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U.S: Army 
Coast: Ens. Res-Ctr. 
MR 77-7 ( MI) 
(AD-Aose 7103) 


Laboratory Effects in Beach Studies. 
Volume MII. 


Analysis of Results from 
10 Movable-Bed Experiments. 


by 
Charles B. Chesnutt 


MISCELLANEOUS REPORT NO. 77-7 (VII) 
JUNE 1978 


W HOTS 


Approved for public release; 
distribution unlimited. 


U.S. ARMY, CORPS OF ENGINEERS 
COASTAL ENGINEERING 
ay RESEARCH CENTER 


ayes 
Bs Kingman Building 
S Fort Belvoir, Va. 22060 
Osg| 
Mie AEL 


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 this Center. Additional copies are 
available from: 


National Technical Information Service 
ATTN: Operations Division 

5285 Port Royal Road 

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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 


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READ INSTRUCTIONS 
REPORT DOCUMENTATION PAGE 
1. REPORT NUMBER 2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER 


4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED 
LABORATORY EFFECTS IN BEACH STUDIESs Miscellaneous Report 
Volume VIII. Analysis of Results from 10 

Movable-Bed Experiments 


6. PERFORMING ORG. REPORT NUMBER 


8. CONTRACT OR GRANT NUMBER(a) 


7. AUTHOR(s) 
Charles B. Chesnutt 


10. PROGRAM ELEMENT, PROJECT, TASK 
AREA & WORK UNIT NUMBERS 


D31192 


12. REPORT DATE 
June 1978 
13. NUMBER OF PAGES 


VA OS Si ye 


15. SECURITY CLASS. (of this report) 


o PERFORMING ORGANIZATION NAME AND ADDRESS 
Department of the Army 
Coastal Engineering Research Center (CERRE-CP) 
Kingman Building, Fort Belvoir, Virginia 22060 


11. 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) 


UNCLASSIFIED 


15a. DECLASSIFICATION/ DOWNGRADING 
SCHEDULE 


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) 


Breakers Model studies Wave height variability 
Beach profiles Movable-bed experiments Wave reflection 

Coastal engineering Wave envelopes Wave tanks 

Currents Wave generators 


20. ABSTRACT (Continue om reverse side if neceasary and identify by block number) 


Variation in wave reflection from a movable bed as it adjusted to the 
impinging waves was the primary source of wave height variability in 10 

experiments in 6- and 10-foot-wide wave tanks. Re-reflection of waves from 
the wave generator, secondary waves, transverse waves, and cross waves also 
contributed to the wave height variability. 


(continued) 


FORM 
DD . jan 7a 1473 = EDITION OF ? NOV 6511S OBSOLETE 


SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) 


UNCLASSIFIED 


SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) 


The reflection coefficient, Kp, variation ranged from 0.02 to 0.12 in 
one experiment to as much as from 0.04 to 0.27 in another experiment. Changes 
in the foreshore slope and berm-crest elevation, the breaker type, the slope 
and top elevation of the offshore slope, and the distance between the fore- 
shore and offshore were the sources of the Kp variability. For a constant 
initial profile slope, the average K increased with increasing wavelength; 
but for a constant wavelength, the average Kp, decreased with increasing 
initial profile slope. In nine experiments the Kp tended to increase as 
the profile developed, indicating that the profile was reflecting, rather 
than absorbing, energy. 


Profile equilibrium was not easily attained, particularly in five experi- 
ments with a wave steepness of 0.021, which. is in the transition region betwee 
"winter" and "summer'' waves. Experiments with winter or summer waves reached 
equilibrium more readily. 


Laboratory effects, caused by differences in initial profile slope, initia 
test length (distance between the wave generator and the initial shoreline), 
tank width, and water temperature, affected the profile development and the 
wave height variability. Initial profile slope and initial test length should 
be kept constant to assure test repeatability in movable-bed experiments. The 
wavelength-to-tank width ratio should be greater than or equal to 3 to assure 
two dimensionality of profile development, but two-dimensional profiles may 
not be realistic replications of three-dimensional profiles. 


2 UNCLASSIFIED 


SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) 


PREFACE 


Ten experiments were conducted at the Coastal Engineering Research Center (CERC) 
from 1970 to 1972 as part of an investigation of the Laboratory Effects in Beach 
Studies (LEBS), to relate wave height variability to wave reflection from a movable- 
bed profile in a wave tank. The investigation also identified the effects of other 
laboratory constraints. The LEBS project is directed toward the solution of problems 
facing the laboratory researcher or engineer in charge of a model study; ultimately, 
the results will be of use to field engineers in the analysis of model studies. The 
work was carried out under the CERC coastal processes research program. 


This report (Vol. VIII) is the last in a series of eight volumes on the LEBS ex- 
periments. Volume I describes the procedures used in the 10 LEBS experiments, and 
serves as a guide for conducting coastal engineering laboratory studies; Volumes II 
to VII are data reports covering all experiments. 


This volume is a comprehensive analysis of results from all 10 experiments, and 
includes a further analysis of each experiment and how it relates to the other 9 ex- 
periments on wave height variability, profile equilibrium, and laboratory effects. 


This report was prepared by Charles B. Chesnutt, principal investigator, under 
the general supervision of Dr. C.J. Galvin, Jr., Chief, Coastal Processes Branch. 


The author gratefully acknowledges the assistance of the following CERC employees 
who were involved in the LEBS data collection or reduction: J.C. Ahlquist, R.J. Brown, 
W.J. Brown, S.M. Bruce, J.W. Buchanan, E.G. Burroghs, D.A. Clark, D.M. Clark, G. Davis, 
W.O. Doll, J.M. D'Ottavio, J.M. Fairchild, E. Fishman, A.B. Frankle, D.C. French, M. 
Fuhr, H. Goldstein, B.H. Gwinnup, W.J. Herr, F. Holcombe, R.R. Kohler, F. Lago, M.W. 
Leffler, F.S. Moore, J.J. Moore, D.A. Mowrey, M.J. Murphy, P.C. Pritchett, B.D. 
Schiappa, K.E. Schreiter, Jr., R.M._Small, L.C. Tate, C.F. Thomas, W.A. Thompson, T.M. 
Thrall, and C.V. Willard. Computer programs used in the data reduction were written 
by J.C. Ahlquist, S.M. Bruce, J.W. Buchanan, and B.A. Sims; programs written by J.C. 
Ahlquist used techniques developed by W.R. James and 0.S. Madsen. Significant contri- 
butions were made by C.H. Everts, R.J. Hallermeier, C. Mason, and E.F. Thompson through 
numerous discussions with the author and by reviewing one or more of the early manu- 
scripts. 


The author extends special appreciation to the following: M.W. Leffler for his 
assistance in the preparation of the eight manuscripts; C.J. Galvin, Jr., for his 
guidance and assistance; and R.P. Stafford, for the high quality of the data collected 
and who coauthored the first seven volumes. 


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. 


