers for the
data points of this report are noted in Figure 28.
Two major observations are immediately apparent. The first is that the
laboratory data in this report, as in laboratory data from past reports, have
considerable scatter. Since the surf similarity parameter, €, in this
report varies by a significant amount for the different tests, as shown in
Figures 26 and 27, some scatter is expected. The surf similarity parameter,
of course, does not explain all of the scatter in the laboratory data- There
are still some laboratory and scale effects which are not yet understood.
42
1.00
0.75
20.50
Figure 26. Relation between K, and the surf similarity
parameter, €, using test cycle data
(tests 8 and 11 excluded).
43
1.00
0.75
Kp =0.89€ -0.22
r2 = 0.56
0.50
0.25
Figure 27. Relation between Kp and the surf similarity
parameter, €, using test cycle data
(tests 8 and 11 excluded).
43
Longshore Transport Rate, Q ( yd>/yr)
ore
10°
102
10°
Ome
Figure 28.
7
%
Hy
7
*
Vi os
% ¥e a
¥
eae s © 14
15
i 92
13 i
6e 236 e10
2@ Se7
I° ge9
© Present Lab Data (Test No. Included )
* Past Field Data
e Past Lab Data
Ome Om lowe 10!
Longshore Energy Flux Factor, Py, (ft-lb/s/ft)
Comparison of data in this report to past reports,
using SPM Figure 4-36 (tests 8 and 11 excluded).
44
ye j
%
SPM Design Curve *
102
The second observation is that most of the data fall beneath the SPM curve
connoting low values of « Since the SPM curve is based on field data,
mostly from Komar and Inman (1970), a possible explanation is that the field
data were collected under conditions of higher values of &€ than those for
the laboratory data. Kamphuis and Readshaw (1978) suggest that Komar and
Inman's data were indeed collected under conditions of high Epe It seems
reasonable to assume that the &€ values were also high.
VII. SUMMARY AND CONCLUSIONS
An analysis of the radiation stress, S,y» and the energy flux factor,
Pop» shows that both predict longshore tranSport rate, Iz, to comparable
degrees. Approximately 70 percent of the variance of Ip about its mean is
explained by each term. There appears to be no major advantage in choosing
one over the other to predict the longshore transport rate. However, Sy.
has the advantage of being constant seaward of the breaker zone while Pop
is note This makes the calculation of S§& more convenient than P»),
which must be determined at the breaker lines On the other hand, Pop has
the advantage of having the same units as Ip, which means that K is
dimensionless.
The empirical coefficients, K, and » are far from constant although
is commonly assumed to be so in practice. Part of the variation of the
coefficients can be related to the variation of the surf similarity parameter,
—&, as shown in Figures 26 and 27. These figures show that K, and will
increase with §. The considerable scatter evident in Figure 28 can be partly
explained by the relation between the empirical coefficients and &. The data
in this report and past laboratory and field data are compared in Figure 28.
The laboratory data generally predict lower values of I for a given P
compared to the field datas Part of this trend can be explained by the dif-
ferences in the surf similarity parameters, assuming the field data were
collected under conditions of high €.- Also, laboratory and scale effects
probably contribute to the lower laboratory transport rates. The relative
importance of these factors is suggested as a subject of future research.
45
LITERATURE CITED
CHESNUTT, C.Be, “Analysis of Results from 10 Movable-Bed Experiments,” Vol.
VIII, MR 77-7, Laboratory Effects itn Beach Studtes, U.S. Army, Corps of
Engineers, Coastal Engineering Research Center, Fort Belvoir, Vae, June
1978.
FAIRCHILD, J.C., “Laboratory Tests of Longshore Transport,” Proceedings of the
12th Conference on Coastal Engineering, American Society of Civil Engineers,
Vol. Il, 1970, pp. 867-889.
GALVIN, C.J., “Relation Between Immersed Weight and Volume Rates of Longshore
Transport,” TP 79-1, U.S. Army, Corps of Engineers, Coastal Engineering
Research Center, Fort Belvoir, Va, May 1979.
GALVIN, C.Je Jre, and EAGLESON, P.S., “Experimental Study of Longshore
Currents on a Plane Beach,” TM-10, U.S. Army, Corps of Engineers, Coastal
Engineering Research Center, Washington, DeC., Jan. 1965.
GALVIN, C. and SCHWEPPE, C.R.e, “The SPM Energy Flux Method for Predicting
Longshore Transport Rate,” TP 80-4, U.S. Army, Corps of Engineers, Coastal
Engineering Research Center, Fort Belvoir, Va-e, June 1980.
KAMPHUIS, JeWe, and READSHAW, J.S.-, “A Model Study of Alongshore Sediment
Transport Rate,” Proceedings of the 16th Conference on Coastal Engineering,
American Society of Civil Engineers, Vol. II, 1978, pp.e 1656-1674.