JOHN H. COUSINS 
Colonel, Corps of Engineers 
Commander and Director 


CONTENTS 


Page 

CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI) ....... 9 

Th: DNBRODUWGTLON aiydih SERRANO ed OR | RO OR RA tai PLS ee in a eave a Mn Sion aeme a Le 

LSS Baek er Oui Arie » Wes RAE 8 ey Pare tema eae taste) wileya Oeraieteee otra tee Tie pe toutes meme 

7h ee ay Bil oxoU aI NS] OKOMGLASE. is NNEC cls Mio oe ‘Go oko Toe Mol ohiGi,Jo.- 6) kom lah otros! vo UT 

Se SCOP Cs eu china astece el aouesclpieiys shinee) ngohece Phccliee ares SMM clamy Sure CR pe Wyow) (oaks uae Oe 

LL, sWAVE sHELGHTSVARTABIOLIIYG tran a. as sree Sit Wb lod aa Seid otmerome-m veunrem 9105) 

li Detainittion) ot Merms <5. Ap a eo POSED OT RESON. 5 GS Aare ETE 

2. Variations in Wave Reilocihion. PSG ck ooh comets a tea een oactomgerc ion elh7/ 

So Webmlarcioms sin imengcemic Were OREN so 6 66 60 6 6 0 6 a 4 

1 EQUTEEBREUMPPRO EIGE Saas) scutes ere SO) 

1. Definitions and inypomeemes of Boma lates: Broelles oo 6 0 OY 

Be jesesyers: Ose) Ibpalicaleul escosentiley, Salojseno “ao og o d- 0 6 0 6 oo. 0 Sil 

Je bitect.of WaverPerlod® ver: ii soli Pot eRe Sei eee Si 

[Vj LABORATORY sERPE GIS 6 iy vig viele caqie)taliamoree ek Rene ae = temitog te) garcia mee eee S/S) 

1. Definitions of Terms . . SARA Me bars n  oesulr 210 ie MITA 

2. Test Length and Initial Slope feeecces! Si EMRE HRS bv: aA M/S 

53 ante: Wares bie CES coer yais cc 2) brs crseay Beye ss, Bs MoI gs, PReHACIRY Ed ELEC el ES, 

AV WekeGre Temperature BIBFECES 6 6560 5 6 5 0 Bo oo oo OZ 

So Onciaesp Welbyonrenconay WimreeeS 6° 6566 6 6 0 690 6 6b oO 6 oo co LID 

V CONCLUSIONS .. . BUNS RE, Ses RD DE What 2a Goewl KO 

1. Wave Height Wai cihacsy . MERU RON nO MbeRC Ec MD Mo CeMde sas oaks. oso LID 

2 PrOt le xe Guile UMen ve vos, , fargass ae ie) eh gore ony ot pete enna Ope Magee: 

3. sLaboratory, BERCCES we c.ckisciis <u>) Worm erechsciy om coh Gil sWh cnctbieme-yer tr mire LOS 

VI RECOMMENDATIONS FOR CONDUCTING MOVABLE-BED COASTAL EXPERIMENTS. 123 

1. Modeling Criterion... SHUTS, ARTIS BD LOE SL 2S 

2. Tank Setup and Test Gondteions She eer ual als indi eka Siadit Sem towne “ca cel La) 

Loads R EUS) on YS eaWeeneIbON Ns ome. Woe Ma GuieneaRaGysdeno Go. or ou oro oo! 6 LDA 

EETERATUREWGDRDEDS (2) 39.0. Ee meee ht emrcy oes kom WaCoN CRE pa WR ene maton e 
TABLES 

i Semmes Oi SxqoSrelinemcal GomGkelOMS oo 5 605650050660. &2 


2 Average reflection coefficient and limits of values in each 


DBAS SGI 5 5 0 0 6 oo KOK OHO Ooo CY 
3 Summary of profile development in experiment 72C-10. ...... 21 
4 Summary of profile development in experiment 70X-06. ..... . 23 
5 Summary of profile development in experiment 70X-10. ..... . 26 
6 Summary of profile development in experiment 71Y-06. ...... 28 


7 Summary of profile 
8 Summary of profile 
9 Summary of profile 
10 Summary of profile 
11 Summary of profile 
12 Summary of profile 


13 Incident wave heigh 


CONTENTS 


TABLES--Continued 


development in experiment 71Y-10. 


development in experiment 72D-06. 


development in experiment 72B-06. 


development in experiment 72B-10. 


development in experiment 72A-06. 


development in experiment 72A-10. 


ts. 


14 Known laboratory effects 


FIGURES 


1 Definition sketch of profile zones (experiment 71Y-06) 


2 Reflection variabil 
in experiment 72C- 


3 Reflection variabil 
in experiment 70X- 


4 Reflection variabil 
in experiment 70X- 


5 Reflection variabil 
in experiment 71Y- 


6 Reflection variabil 
in experiment 71Y- 


7 Reflection variabil 
in experiment 72D- 


8 Reflection variabil 


ity and 
10. 


ity and 
06. 


ity and 
OF: 


ity and 
06. 


ity and 
10. 


ity and 
06. 


ity and 


with a 2.35-second wave . 


9 Reflection variabil 


10 Correlation between 
experiment. 


11 Correlation between 


ity and 


Kp and offshore slope steepness in each 


Kp and shelf length in each experiment . 


movement of the -0.8-foot contour 


movement 


movement 


movement 


movement 


movement 


of the -0.7-foot 


of the -0.7-foot 


of the -0.7-foot 


of the -0.7-foot 


of the -0.7-foot 


contour 


contour 


contour 


contour 


contour 


contour movement in experiments 


movement of critical contours in 
experiments with a 3.75-second wave . 


12 Contour movements along center range of experiment 71Y-06. 


Page 


31 
34 
37 
38 
41 


43 
47 


120 


14 


20 


22 


25 


27 


30 


32 


35 


39 


13 
14 


15 


16 


107, 


18 


19 


20 


21 


22 


23 


24 


25 


26 


Bi 


28 


29 


30 


31 


32 


CONTENTS 
FIGURES--Continued 


Contour movements along center range of experiment 72D-06. 


Comparison of final profiles with a 1.90-second wave and 
different initial slopes. 


Contour movements along center range of experiment 72C-10. 


Equilibrium profile in experiment 72C-10, with steep 
"winter'' wave . 


Contour movements along center range of experiment 70X-06. 


Contour movements along center range of experiment 70X-10. 


Greater seaward development of profile in experiment 70X-10 
than in experiment 70X-06 


Profile changes in experiment 70X-10 during the last 35 hours. 


Contour movements along center range of experiment 71Y-10. 


Greater seaward development of the profile in experiment 
71Y-06 than in 71Y-10 . 


Final profiles in experiments 71Y-06 and 71Y-10, with the 
longest test durations in the series. Aims) Mamites, 


Comparison of final profiles with a wave period of 1.90 
seconds and an initial slope of 0.10. 


Contour movements along center range of experiment 72B-06. 
Contour movement along center range of experiment 72B-10 . 


Development of different offshore shapes: concave upward in 
experiment 72B-06 and convex upward in experiment 72B-10. 


Contour movements along center range of experiment 72A-06. 
Contour movements along center range of experiment 72A-10. 


Development of a higher foreshore in experiment 72A-10 and 
a steeper offshore in experiment 72A-06 . 


Profile change in experiment 72A-06 during the last 55 hours . 


Comparison of the equilibrium or representative profile for 
each wave steepness . 


Page 
5S 


54 
56 


57 
58 


59 


60 
61 


62 


63 


65 


65 
66 


67 


68 
69 


70 


71 


72 


74 


33 


34 


35 


36 


SU 


38 


39 


40 


41 


42 


43 


44 


45 


46 


47 


48 


CONTENTS 


FIGURES--Continued 


Preliminary beach profile of Vitale (personal communication, 


1976), developed from the final profiles of experiments 
72C-10, 71Y-10, 72B-10, and 72A-10. Sich Be RCS, tact 


Comparison of shoreline movement in four experiments with a 
1.90-second wave and a 0.10 initial slope . 


Shoreline movement of five ranges in experiment 72C-10 
(L/W = 1.03). 


Foreshore variability over 35-hour period in experiment 
72C-10 (L/W = 1.03) 


Lateral variations in movement of inshore zone contours in 
experiment 72C-10 (L/W = 1.03). 


Lack of lateral variations in movement of offshore zone 
contours in experiment 72C-10 (L/W = 1.03). 


Profile shape at end (140 hours) of experiment 72C-10 
(L/W = 1.03). ; 56 tet Spano Ree “ota 


Shoreline movement in experiments 70X-10 and 71Y-10 
(L/W = 1.43). 


Comparison of the movements of the -0.6-foot contour in 
experiments 70X-10 and 71Y-10 (L/W = 1.43). 


Profile shape at end of experiments 70X-10 and 71Y-10 
(L/W = 1.43). : eased nei. 


Shoreline movement in experiments 70X-06, 71Y-06, and 72D-06 


(L/W = 2.38). 


Comparison of the -0.6-foot contour movements in experiments 


70X-06, 71Y-06, and 72D-06 (L/W = 2.38) 


Profile shape at end of experiments 70X-06, 71Y-06, and 
72D-06 (L/W = 2.38) A CASES A Atl meh ae ar SORE Mae a 


Shoreline movement in experiment 72B-10 (L/W = 1.86) 


Lateral variations in the movements of inshore zone contours 


in experiment 72B-10 (L/W = 1.86) 


Lateral variations in the movements of offshore zone contours 


in experiment 72B-10 (L/W = 1.86) 


Page 


74 


Tei 


81 


82 


83 


84 


85 


87 


88 


89 


90 


91 


93 


94 


95 


96 


49 


50 


51 


52 


53 


54 


55 


56 


57 


58 


59 


60 


61 


62 


63 


64 


65 


66 


CONTENTS 
FIGURES--Continued 


Profile shape at end (150 oe of auras 72B-10 
(L/W = 1.86). Beate : : sigs isTye 


Shoreline movement in experiment 72B-06 (L/W = 3.10) 


Comparison of the movements of inshore zone contours in 
experiment 72B-06 (L/W = 3.10). 


Comparison of the movements of offshore zone contours in 
experiment 72B-06 (L/W = 3.10). 


Profile shape at end (150 ee of experiment 72B-06 
(L/W = 3.10). 5 0 0 Rie AP EE A Meee crate 


Shoreline movement in experiment 72A-10 (L/W = 3.14) 


Comparison of the movements of offshore zone contours in 
experiment 72A-10 (L/W = 3.14). 


Profile shape at end (80 pane of coed Onna 72A-10 
(L/W = 3.14). auliin : : advtel 6. Gunes 


Shoreline movement in experiment 72A-06 (L/W = 5.23) 


Comparison of the movements of upper offshore zone contours 


in experiment 72A-06 (L/W = 5.23) 


Comparison of the movements of lower offshore zone contours 


in experiment 72A-06 (L/W = 5.23) 


Profile shape at end Ose cae of ee” 72A-06 
(E/We= 85925) eos cieacatae ative saan. 


Comparison of daily mean water temperatures and shoreline 
positions in experiment 72C-10. 


Comparison of daily mean water temperatures and shoreline 
positions in experiments 70X-06 and 70X-10. 


Comparison of daily mean water temperatures and shoreline 
positions in experiments 71Y-06 and 71Y-10. 


Comparison of daily mean water temperatures and shoreline 
positions in experiment 72D-06. 


Comparison of daily mean water temperatures and shoreline 
positions in experiments 72B-06 and 72B-10. 


Comparison of daily mean water temperatures and shoreline 
positions in experiments 72A-06 and 72A-10. 


Page 
7 
98 


100 


101 


102 
103 


104 


105 


106 


108 


109 


110 


112 


114 


116 


117 


118 


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: 


eee __eeeeeeee_____s_______ Ee 


Multiply 


inches 


Square inches 


cubic inches 
feet 


square feet 
cubic feet 


yards 
square yards 
cubic yards 
miles 


square miles 
knots 
acres 
foot-pounds 
millibars 
ounces 


pounds 


ton, long 
ton, short 


degrees (angle) 


by To obtain 
ee eee ______|_ le 
25.4 millimeters 
2.54 centimeters 
6.452 Square centimeters 
16.39 cubic centimeters 
30.48 centimeters 
0.3048 meters 
0.0929 square meters 
0.0283 cubic meters 
0.9144 meters 
0.836 square meters 
0.7646 cubic meters 
1.6093 kilometers 
259.0 hectares 
1.852 kilometers per hour 
0.4047 hectares 
1.3558 newton meters 
1.0197 x 1073 kilograms per square centimeter 
28.35 grams 
453.6 grams 
0.4536 kilograms 
1.0160 metric tons 
0.9072 metric tons 
0.01745 radians 
5/9 Celsius degrees or Kelvins! 


Fahrenheit degrees 


eee 


1To obtain Celsius (C) temperature readings from Fahrenheit (F) readings, 


use formula: 


Co= (5/9) (Es =32)). 


To obtain Kelvin (K) readings, use formula: 


K = (5/9) (F -32) + 273.15. 


i oie i scigroesen % 


a mre ie 


des fi ge a 


ah: tae 10 i 


LABORATORY EFFECTS IN BEACH STUDIES 
Volume VIII. Analysis of Results from 10 Movable-Bed Experiments 


by 
Charles B. Chesnutt 


I. INTRODUCTION 


Laboratory effects, caused by differences in tank width, initial 
slope, distance between the generator and the profile, gaps at the end 
of the generator blade, and, perhaps, even water temperature, can hinder 
the solution of coastal engineering problems in movable-bed laboratory 
studies by distorting the development of the movable-bed profile and 
causing spatial and temporal variations in the wave height. Temporal 
wave height variability caused by the changing reflectivity of the 
developing profile complicates the study of the laboratory effects, as 
well as the investigation of coastal engineering problems. Temporal 
reflection variability would presumably be eliminated after the profile 
reached equilibrium, but equilibrium is difficult to define and attain 
in the laboratory. 


1. Background. 


The Laboratory Effects in Beach Studies (LEBS) project (called the 
Wave Height Variability project until 1971) was initiated in 1966 to 
investigate the sources of and possible solutions to the wave height 
variability observed in longshore transport experiments at the Coastal 
Engineering Research Center (CERC) in the late 1950's and early 1960's. 
Three-dimensional experiments were performed in 1967 to isolate the 
major sources of wave height variability. The superposition of incident 
and reflected waves was found to be a major source of spatial variability, 
and changes in the profile reflectivity was found to be a major source of 
temporal variability. 