KOMAR, P.D., and INMAN, D.L., “Longshore Sand Transport on Beaches," Journal
of Geophysical Research, Vole 75, Noe 30, Octe 1970, ppe 5914-5927.
LONGUET-HIGGINS, M.S.~, “On the Statistical Distribution of the Height of Sea
Waves, 1," Journal of Marine Research, Vole 11, 1952, ppe 245-266.
LONGUET-HIGGINS, M.S., “Longshore Currents Generated by Obliquely Incident Sea
Waves," Journal of Geophysical Research, Vole 75, Noe 33, Nove 1970,
SAVAGE, ReP., “A Sand Feeder for Use in Laboratory Littoral Transport
Studies," The Annual Bulletin of the Beach Erosion Board, Vol. 15, U.S.
Army, Corps of Engineers, Washington, D.C., July 1961.
STAFFORD, R-eP.-, and CHESNUTT, C.Be, “Procedures Used in 10 Movable—-Bed
Experiments,” Vol. I, MR 77-7, Laboratory Effects itn Beach Studies, U.S.
Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir,
Va., June 1977.
U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore
Protection 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.
46
APPENDIX A
HOURLY AND DAILY DATA
The data in this appendix are available on computer cards from CEIAC.
47
RUN
SCCHOKBH OB POVVYVATTANACC SCH BABU NMRKK——-—Ooae
ee
ech wane
14
SE EHWUANN KKH OOO
TIPE MINUTES
BTOPPEDA
ce
CFO
thet
CFD
WeooMmMoOD000S
a
ay
we
we
CFD
Se
cw
40
a
w
CFD
we ow
40
ow
COSCO SCOO MOC HOCOROMBOMOTCONOOCWODTDOMCSCOCOCOCOCCOSOSO
cro
le ltee
oo
w
oo
60
ee)
ocowo
CFO
) 60
0 vc
WATER
TEMP
CeLs tus
25.5
2205
2205
22.8
24.5
WATER
vee’
PERIOD 2,35 SECONDS
cM LBs
71,0
3600
y1,0
a2
71,0
1376
1810
71,0
2508
71,0
3260
71,0
2644
PERIOD 2,39
71,0
IMMERSED
DEPTH WEIGHT
GaGe 1
10,0
veer
SECONDS
1004
1004
1004
10,0
10.4
“CKD = testing completed for day;
os
GENERATOR ANGLE 10 DEGREES
WAVE HEIGHT BREAKER
cr ANGLE
GaGE 2 GaGe § GAGE 4AasuB DEGREES
t)
6,4
9
6.8
8
602
6,6
6
7,0
10
0,4
t)
6.8
6
6,4
7
6,0
9
7.2
8
7.2
9
$,6
9
602%
si.
oe
6
8,0
6
7,4
6
7,4
6
ove
6
6,8
6
6,0
6
5,6
7
7,0
7
6,6
7
5,8
6
©,0
t)
02
GENERATOR ANGLE 10 OGGREES
V
5,6
y
5,8
7
0,4
6
6,4
6
6.8
TC = testing completed.
48
LONGSHORE
CURRENT
crs
BREAKER
TYPE
TES’ 08
RUN
xz
D
SSCHODPOSBBOWMYSSTAAS
-
=
pe be ee we ee ee
eaowanwe
14
TIME
wn
Cont
MINUTES ATER
avopPco! TOMP
C2Ls Us
cro
CFO
21.5
cFo
2005
CFO
CFO
2800
60
cro
23.0
75
CFD
23.7
65
WATER JMHERDEO
OEP TH HESGHT
cM Los
3252
71,0
1644
71.0
2944
71,0
3290
71,0
28u4u
71,0
2754
71,0
71,0
Gace 1
10.2
WAVE HEIGHY
5,6
5.4
49
Ca
GAGE 40708
ORE AKER
ANGLE
DEGREES
so
LONGSKORE
CURRENT
(2)
BREAKER
TvPE
ODOCSCBPSTSOrMVYYUYTSCTMMMESSCHSVYUBUYN=—— COO
10
Cony
MINUTES WATER WATER IMMERSED
stopPep! TEHP DEPTH WEIGHT
Ceussus ‘cH Los
CFO
23.5 71,0
60
CFO
24,5 71,0
So
ve
y
PERIOD 1,390 96CONDS
22.5 71,0
5
s
80
cFo 2200 70,9 2792
21.8 Tol
5
5
CPD 21.8 70,7
24.00 71,0
CFD 2300 71,0 a7se
2200 71,0
5
110
g
cro 24.0 70.9 3016
2005 71,0
5
115
+}
CFD 2002 70.9 2420
19.5 1,0
5
GaGE 1
10.8
10,0
%o2
cer
1302
1301
120?