Two-dimensional tests were performed in 1968 and 1969 to study wave 
reflection and served mainly to develop improved techniques for collecting 
and reducing profile surveys and wave reflection data. 


During 1970 to 1972, 10 lengthy experiments were conducted to define 
the amount of wave height variability due to wave reflection and varia- 
tion in reflection. These experiments were to be continued until the 
profile reached equilibrium and the temporal wave height variability 
ceased. The effect of tank width was to be studied by conducting tests 
in both 6- and 10-foot-wide (1.8 and 3.0 meters) tanks. The results of 
these experiments have also pointed out other laboratory effects. 


2. LEBS Reports. 


This report (Vol. VIII), the last of a series of eight volumes on 
LEBS, analyzes the results of the 10 experiments. 


The experimental conditions, facilities and equipment, quality con- 
trol procedures, and data collection and reduction procedures common to 
all 10 experiments are documented in Volume I (Stafford and Chesnutt, 
1977). Data reduction and collection procedures unique to individual 
experiments are described in appendixes to Volumes II to VII (Chesnutt 
and Stafford, 1977a, 1977b, 1977¢c, 1977d, 1978a, 1978b). 


Volumes II to VII discuss the results from the 10 experiments and 
draw conclusions from the one or two experiments described in each 
volume. The experimental conditions of the 10 experiments are summarized 
in Table 1; the volume in which each experiment is reported, and ref- 
erence to three other studies which discuss some of these experiments 
are also given in the table. 


Table 1. Summary of experimental conditions. 


Other references 


Chesnutt, et al. (1972) 
| Chesnutt and Galvin (1974) 
Chesnutt (1975) 


Chesnutt, et al. (1972) 
Chesnutt and Galvin (1974) 


Chesnutt, et al. (1972) 
Chesnutt and Galvin (1974) 
Chesnutt (1975) 


Chesnutt, et al. (1972) 
| Chesnutt and Galvin (1974) 


Chesnutt (1975) 


72A-10 5 4 


\The first two digits of the experiment number indicate the year of experiment; the 
letters X, Y, A, B, C, and D indicate the separate volumes in the LEBS series of reports. 
The last two digits indicate either the 6- or 10-foot-wide wave tank used for the 
experiment. 


2Distance from generator to the initial stillwater level intercept. 


3Determined for given wave period and constant water depth of 2.33 feet, so that the 
generated wave energy flux had a constant value of 5.8 foot-pounds per second per foot. 


3. Scope. 
The primary purposes of the LEBS reports are to: 


(a) Relate temporal and spatial wave height variability to 
the changing reflectivity of the developing profile; 


l2 


(b) measure the approach of the profile to an equilibrium 
condition; and 


(c) identify, and if possible quantify, the effects of 
other laboratory constraints (e.g., water temperature, tank 
width and length, and initial slope) on the resulting labo- 
ratory profile. 


The discussion of results in Section IV of Volumes II to VII covered 
(a) wave height variability, (b) profile equilibrium, and (c) laboratory 
effects. This volume discusses those topics in Sections II, III, and 
IV, respectively. The data from individual experiments are not repeated 
in this volume, but the results from Volumes II to VII are compared to 
develop more generalized conclusions (Sec. V) and recommendations 
(Sec Vr 


Definitions of coastal engineering terms used in LEBS reports conform 
to Allen (1972) and the Shore Protection Manual (SPM) (U.S. Army, Corps 
of Engineers, Coastal Engineering Research Center, 1977). A definition 
sketch of typical profile zones is shown in Figure 1. The backshore- 
foreshore boundary is at the upper limit of wave uprush, the foreshore- 
inshore boundary at the lower limit of wave backrush (low water line), 
and the inshore-offshore boundary at a point just seaward of the breaker. 


Plots of contour movement (CONPLT plots) are used in all experiments 
to show, in one figure, the changes in profile shape along a given pro- 
file line throughout an entire experiment. An interpretation of these 
CONPLT plots is given in Section II,2 of Volumes II to VII. 


The LEBS data have other uses to both the laboratory and field engi- 
neer. For example, the profile surveys, sediment-size distribution data, 
and breaker conditions reported in Volumes II to VII, and color slides 
of the ripple formations (available at CERC) can be used in a more 
detailed analysis of coastal processes. The shoreline recession rates 
from several of the experiments can be used by the field engineer, after 
consideration of scale and laboratory effects, in determining generalized 
shoreline recession rates. A further analysis of the profile surveys is 
currently being conducted by CERC to determine temporal variations in 
net onshore-offshore material transport. The profile data would be use- 
ful in calibrating a numerical model of profile evolution. 


The LEBS reports are not an all-inclusive study of laboratory 
effects, because several other known laboratory effects have yet to be 
examined intensively. These reports serve as an introduction to the 
subject of laboratory effects and as a guide to some of the problems 
involved in performing movable-bed coastal engineering model studies 
and research experiments. 


II. WAVE HEIGHT VARIABILITY 


The nominal (generated) wave height, H,, in Table 1 is the height 
of the wave traveling from the generator toward the profile unaffected 


13 


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14 


by reflection, wave instabilities, or tank oscillations. This wave 
height (referred to as the generated wave height in Vols. I to VII) is 
assumed to remain constant as long as the generator operates smoothly. 


Wave height variability is any deviation in wave height from Hc. 
This variability can be spatial (the wave height varies with position 
along the tank (longitudinally) or across the tank (laterally)), or 
temporal (wave height varies with time at any point). 


The terms used in describing and calculating wave height variability 
are defined below. Variation in wave reflection from the profile, which 
is the major source of wave height variability, and other sources of wave 
height variability are discussed in this section. 


1. Definitions of Terms. 


a. Operational Terms. The following terms were used in the measure- 
ment and calculation of wave height variability parameters. 


(1) Wave record--a strip-chart recording containing all the 
water surface elevation measurements during a given run. Wave records 
include recordings made with a stationary gage or a slowly moving gage. 


(2) Crest and trough elevations and postttons--determined from 
wave records using a digitizer, which produced a deck of punchcards 
containing the (a) position (on the recording) and elevation of all wave 
troughs, (b) position and elevation of all wave crests, and (c) position 
of all tick marks relating chart paper position to stations along the 
wave tank. 


(3) Computer programs WVHTCN and WVHTC2--written to automate the 
analysis of wave height variability data. 


(4) Local wave hetght (Hg)--the difference in elevation between 
a trough and the succeeding crest, with its position defined midway 
between the two points (determined by the program WVHTCN). 


(5) Average wave hetght (Hy)--the average of all the local wave 
heights in a record (determined by the program WVHTCN) . 


(6) Running average wave height (H,,)--the average of all local 
wave heights within a standing wavelength (one-half the generated wave- 
length) of a point (calculated for each Hg by the program WVHTCN). 


(7) Running average wave height deviation (D,,)--calculated by 


subtracting Hy from each Hy, along the tank (plotted as a function of 
tank position by the program WVHTCN). 


(8) Amplitude of the running average deviation (Am)--determined 


by measuring the maximum deviations on the plot of Dy, versus tank 
position and averaging the absolute values ot the maximum deviations. 


fe) 


(9) Local wave height deviation from the average (Dp)--calcula- 
ted by subtracting Hy from each Hp and then removing any long waves 
or tank oscillations from this curve by subtracting the local Dy, value 
from each Hg (calculation is performed by the program RVEGNE which 
then plots Dg as a function of tank position). 


(10) Amplitude of local wave height deviation from the average 
(A)--the amplitude of the best fit size curve to the plot of Dg versus 
tank position (computed by program WVHTC2). 


(11) Reflection coefficient (Kp)--calculated by dividing A by 
Hy. This procedure for estimating Kp is referred to as the automated 
method in Volumes I to VII. A manual method for determining Kp is 


described in Volume I, which also contains a description of the automated 
method. Most Kp values in this volume were obtained with the automated 
method. The Kp values not determined directly by the automated method 
were determined by the manual method and adjusted by an amount equal to 
the average difference between the two methods to make the values com- 
parable to the automated Kp's. Volumes II to VII contain further infor- 
mation on this difference. 


b. Conceptual Terms. The following terms describe the different 
physical components of the deviation of the water surface from the still- 
water level. 


(1) Reflected wave hetght (Hp)--the height of the seaward- 
traveling waves which have been reflected from the profile. Waves are 
reflected from any segment of the profile where the depth change is 
significant; i.e., the depth change is an appreciable fraction of the 
average depth over a horizontal distance less than one wavelength. Thus, 
waves can be reflected from more than one segment of the profile so that 
more than one reflected wave component with the same period may be 
present. However, over the constant depth section of the wave tanks 
the various components superpose, and in effect, they become a coherent 
reflected wave. The amplitude, A, of the deviation of the local wave 
height from the average (defined above) is a measure of the reflected 
wave height, Hp, in the constant-depth section Of them tanks Eppes 
also equal to the product of Kp and Hy. Hy is defined in (3) below. 


(2) Re-reflected wave hetght (Hpp)--the height of the shoreward- 
traveling wave which has been reflected from the profile and then reflec- 
ted from the wave generator. This wave height is the product of H,, Ky, 
of the profile, and the reflection coefficient of the generator, Kpp. 
Since wave filters were not used in front of the generator in the LEBS 
experiments, Kpp is assumed to be 1 and thus Hpp is equal to Hp. 


(3) Inetdent wave hetght (Hyz)--the height of the shoreward- 
traveling wave that results from the superposition of the nominal gene- 
rated wave height, Hg, and the re-reflected wave height, Hpp. Hy 
varies with time as the phase difference between Hp and the generator 


motion varies. At any given time, H; is equal to Hy (defined above). 


16 


(4) Lateral tank oscillattons--long waves (with a period other 
than the period of the generator) resulting from critical combinations 
of wavelength and tank width, which occurred in some experiments and 
could not be controlled. These waves can be identified by examining 
the deviation of the running average wave height, D,, along ranges 
other than the center range. 


(5) Wave instabiltties--variations in wave shape, which result 
from nonlinear shallow-water waves propagating in the tank. 


2. Variations in Wave Reflection. 


Reflection coefficients varied noticeably throughout the LEBS experi- 
ments (Table 2), and an important part of the experiments is the attempt 
to identify the causes of this variation. 


Each of the two tanks had an adjacent control tank situated so that 
the same generator simultaneously produced the waves in both the test 
tank and the control tank. The control tank had a 0.10 smooth concrete 
Slab instead of a movable bed. Kp variability in the fixed-bed tank 
is a measure of the Kp measurement accuracy in the movable-bed tank. 


Table 2. Average reflection coefficient and limits of values 
in each LEBS experiment. 


Experiment Movable-bed tank Fixed-bed tank 
Limits of Kp Avg Kp Limits of Kp 


j=) 


0. 
0. 
0. 
0. 
0. 
0. 
0. 
0. 
0. 


a. Processes. Three processes are involved in wave reflection from 
a movable-bed profile. These are the conversion of potential energy 
stored in runup on the foreshore into a seaward-traveling wave, the sea- 
ward radiation of energy from a plunging breaker, and reflection of the 
incident wave from the submerged profile, particularly where the depth 
over the movable-bed changes significantly (Chesnutt and Galvin, 1974). 


\7 


(1) Reflection from the Foreshore. The foreshore developed a 
relatively stable shape within the first 10 minutes to 5 hours of each 
experiment. Since the foreshore shape remained fairly constant through- 
out each experiment, the reflection coefficient of the foreshore probably 
remained constant. The height of the wave reflected from the foreshore 
is assumed to vary directly with the height of the wave incident to the 
foreshore for each experiment. 


Measuring the reflection from the foreshore alone was difficult, 
because the distance between the foreshore and the breaker was frequently 
too short to make an accurate measurement. Fluctuations in the measured 
Kp during the first 5 to 10 hours are likely due to fluctuations in the 
foreshore reflection. 


(2) Reflection as a Result of Wave Breaking. Since surging and 


collapsing breakers break on the foreshore they do not contribute to the 
reflection process separately, but rather as part of the foreshore re- 
flection. Spilling breakers, essentially a crumbling of the wave crest, 
do not involve any change in direction of the water particles, and thus 
are not a source of reflection. The plunging breaker propagates energy 
in both directions as the crest of the wave plunges into the water. How- 
ever, in most experiments the breaker type changed from plunging to spill- 
ing as the profile developed, and thus the breaker reflection is assumed 
to decrease throughout an experiment. 


Measuring the breaker Kp was even more difficult than the foreshore 
Kp, since the breaker reflection component is always superposed with the 
foreshore component and in a short distance becomes superposed with the 
offshore component. Estimates can be made from comparisons of the re- 
flection from the concrete slope, which had a breaker and no foreshore, 
and reflections from the early profiles of the movable bed, which had 
reflection from both the foreshore and the breaker but very little from 
other parts of the profile. 


(3) Reflection from the Inshore and Offshore Zones. Wave energy 
is reflected all along the submerged profile, but the reflection does not 
become significant until the profile slopes become significant. In most 
experiments, the profile developed into an almost flat shelf between two 
steep slopes (see Fig. 1). The development of these zones contributed 
greatly to the reflection variability and hence the temporal wave height 
variability. Three particular profile changes apparently caused signifi- 
cant wave height variability: changes in the steepness of the offshore 
slope, changes in the elevation of the shelf at the top of the offshore 
slope, and changes in the length of the shelf. 


Increases in the offshore slope steepness increased the reflection; 
likewise, decreases in the slope steepness decreased the reflection. As 
the elevation of the shelf and top of the offshore slope increased, the 
reflection increased; as that elevation decreased, the reflection de- 
creased. Increases in the length of the flat shelf, which was the dis- 
tance between the two reflecting slopes, caused the phase difference 


18 


between the two reflected wave components to vary. When the components 
were in phase, the measured Hp (in the constant-depth section) was 
high; when the components were out of phase, the measured Hp was lower 


than the absolute sum of the two reflected waves. 


Because the phase difference between the two reflected components 
varied, the amount of energy reflected from the submerged profile could 
not be measured. However, the effect of the three profile changes can be 
seen in the reflection variability of some of the experiments. 


b. Reflection of the 1.50-Second Wave. Figure 2 shows the Kp 
versus time for experiment 72C-10, the only experiment with a 1.50-second 
wave period. The Kp varied between 0.02 and 0.12 during the experiment, 
with no apparent increasing or decreasing trend in the maximum or minimum 
values or in the amount of variation. Minimum values occurred at 35, 60, 
90, 95, and 120 hours; maximum values occurred at 1.5, 25, 55, and 105 
hours. 