12.4
13ol
13.2
1306
1103
13.2
1104
12.8
12,0
1261
50
WAVE HEIGHT
Cr
Gace 2 GAGE 3 GAGE 4Asa8
GENERATOR ANGLE 10 ORGREEO
12,3
11,6
12.4
15,1
14,0
14,7
13,3
12,9
13.9
15,3
14,4
14,0
15,0
13,2
10,6
14,5
12,2
11,6
BREAKER
ANGLE
DEGREES
LONGSHORE
CURRENT
cuss
GREAKER
TyvPE
TEST 03 CONT
RUN TIME MINUTES WATER water IMMERSED WAVE HEZGHT ORE AKER LONGSHoRE OREaKER
avoPPEo! TEMP DEPTH WEIGHT ] ANGLE CURRENT TvPE
HR MN COLS 2U9 ce Loo GAGE 1 GAGE 2 GAGE S$ GAGE Ga/aH DEGREES cused
18 0 100
10 3 7
18 30 1204 12,2
19 0 5
19 2 6
19 30 12.8 11,8
20 0 cro 19,0 %1,0 2626
20 0 18.0 71.0
20 3 10
20 30 130! 13.2
21 0 Ss.
21 64 14
21 30 1201 1103
e2 0 115
22 8 8
22 3o 12.9 11.8
23 0 s
23.3 2
23 30 1302 13,0
240 0 us 2700 4
reas’ 0a
PERIOD 1,90 S&CONDS GENERATOR ANGLE $0 OGGREES
a) 1900 71,0
0 38 t)
0 30 9,6 11.5
1 0 5
15 6
1 30 1004 13.2
2.0 gis
a3 6
2 30 fiol 13.6
3.0 +)
32 o
3 30 11.0 15.4
a0 eFo “1500 71,0 2300
a0 1600 71,0
a 6 C)
a 30 1109 1602
$ 0 5
Sirs 6
S$ 30 1400 19,2
6 0 11s
6 34 8
6 30 10.8 13,8
% 0 $
2 8 ?
7 30 1002 12,8
8 0 cho 15.8 70,9 2164
8 0 14,0 71,0
ai C)
8 30 1108 12.5
9 0 5
Oe" tC)
9 30 ioe 13.2
10 0 115
10 S$ 7
10 3o 1000 12,7
1100 +} °
11 7 6
11 3o 10.0 13,7
12 0 co 1902 71.0 1912
12,0 1002 71,0
1a 6 7
12 30 1003 12,3
130 S
135 9
13 30 100! 12.5
14 0 115
1 6S 6
19 30 904 12,0
13 0 5
1s S$ 6
13 30 905 12,8
16 0 CFD 15.8 71,0 1896
16 0 1700 71,0
16 4 c)
16 30 909 13.3
1) © s
17°~3 t)
17 30 904 11,8
18 0 110
18 «3 7
18 30 8,8 11,8
19 0 Ss
19°«S 7
19 30 6,8 12.4
20 0 CFO 1605 71,0 1968
20 0 1005 71,0
20 3 6
20 30 10.4 13,7
21 0 S
213 6
21 30 1004 12,4
22 0 115
22 4 8
2a 30 805 11.3
230 5
51
TEST 94 CONT
RUN TIME MINUTES WATER WATER IMMERSED WAVE HEIGHT BREAKER LONGSHoRE OREAKER
svopPco! TEMP DEPTH WEIGHT cw ANGLE CURRENT TyPE
HR MN CLS IUS cM Loe GaGEe 1 Gace 2 Gack $ GAGE Savana DEGREES case
23°53 8
23 30 Bol 11.6
23 Se 6
2a Te 1005 71,0 1720
Teoy 0S
PERIOD 3,00 SECONDS GENERATOR ANGLE 10 OBGREES
0 0 12.00 v1,0
os 6
0 30 600 0,9 8.2 1106
1 0 5
1.0 2
1 3o 7,0 6,1 7,9 10.0
2 0 iT)
2e 2
2 30 6.8 7,0 7.9 908
doo 5
3k a
3 30 6.8 7.6 602 1104
a) cro 1105 70,9 1832
ao 1)0S 71,0
a3 6
a 30 5.9 7.4 7.6 1004
3 0 5
3 a 1
S 3o 600 6,8 609 908
6 0 115
6 3 a
6 30° 607 7.8 801 1100
7 0 5
Lee) 3
7 30 700 7,4 8,6 1000
8 oo cro 1105 70,9 2724
8 oO 1200 71,0
8 2 1
O80 6.8 9,0 1092 1004
9 0 8
9 4 r
9 30 6.4 8,0 8,6 1002
10 0 85
10 4 a
10 30 656 802 91 1006
11 0 3
Aiteees a =
11 So 602 @,0 8,0 1004
120 cro aor
12.0 13.0 7100 .