Steep foreshore and offshore slopes developed almost immediately and 
then began to separate as the foreshore eroded landward and the offshore 
prograded seaward (Table 3). As the two reflecting zones separated, the 
change in phase difference between the two reflected waves would have 
caused a variation in the measured (total) Kp. Assuming linear theory 
and an average depth of 0.6 foot (18.3 centimeters), an increase of 3.12 
feet (0.95 meter) in the distance between the two reflecting zones (i.e., 
the width of the inshore) would have caused a 360° change in phase dif- 
ference. The distance between the O- and -1.0-foot (0 to 30.5 centi- 
meters) contour increased from 10 to 28.5 feet (3.0 to 8.7 meters) during 
the experiment. Therefore, five cycles of 360° phase-difference change 
were possible and if the cycle started with the two waves 180° out of 
phase, four in-phase (maximum) values were possible, as observed. The 
average Kp was 0.05 (Table 2). 


The seaward movement of the seawardmost -0.8-foot (24.4 centimeters) 
contour (Fig. 2) is an indicator of the general steepening of the off- 
shore zone and the shoreward movement of this contour that the elevation 
at the top of the submerged offshore slope dropped to -0.9 foot (27.4 
centimeters). The shoreward movement of the -0.8-foot contour near the 
end of the experiment did not cause any noticeable reduction in K,, as 
was observed for -0.7-foot (21.3 centimeters) contour during tests with 
the 1.90-second wave (see Fig. 45 in Vol. III), but here the average Kp 
was already smaller than the 1.90-second wave. 


c. Reflection of the 1.90-Second Wave. 


@)) Experiment —/0X=06" The meflection) coerfilcient. iKor 
versus time for experiment 70X-06 is shown in Figure 3. During the first 
10 hours, Kp varied between 0.03 and 0.14. At 10 to 25 hours, Kp 
remained fairly constant (0.08 to 0.11) and then dropped to 0.02 at 31 
hours. From 33 to 45 hours, the Kp was lower, between 0.04 and 0.08, 


19 


0.15 


(Bay) 4u9!9154009 U0!49e}40Y 


0.10 
0 


Reflection Coefficient 


-10 


_—— 
-_-— 
—_—— 
_-_— 


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SOS tit contour 


100 150 


Cumulative Time (hr) 


50 


10 


Reflection variability and movement ° 
of the -0.8-foot contour in experi- 


ment 72C-10. 


Figure 2. 


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15 OQ 
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Cumulative Time (hr) 


Figure 3. Reflection variability and movement of the -0.7-foot 
contour in experiment 70X-06. 


a2 


and was very gradually decreasing; after 95 hours, Kp fluctuated be- 
tween 0.06 and 0.14 and, in general, increased. 


While Kp was fluctuating so greatly during the first 31 hours, the 
foreshore developed and eroded landward, a longshore bar developed, the 
bar and the plunging breaker moved landward and then seaward, and (after 


26 hours) the offshore zone began to steepen (Table 4). All of these 
profile and breaker changes could have contributed to the Kp variations 
during that time. Between 33 and 95 hours, when Kp was less variable 
and very gradually decreasing, the foreshore position stabilized, the 


breaker type changed to spilling (and thus no longer reflected any energy), 
the longshore bar eroded (and thus was no longer a reflector), and the 
offshore slope gradually steepened at the base and prograded slowly sea- 
ward (and thus the phase difference between waves reflected from the two 
zones may have gradually changed). A change of 4.5 feet (1.4 meters) 
between the foreshore and offshore would have caused a 360° change in 
phase difference. After the shelf developed, the distance between the 

O- and -1.5-foot (45.7 centimeters) contour increased only 1.9 feet 


(57.9 centimeters). 


Table 4. Surmary of profile development in 2 Se 70X-06. 


Tine Foreshore Offshore Breaker | Breaker conditions ——_| Gater tecperature 
(hr) (9) 


Gtol developed 

charecteristic 

shupe 
elevation of bar 
increased to -0.3 ft 


bar moved shoreward, 
depth 0.3 ft 


ber stable 
(depth and position) 
bar moved seaward, large deposition at | 0.s 
depth 0.4 ft deposition at 0.9 ft 

depths of 

0.7 and 0.8 ft 


large deposition P 17 to 16 


at 1.1 and 1.0 ft 
position moving 17 to 20 
seaward to 
0.0-ft depth 
changed froe 
P to SP 
Ree ee cea 
Position moving 14 to 18 
seaward to 
0.7-ft depth 
sP 14 to 15; drop to 11 


SP 
11; rise to 15; 
drop to 8 
stable slope 0.7-ft seiatansneTg ONG, ile tereeeeren | at 
seavard seiatansneTg ONG, ile tereeeeren | 


range 0.34 to 0.56 |0.27 to 0.33 0.26 to 0.31 -22 to 0.29 
avg. 0.39 0.31 0.28 otis 


Ip a plunging; SP = spilling-plunging. 


deposition > 1.) ft 


avg. erosion rate 
of 0.06 ft/hr 


deposition > 0.8 ft 


Mahe re, 


26 to 30 


deposition > 0.8 fr 


28; drop to 18 


22 to 26 | avg. erosion rate 


of 0.14 ft/hr 


deposition at 
0.8 ft 


position of bar stable, 
depth varied 0.3 to 0.4 ft 


deposition at all 
depths 


SkL stable erosion Bee at 

of last of scarp 0.5 and 0.6 Bee 
fill started bar eroded erosion at 
erosion of 0.5 ft 

fill << avg. 


erosion < avg. shoreward edge 
stabilized for 
remainder 
erosion >> oenoee 
seaward edge 
stabilized for 
remainder 


deposition >» 0.9 aie 


erosion formed deposition at 
steeper slope 0.6 and 0.7 ft 


17s 
(median 
grain size 
in mm) 


2® 


After 85 hours the seaward movement of the -0.7-foot contour in Fig- 
ure 3 corresponds to the steepening of the upper part of the offshore 
slope and that roughly corresponds to the increase in Kp after 95 
hours. The large fluctuation in Kp did not result from any apparent 
profile change, but the general relationship between the -0.7-foot con- 
tour and Kp did exist. 


(2) Experiment 70X-10. Kp versus time for experiment 70X-10 is 
shown in Figure 4. During the first 20 hours, Kp varied from 0.07 to 
0.12, and between 21 and 89 hours, Kp ranged between 0 and 0.08. From 
89 to 174 hours, Kp increased from 0.04 to 0.14 with a maximum of 0.15 
at 139 hours. After 174 hours, Kp decreased, to as low as 0.06 at 204 
hours. 


The higher Kp values during the first 20 hours occurred while the 
foreshore developed and eroded landward, a longshore bar developed, and 
the bar and the plunging breaker moved landward (Table 5). Between 21 
and 89 hours, while Kp was lower but gradually increasing, the fore- 
shore and the bar moved landward, then the foreshore stabilized and the 
bar eroded. During the same time the breaker moved seaward and changed 
to plunging (at 70 hours), and the offshore slope slightly steepened and 
prograded seaward. The distance between the O- and -1.5-foot contours 
increased 2.2 feet (67.1 centimeters), enough for a 180° change in phase 
difference between the two reflected wave components. 


The gradually increasing Kp after 21 hours followed the general 
seaward movement of the -0.7-foot contour (Fig. 4), but individual Kp 
fluctuations were not directly relatable to the movement of this or 
other contours. The increase in both Kp and Kp variability between 
89 and 174 hours occurred while the foreshore was stable, the breaker 
was spilling (no reflection), and the offshore was gradually steepening. 


(3) Experiment 71Y-06. KR versus time for experiment 71Y-06 is 
shown in Figure 5. During the first 10 hours, K varied from 0.01 to 
0.10. Then, for 115 hours the Kp remained relatively low, ranging from 
0.01 to 0.07 with most of the values near 0.05. For the remainder of the 
experiment, Kp increased in mean value and in variability, varying from 
O5605 0 0624. 


The higher Kp values during the first 10 hours occurred while the 
foreshore zone and longshore bar were developing and retreating landward 
(Table 6). Between 10 and 125 hours, when Kp was low and fairly con- 
stant, the foreshore zone and longshore bar.were retreating landward and 
the offshore zone was prograding seaward but did not steepen.. After 125 
hours, when K, was increasing and becoming more variable, the foreshore 
zone éontinued te erode, the onshore zone developed into a flat shelf 
with the depth over the shelf varying between 0.7 and 0.8 feet, and the 
offshore zone became steeper and continued to prograde seaward. 


Some variations in Kp were related to the movement of the -0.7-foot 
contour (Fig. 5). The general seaward movement of the -0.7-foot contour 


24 


-10 0.20 


-0.7 — ft Contour 


= 0.15 
a 
i<b) 
[S) 
® ple 
c 5 
if, 0.1070 
= = 
= cs 
oe: ° 
So (Ss) 
e Cc 
So (2) 
2 O e) Ke QR O = 
[e) 5 O oO OO} O\O 0.05 o 
i= O O OO O © — 
= O O O | NS) . 09 & 
-. Reflection Coefficient 
2 ij '@ © 
AS 
@ {0 0 0 0 
a 

15 

50 100 150 200 250 


Cumulative Time (hr) 


Figure 4. Reflection variability and movement of the -0.7-foot contour 
in experiment 70X-10. 


25 


Table S. Summary of profile development in experiment 70X-10. 


Inner inshore Quier inshore 


Tipe 

(nr) 
developed 
characteristic 
shape 


bar forsed | Mo change 


bar moving 
shoreward 


no erosion; 
no change 


eroded at rate 
of 0.08 ft/hr 


position of 
bar stable; 
elev. varied 
0.3 to 0.4 ft 


extending sesward 


erosion at 
derth of 0.5 ft 


erosion of 

bar started; 

range -1 at 40 hr, 
range -1 at S6 hr, 
and range -9 at 84 hr 
completed 


erosion ut 
depth of 0.6 ft 


SWL retreated still; 
beach fill began 


70 to 8 


further erosion 


94 to 130 


130 to 140} rate of 

fill >> avg. 
140 to 150 
eee oe eis 
160 to 170} rate of 

fill << avg- 
170 to 190] rate of 

fill = avg. 
“a Lame | 
200 to 210 Tate of 

fill << avg. 
200 sand 0.29 to 0.68 0.27 to 0.50 
samples 
mean (mm) 


\p = plunging; SP © spilling. 
7R © breaks first along range 1; C = breaks uniformly across tank. 


still extending 
seaward; lateral 
variation in 
depth R-l, 

0.6 to 0.7 fe; 


further erosion 
along ranges 
-l and -3 


0.26 to 0.33 


26 


R-9, 0.7 to 0.9 ft 


, deposition between 


depth of 
-1.0 and -1.5 ft 


deposition at 
-1.0 ft 


deposition at 
-0.9 and -1.0 ft 


depositaon at all 
depths except 
-2.0 and -2.1 ft 
along range -1 


deposition at 
all depths 


contours stable 

for -1.0 to -1.5 ft; 
ft; depus:tion 
below -1.5 ft 


Breaaser conditions 


Depth 
(tt) 


tecperature 
Cc) 


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indicates the steepening and increasing of the reflectivity of the off- 
shore zone. The highest Kp values, at 235, 320, 360, and 375 hours, 
occurred at times when the -0.7-foot contour was at its seawardmost 
position; low Kp values at 195, 240, and 340 to 355 hours occurred 

when the -0.7-foot contour was at more shoreward positions. An exception 
to this occurred at 270 to 275 hours, when the -0.7-foot contour was in 

a seaward position and the Kp was low. At other times the relation- 
ship existed, but the variation was not as great. 


The continued separation of the foreshore and offshore zone would 
have caused the phase difference between the two reflected waves to vary ” 
and the measured reflected wave to have a long-period variation. After 
the shelf developed, the distance between the O- and the -1.5-foot con- 
tour increased 8.6 feet (2.6 meters), enough for two cycles of phase- 
difference change, which may have contributed to some of the long-term 
Kp variation. 


(4) Experiment 71Y-10. Kp versus time for experiment 71Y-10 is 
shown in Figure 6. During the first 10 hours, Kp varied from 0.05 to 
0.11. Then, for 195 hours the Kp remained relatively low, varying from 
0.01 to 0.08. For the remainder of the experiment, Kp was generally 


higher, varying from 0.05 to 0.13. 


The higher Kp values during the first 10 hours occurred while the 
foreshore and longshore bar were developing, the breaker was plunging, 
and the foreshore was eroding (Table 7). Between 10 and 205 hours, while 
K was low, the foreshore retreated at a rate of 0.016 foot (0.5 centi- 
meter) per hour, the bar was first stationary and then eroded, the breaker 
type changed from plunging to plunging and spilling, the inshore developed 
into a long, flat shelf, and the offshore zone gradually steepened. The 
Kp was higher, after 205 hours, when the inshore zone had fully devel- 
oped, the foreshore was eroding and the offshore prograding. The dis- 
tance between the O- and -1.5-foot contours increased 7 feet (2.1 meters), 
enough for a 560° change in phase difference, after the shelf developed. 


Variations in relate only generally to the movement of the -0.7- 
foot contour (Fig. &. i.e., the Kp increased about the time the -0./7- 
foot contour began moving seaward with the prograding offshore zone. The 
development of the profile in this experiment varied laterally, the devel- 
opment of the shelf began first along one side and progressed across the 
tank. This lateral variation in development obviously created a lateral 
variation in the profile reflectivity. Although this variation could not 
be measured by the one gage in the center of the tank, the variable pro- 
file reflectivity certainly contributed to the variations measured along 
the center of the tank. 


(5) Experiment 72D-06. This experiment varied from the four 
other experiments with a 1.90-second wave in having an initial slope of 
0.05 rather than 0.10. The Kp versus time for experiment 72D-06 is 


shown in Figure 7. During the first 15 hours, Kp varied from 0.04 to 


29 


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Figure 7. Reflection variability and movement of the -0.7-foot 
contour in experiment 72D-06. 


32 


0.08. Between 20 and 130 hours the Kp was higher and highly variable, 
varying between 0.08 and 0.27. For the remainder of the experiment, Kp 


was lower and less variable, varying between 0.07 and 0.10. 