12.9 1
12 30 6.4 7.7 8.0 906
130 5
13 2 ‘
13 30 600 8.0 8.2 Gee
100 40
ig a 5
14 30 700 7,8 Tol 9.0
18 0 5
Sees) a
1$ 3o boa 8,2 6.3 907
16 0 CFO 1500 70,9 2370
16 0 14,0 71,0
1o 3 = a
16 30 7.4 7.7 72 92 2 PesG
My 0) +] 5
1% 8
17 30 7.0 7,8 8,4 902 3 PesG
1@ 0 115
18 3 7
18 3o 604 0,7 91 909 2 PasG
19° 0 5
19 3 4
19 30 605 8.5 10.0 3
20 0 CFO 14,0 70.9 2788
20 0 1400 71,0
20 10 3
20 30 604 7.4 7.7 900 3 3G
a1 0 5
21 2 0
21 30 702 6,8 7.3 8.8 3G
22 0 85 é
22m 10
22 30 609 7,8 6.1 905 J 86
23 0 $
23 4 2
23 30 607 8,0 7,8 906 3 86
23 So 3
24 0 TC 153.6 70,9 2206
TEST 06
PERIOD 2,33 SECONDS GENERATOR ANGLE B80 OGGREES
0 0 71,0
Oe 13
0. 30 1001 5.7 7.9 10.0 17 P
1 0 5
Sea 8
1 30 9,6 5,6 7.3 8.6 15 Pp
52
TEST 06 CONT
RUN TIME MINUTES waTER WATER IMMERSED WAVE HEIGHT BREAKER LOnosHoRE OReaKER
evorPcD! TEMP DEPTH WEIGHT (a ANGLE CURRENT TvPe
BRD AN COLS US en Lee GaGE 1 GaGE 2 GAGE 3 GAGE SA708 OEGREES cuss
2 0 119
2e 10
2 3o 1002 3.3 6.4 802 17 SPoP
30 3
308 ii
3 30 9,8 50% 6.6 6.6 17 SPoP
a0 1) 100% 91,0 3aa2a
a 0 1009 ¥1,0
ay om)
a 3o @,6 o,6 7,8 900 19 e
5 0 $
3 3 10
§ 30 92 6.0 7.0 6.6 17 °
e 0 415
6 7 9
6 30 8.9 . 6,0 Tol 6.8 1a iY
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RUN TIME
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PERIOD 1,30 SECONDS
71,0
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18,0
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RUN TIRE
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Br-——FTCSCC CSS SBSOYWYSOSTD
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year
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GENERATOR ANGLE 30
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BREAKER
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DEGREES
13
20
16
16
10
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20
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34
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CURRENT
chs
33
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HR BN
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PERIOD 1,90 sGConds
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Ca
GaGE 2 GaGE §
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18
60
GENEBATOR ANGLE
16,0
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17,6
15,8
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BREAKER
ANGLE
DEGREES
30
3o
31
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19
1o
10
1y
19
10
19
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190
20
LONGSHORE
CURRENT
css
20
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RANGE 1.3 RANGE Bo0 RONGE 9,0 RANGE 690 RANGE 7,0, RANGE 706
Ta LEV Ola ELEV STA ELEY ota ELEV Sta = EL Ev
cM) cm) (A) cM) cm) cm) cm) Cm) (my qm)
0000 oa73 0000 0,00 o@75
1039 0135 1030 085 6090
1075 0105 1065 1030 0350
1058 11S
2000 20010
3,00 ©0085
3o20 20090
G@o34 eof79
oo2iS
20240
02a0
20305
20330
11000 00380
11093 11093 eoViB ©0320
29500
20670
ooFkS
TEST 2 (after 25 houre)
RANGE 1093 RANGE BoO RANGE 300 RANGE 4.0 RANGE 5.0 RANGE 6,0 RANGE ¥,0 RANGE Too
STA ELEY eva ELEY BTA ELEW 8Ta ELEV Bla ELEV Sta ELEY Sta ELEY Bra = ELev
(rm) (My (mn) (m) (mM) cM) (my (M) (m) CM) (rm) (m) (m) cm) (m) (*)
0000 0295 6000 0000 0060 295 0000 290 0.00 285 0000 0,00 300
1.74 otis 1091 1095 1.98 150 1049 14S 1051 0155 1o3@ 1,08 0150
2015 So Qote 2.97 1098 0135 1086 0160 1078 9160 todo 2039 20005
3.65 00605 3.05 3017 2.98 .003 2eovd 00005 205% 0.000 2058 3.13 ooVFS
3.34 00080 3037 3.20 3.14 ©0100 2099 ool1l0 3.06 3.08 3,60 20090
3073 e030 3060 9048 3.43 00160 3040 ©0200 3.49 Soga 5.00 ecdeS
6 000% 307 Jobo 3o01 00095 3079 ©6100 3081 3090 6078 0510
Pei y) Go13 4,33 170 GeS1 2180 4,45 aoa7 8,03 oo375
20855 4049 $.99 3038 oo23S Soo? oo240 Soa 5066 9019 Soo
oo Iho 5.98 6098 ©.76 oo325 095 0345 6060 6093 10,67 2s
2049 6068 68.38 8.08 ©0400 8023 00425 8035 0,455 8020 12000 0710
0085 7.88 053 9,08 0.520 96a ©0335 9,08 9005
eobTs 0,48 10070 10073 00635 10082 2,060 10.90 0,060 10073
OoV8g 30070 11.00 11087 oo718 11087 ooV1S 11090 oo710 1108) eof05
11.98
TEST 2. (after 50 hours)
RANGE 1,9 RANGE 2.0 RANGE 3,0 RANGE 440 ROnGE 3,0 RANGE 6,0 RANGE 7,0 RANGE Too
Sta Ley eta Elev eva eLev 81, = ELEV Ola ELE STA) ELEY Ta Elev Ora = EL ev
Cm) cM) cm) Cm) (Mm) cM) (my (my Cm) (mH) (A) (A) cm) (A) (ms) (4)
024s 0.00 029s 0000 865 0.00 0300
ebko 1047 0195 092 «9185 1024 0160
0138 aol2 0140 1038 0145
0185 20% 0145 1075 160
©0085 3,22 0090 1086 0120
22030 3.52 20005 2026 0045
e00%g 3,%a 2052 0,005
@o2o 3.92 8092 070005
2007s 4013 20080 3010 0,089
doh30 5.00 20160 3032 00130
eohts 0.08 ©0260 3098 oo210
oo98s 7.as 11080 0.719 20389 G@o32 e160
00% 16010 9,09 06920 Oot? 06300
0608 $1068 11070 oo 719 9066 00739
0.709
TEST 3
RANGE 1,3 RANGE 2,0 RANGE 4,0 RANGE 4,0 RANGE 500 RANGE 6,0 RANGE 700 RANGE 796
STA ELEY ots =eLev OTs ELEY Bra Lev BTa ELE OTA elev sta ELE Gra Lev
CH) (hy cM) (4) cm) (M) (my CM) cm) OM) (C5) () cH) cy) (my cm)
0200 fT 0.00 0310 000 898 0.00 2890 0000 0895 0.00 0310
1.86 085 1080 6100 1009 130 1040 14% 1094 0130 1047 0130
2.30 00000 2202 060 1051 095
2.80 20105 @o1e 2060 1,06 085
3.20 20150 2006 0,000 1o7l 9080
3,90 20105 3e19 0,075 2.09 0,000
3,75 20270 Bo33 eollS 3040 0,090
O,18 eoa7d Bobo ©2063 3,66 0,150
4,60 20260 Go3G ©1770 3093 0,090
5.07 20299 G0%8 0,200 Soll e230
5,05 20509 S029 0,235 5.93 ©260
5.95 0638 5080 0215 53 0.255
6070 ©0710 0270 0205
7,00 2230 0295
8.20 20300 0,00 ©,300
9,08 2290 6,85 0,435
40,03 10.60 °,395 9,75 0,555
41,097 11008 2815 11.98 0,708
41,90
63
TEST 4
RANGE 1,3 RANGE 8,0 RANGE 3,0 RANGE 4,0 RANGE 5.0 RANGE 6,0 RANGE 7,0 RanGE 7.6
8Ta ELev ora ELev ora ELEY Sta ELEV Bla ELEv ora
CH) Ls) 4) o*) (HM) CM) Cm) CM) (A) (4) cm)
0,00 885 0200 28% 0.00 .a75 0.00 285 0000 295 0.00
1o10 0155 1ed2 0125 207 =,a3s 1o34 0135 268 230 1.34
etfs feet 2095 1e4) ,taS 1,44 1065 e115 1035
of0s 1087 2095 1061 ,090 1.71 2007 4050 1077
ello 2010 2080 1083 .100 1,47 20a5 2014
02000 2029 0088 2.40 2095 2.91
2008p ao 3050 3,42
2003S 3.0u 4007 Sei
cello 3029 ©0000 9000 30%
eotto 0.95 Goa
2022S S072 4.65
eoR's 094 5301S
206g 7045 5.75
20375 7086 7018
e030 0.03 7020
11098 ofits 9050 7.81
9.98 8,57
10040 9015
11001 9,76
11090 10,38
TEST $
RaNGE 1,3 QanGe 2.0 RANGE 3.0 RANGE 9,0 RanGe 53,0 RANGE 6,0 RANGE 7,0 RANGE 7,0
sta ELEv STA ELEV STA LEV 8Ta ELev Sta) ELEV BTA ELEV Sra ELEV Sta ELEY
(4) (My cm) cm) Cm) cH) (may > Cm) Cm) cm) (A) CH) cA) (A) (mH) (#)
0.00 o&275 0.00 260 0,00 280 0000 265 0,00 280 0000 e&75 0,00 290
290 «08S 298 17S 098 175 290 0490 285 190 097 «0185 1,00 «180
1052 225 10865 155 1,02 1eo2 235 1.24 .a05 1019 0185 1,00 0135
2.72 20008 2076 0,005 1,74 Bod 7,010 2065 0,010 2053 00010 2,00 0060
2.80 3.65 3o24 0,090
3,43 G,00 ©,220
ayi4 G,88 0,190
G,9} 5,74
5,09 6,80
o.a2 7.08
Toa? 8.23
8,80 6,00
9091 10012
11,95 11090
11,007 11.97 11008 0710
RANGE 1,5 RANGE Be0 RANGE 3,0 RANGE 4,0 RANGE 3,0 RANGE 6,0 RANGE 7,0 RANGE Ty6
Sta ELEy ara ELE STA ELEY 8Ta ELE Sta ELEV sta ELEV ota ELEV Sta) ELeV
Cm) My «m) om) cM) CH) (my (mH) (A) (M) cM) (M) (#) cm) tm) cm)
0,00 875 0200 R85 0.00 298 3000 0275
1,00 e178 1000 195 1,40 145 1.30 0195
1085 0158 1030 135 2e30 6100 2015 0055
2.40 «2095 2020 110 2.80 005 2,85 2005S
3410 20035 2.90 020 3030 00065 3010 Pol1S
3.30 ©2085 3030 0,005 4.00 140 3.50
3.80 2.045 3020 20039 020 02140 9.90 20165 4900
4.40 e155 3030 20100 ae7%0 9,40
3.20 o.835 3.36 ©.50
5.90 e626) 6.40 7,80
6070 24300 Yoko 6,65
7.10 6335 6 ®,80
7.70 9.20 10,00
8,00 100 11,90
8,00 11010 090 @ 0
9,20 11.090 0,708
9,00
10,30
10,90
11,40 11.20 ©0079
$1090 $1090 eo710
TEST 7
RANGE 1,5 RANGe 2,0 RANGE 3,0 RANGE 4,0 RANGE 3,0 RANGE 6,0 RANGE 7,0 RANGE 7.6
Sta ELEV ata 6 ELEY 81a ELEY Sta ELEY Bia ELEY STA ELEY Sta ELEY Sts ELV
(4) (Hy (4) (¥) cH) (4) (my (4) (hy (my cm) (4) (mM) cm) (a) cH)
0.00 0000 295 0.00 2290 0090 295 0.00 290 0.00
1,53 1083 ,085 1.30 150 1e23 4180 295 185 208
2,02 2.30 ,04S 1.394 ,085 1023 2095 295 4100 208
2.38 2079 ©,030 1.23 .090 1,35
2.82 3.38 1e72 0,025 1,75
3.30 Gell 2029 ©,100 2.65
Ge66 108 040 o,135 3.07
5.78 2.200 3,04 oo11S 3,09
6546 0.230 3.35 0.135 3,90
Ye2a 4.00 -205 4,69
7.80 4,76 2,165 Soi?
6.77 5030 o.adS Soot
9,00 6e10 e220 o.32
10,00 6,70 0,308 ©.68
11200 7o33 0,305 7.07
12.25 8.81 8,36
6.98 9,00
12,85 6718 9.53 0,555 10,00
10,00 ©2390 12088 oo 91S 11,00
11,00 e718 41,90
12,a8 ©, 718 12,29
64
RaNGe 108
ata
(m)
0.00
ELEv
cM)
0845
0B15
oll
2040
20025
2007S
20065
eotlo
20145
eohT9
eos
RANGE 1,5
87a
cm)
0.00
1013
1,38
1,08
1,82
2,03
3,09
3,38
3,85
4,23
4,7?
3,87
$,0a
EL6y
(My
e870
0155
RaNGe 1.3
Sra
(mH)
0,00
1,04
1,04
2,07
2,04
3,48
3091
4,15
9,42
5.05
3.60
6.40
6,95
7.43
6,35
6,90
9,97
10,90
11,15
11,92
ELEev
(My
2280
0133
0135
e0010
RANGE 1.9
Sra Lav
cm) CM)
0,00 285
1e$0 blo
2.30 ec08o
3410 ©6085
3,22 000%0
3,48
3,79
4,25
Soi?
0,62
7,43
6,03
9.91
10.60
$1.90 eoVlo
MaNGe 8.0
67a LEV
Cm) cM)
0.00 280
032 20S
090 oll
079 0030
2.0023
RaNGe
ara
cm)
0.00
098
1207
1.85
2.05
2.85
3.68
Goi3
445
5.02
S079
052
6.97
7000
0,30
9,28
10,00
10,69
11.95
RANGE
ara
cm)
0.00
to3a
1060
1270
a.sa
3.02
ais
6a
$.28
oo10
bo
O)
6
9097
16.353
11,98
1109S
@.0
QLev
(4)
0283
0175,
0135
0018
20015
2009S
20108
20155
eo2l0
20150
20250
20300
eo303
2036S
@o430
20463
2,099
20508
0
8.0
ELEV
cH)
0290
0120
2090
2070
20020
20040
20150
20180
20180
20260
20500
20350
2,440
e520
29010
20090
20710
RANGE 00
ata BLE
cy OH)
0.00
042
045
1038
1086
231
Sot
3076
a.3a
@081
5058
66S
RANGE 3.0
STA ELEY
cm) (M)
0.00 ,a9
todo 115
1073 078
2,02 ,078
8069 0,020
3.03 0,080
3036 0,070
30%
5
$015
6.00
0097
7033
RANGE 3.0
ora ELEW
cm) (*)
RANGE 300
Ta elev
cm) (*)
TEST 8
RANGE 4,0
Sta ELev
Cm) (4)
0.00 299
o79 «0218
09S 0070
1,76 ©0015
2063 oo120
3003 00175
23150
20170
eo2tS
$1.93
TEST 9
RANGE 4,0
Sta ELEV
(m) (m)
0.00 300
1038 090
2.02 0065
2.33
3,07
3,42
3,07
2,08
S.S7
e015
RanGE 4,0
Sta ELEV
(my) CM)
0.00 300
1.99 0115
1.65 0108
2.37
3079
G32
9,70
5.08
0,98
Tae
6,24
9009
10,79
11093
RANGE 4,0
Sta LEV
Cm) (mH)
0.00 .300
093 0190
Leas
1,Aa
2.00
3.05
3.58
G49
11.03
65
RANGE 90
8Ta ELEY
(A) 4)
0000 300
002 0210
006 0130
1063 e010
2oP1 eot2S
Joto
3068
4008
9065
050
7058
RanGe 3,0
ala ELev
cm) cM)
RANGE 600
sta ELev
cm) (4)
0.00 300
076) «oaSd
083 4118
1078 0,015
2005 0,065
2068
3.22
4,03
S018
5055
6092
0,08
RANGE 6,0
ata Lev
Cm) Cm)
10,01 0,000
11.00 0,705
RANGE 650
sya ELEV
(ms) (4)
0.00 300
1.66 115
2.09 0,009
3033 2,070
3079 0,090
4,63 e513
5.63 0,100
6052 0,253
20350
0445
2,390
20078
RANGE 6,0
BTA ELev
(M) cm)
e310
0200
0120
2015
2013 ©.035
3,20 ©,070
2138
4,98 0,205
5.93 0,270
6,92 ©3525
7.31 0,308
11091 90705
W072
RANGE
va
cm)
0.00
1028
1081
203k
2060
7.0
ELev
cm)
RANGE To
BTA tLev
(m) (a)
0,00 «265
0220
0155
e013
e015
eolTS
7018S
eo2es
20233
©0300
eeG0S
0053S
70085
2909S
RANGE 796
Sta =ELEV
Cm) cm)
0.00
1,24
2,00
2,09
3023
3,83
8.62
$000
6
1107) o703
RANGE Too
ya elev
Cm) (LP)
0.00 0305
075 0205
1,02 0165
1.15
1.80
2017
Joid
3.65
4,a2
TEST 12
Rance 1,9 ManNGe 8.0 RANGE 4,0 RANGE 4,0 RANGE 3.0 RANGE 6,0 RANGE
Sra ELty ora ELcy ara eLey $Ta ELEv sta sta ELEV Sta
Cm) My (m) CH) (m) cM) (m) Cm) (A) cm) cm) cr)
0280 0.90 0290 0,00 ,300 0.00 310 0.00 0.00
08g 070 «2208 1.18 ,120 1015 0135 1037 1025
e1a5 0138 1.74 1.37 0095 2001 1.60
2050 2200 2095 2070 2.90
3030 2.28 080 3o10 2.80
3092 2066 4068 3036 3.02
3080 3oG2 00063 3.92 3o61
aou2 3.68 20070 Got O21
5.00 9.00 26130 S030 5.00
5.92 G.70 e140 $082 5.58
6080 Sool 0200 08a 6.93
Pod 7090 7.20
oT 0078 7093
6.45 7,42 000 8,88
@.12 8.80 10020 9.57
10000 9.30 11.08 10015
$007 100a7 11085 10086 10016
itooa 10,00 11040 10068
41,00 14093 oo 705 11020
11083
TEST 13
RANGE 3,0 RANGE 4,0 RANGE 3.0 RANGE 6,0 RANGE 7,0 RanGE 7,6
Sra ELEY Sta ELEY Sta ELEV sta ELEY Sta ELEV Sra + Lev
cH) CH) (my (4) (A) CM) (4) cH) Cm) (*) (my cm)
0.00 ,310 0.00 »310 0,00 o315 0000 310 0.00
088 = ,180 050 «5245 084 4200 082 9810 299
1059 095 175 1o24 210 1050 0130 1.83
2.09 1.02 0140 1.87 130 2020 2005 2,53
2.33 1.84 055 2.48 010 2098 00005 3,39
2.92 294 0010 2075 20050 3053 aaa
3.2 2,80 00093 2.96 0,085 Goa2 So3t
Ho4} 3,40 00195 3,09 ©5450 So0a @,28
G@433 00180 3.68 0,258 5.99 0091
Go42 05180 0088 7678
Sol} eo2l0 0,77
5.95 33
6076 9.30 10,02
7246 10035 t1.at
8,77 11038 11,97
r)
10.d6
11,08 10.39 0,600 11017
11083 2080 11.98
11099 eo710 11005 0.910
TEST 14
RANGE 1.3 RANGE 320 RANGE 4,0 RANGE 3,0 RANGE 0,0 RANGE 700 RANGE Y,6
$Ta ELV eta LEV BTa ELEV Sto ELEV STs ELEY STA ELEY Sta ELEY
(H) 4) cH) (4) (my Cm) (ib) (4) (4) (4) (my cm) (my cm)
0,00 885 0.00 ,300 0,00 305 0000 0505 0,00 0305
040 B40 0000 040 o13 300 0000 0235 033) 0255
039 0225 082 035 ofS 0170 092
070 20% 1035 0,075 1.22 020 1072
1,26 030 1079 2,110 1082 ©,040 2022
1053 ©6020 2026 0,200 2052 e6110 2.95
2023 ©2080 3020 0,220 2061 20155 3065
2091 20200 3093 0,240 3030 ©2240 Goay
3658 062% 0,95 Go23 0,260
$80
6074
Food
8.82
9,85
100%
11039
11093
RANGE 1,3 RANGE 2,0 RANGE 3,0 RANGE 4,0 RANGE 5,0 RANGE 6,0 RANGE 7,0 RANGE 7.6
STA EL Ey STs GLew eva Sta ELEY Blo ELEV STA ELEV Sta ELEY Sta ELE
(4) my 4) CH) cH) (ny (4) (m) cH) cm) cH) Cm) cM) CH) cm)
0,00 88 0.00 «285 0.00 0.00 .@AS 0200 295
1,10 2340 085 0178 263 285 2180 295 0190
1,15 265 6135 263 085 0125 1e3o 0125
1,35 1.83 20010 1.83 1.13 0120 1e6a
2,05 2.46 22090 2.24 1077 6015 2060
2,60 3035 on230 2631 3.00 26085 2090
3,35 3.92 ev231 2.95 3.30 06155 3o3a
4.20 G.00 70285 3.48 S.o2
5,50 05 6300 W@o28 3.83
6,75 0,95 e326 S017 4004
7.75 7.93 ©2400 6026 G25
8,75 6.80 7.455 5.05
10,07 16.08 05509 6.45
41,515 11010 7007
41,93 11593 6.78
10,97 20420 10010
11593 ©3570 11020 14093 00700
11,93 e709 11093
66
APPENDIX C
PLOTTED BEACH PROFILES
67
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APPENDIX D
SELECTED BREAKER BAR AND WATERLINE PHOTOS
The following photos from 35-millimeter slides were taken at approximate
Gun—hourcse sO 03)0) lo. andi 24% Figure 15 provides an explanation of
features. The complete set of slides is available from CELIAC.
76
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APPENDIX E
HOURLY CYCLE CALCULATIONS
A listing of the program which calculates the values in this appendix,
using the data in Appendix A, is available from CEIAC.
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APPENDIX F
DAILY CYCLE CALCULATIONS
A listing of the program which calculates the values in this appendix,
using the data in Appendix A, is available from CEIAC.
93
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