The lower values during the first 15 hours occurred while the fore- 
shore developed (slower than in the other four experiments) and began 
retreating, the longshore bar developed and then eroded, and the breaker 
type was strictly plunging (Table 8). Between 20 and 130 hours, when the 
Kp was high and varied greatly, the foreshore was retreating (except for 
advancing between 125 and 130 hours), the breaker was mixed between plung- 
ing and spilling (indicating minimal reflection), the inshore was becoming 
longer and flatter, and the offshore was steepening, particularly after 
95 hours. Between 135 and 180 hours, when Kp was smaller and less 
variable, the foreshore was stationary, the offshore zone continued to 
prograde seaward, and the inshore zone changed from an almost flat shelf 
with an average elevation of -0.7 foot to a flat region at the seaward 
end of the inshore (elevation -0.8 foot) and a trough at the shoreward 
end of the inshore (elevation -1.3 feet). 


Some Kp variations after 100 hours, when the offshore slope was a 
significant reflector, correlate well with the movement of the -0.7-foot 
contour (Fig. 7). When the -0.7-foot contour was at a more seaward posi- 
tion, Kp was high; when the contour moved shoreward, Kp was low. The 
Kp reached higher values quicker than in the first four experiments, 
even though the initial slope was flatter. This earlier high in Kp 
may have been caused by the earlier seaward movement of the -0.7-foot 
contour in this experiment. 


The Kp was measured over the inshore shelf several times between 
100 and 155 hours and varied between 0.06 and 0.12 (see Vol. IV). This 
measurement included reflection both from the foreshore zone and from 
the plunging breaker near the toe of the foreshore. The distance be- 
tween the O- and -1.5-foot contours, after the shelf developed, increased 
12.4 feet (3.8 meters), enough for more than two 360° phase-difference 
changes. 


(6) Summary of the Five Experiments. The average Kp in each 
of the 1.90-second experiments with the 0.10 slope (70X-06, 70X-10, 


71Y-06, and 71Y-10) varied from 0.07 to 0.09 (Table 2). However, in 
experiment 72D-06 with the flatter initial slope, the average Kp was 
0.12, much higher than the tests with the steeper initial slope, con- 
trary to the hypothesis that as the ratio of the wave steepness to the 
slope steepness increases, the Kp, decreases. The close correlation 
between the -0.7-foot contour and Kp variations in experiments 71Y-06 
and 72D-06 suggests that the elevation of the top of a steep, submerged 
slope can be as important as the steepness of the slope in determining 
the Kp. 


d. Reflection of the 2.35-Second Wave. 


(1) Experiment 72B-06. The Kp versus time for experiment 
72B-06 is shown in Figure 8(a). During the first 10 hours, Kp varied 


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35 


Cumulative Time (hr) 


b. Experiment 72B—10 


Reflection variability and contour movement in experiments with a 2.35-second wave. 


Cumulative Time (hr) 


a. Experiment /72B—06 


Figure 8. 


over the widest range, between 0.04 and 0.15. Between 10 and 150 hours, 
Kp fluctuated (maximum 5-hour fluctuation of 0.06) about an increasing 
mean, reaching peak values at 125 and 140 hours. 


The major profile adjustments in Figure 8(a) and Table 9 were the 
development of an equilibrium foreshore and longshore bar and steepening 
of the offshore zone just below the inshore zone. These adjustments 
occurred during the first 10 hours when Kp was fluctuating greatly. 
Between 10 and 150 hours, when Kp was gradually increasing, the only 
profile changes were the gradual steepening of the upper part of the 
offshore zone and the seaward movement of the offshore bar (crest eleva- 
tion of -2.1 to -2.0 feet or 64.0 to 61.0 centimeters). The steepening 
of the upper offshore most likely caused the increases in Kp. 


(2) Experiment 72B-10. The Kp versus time for experiment 
72B-10 is shown in Figure 8(b). During the first 10 hours, Kp in- 
creased from 0.13 to 0.18, and then between 15 and 35 hours, Kp varied 
only between 0.12 and 0.13. At 40 to 90 hours, Kp was higher, fluctuat- 
ing about a mean of 0.16. Between 90 and 100 hours, Kp increased from 
0.16 to 0.24 and then fluctuated about a mean of 0.21 for the remainder 
of the experiment. 


The increasing Kp during the first 10 hours coincides with the 
development of most of the profile features: the steep foreshore zone, 
the flat inshore zone, and the flat region near station 10 in the off- 
shore zone (Fig. 8,b and Table 10). There was little profile change 
between 15 and 35 hours when the Kp was low and almost constant. At. 
40 to 90 hours the elevation of the flat region near station 10 gradually 
increased while the Kp was higher and more variable. Between 90 and 
100 hours, when Kp increased by 0.08, a longshore bar was forming be- 
tween ranges 1 and 5. The high values of Kp at the end of the experi- 
ment (after 100 hours) occurred while slopes near stations 20 and 14 were 
steepening. 


(3) Summary of the Two Experiments. These experiments with the 
2.35-second wave are compared in Volume VII. The average Kp in experi- 
ment 72B-06 was 0.08 and in experiment 72B-10 was 0.17 (Table 2). The 
gradual steepening of segments of the offshore zone appeared to be the 
primary source of long-term Kp variability in these two experiments. 
The development of a more convex offshore region with several steep 
sections in experiment 72B-10 and a more concave offshore region with 


only one steep section in experiment 72B-06 possibly explains the lower 
Kp values in experiment 72B-06. The distance between the foreshore and 
offshore zones changed very little, so that the Kp variability was not 
a result of phase-difference changes between reflected wave components. 


e. Reflection of the 3.75-Second Wave. 


(1) Experiment 72A-06. The Kp versus time for experiment 
72A-06 is shown in Figure 9(a). The Kp dropped from an initial value 


36 


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39 


of 0.24 to 0.18, then to 0.17 at 3 hours, and then began to increase, 
reaching 0.30 at 25 hours. Between 25 and 80 hours, Kp remained high, 
fluctuating between 0.25 and 0.31. After 80 hours, Kp started to 


decrease while continuing to fluctuate, and was 0.22 at the end of the 
experiment (135 hours). 


Within the first 5 hours the foreshore developed an equilibrium shape, 
which was steep along range 5 and quite flat along range 1 as a result of 
the counterclockwise flow pattern of the wave uprush and backwash (Table 
11; Vol. VI). Since the waves broke on the foreshore, most of the wave 
energy reached the foreshore; as the foreshore became steeper, Kp in- 
creased, except at 1.5 and 3 hours. At those times, the erosion and 
deposition patterns at the base of the foreshore (-0.2 to -0.9 foot or 
6.1 to 27.4 centimeters) were reversed and Kp reached its lowest values. 


An almost flat shelf developed during the first 10 hours in the inner 
offshore region, caused by the erosion at the toe of the foreshore and 
deposition in the outer offshore at depths from -1.3 to -1.6 feet (39.6 
to 48.8 centimeters). As the foreshore eroded landward at a rate of 
0.015 foot (0.46 centimeter) per hour and the outer offshore slope 
steepened and prograded seaward with déposition at the higher elevations, 
the shelf on the inner offshore grew in length in both directions and a 
bar and trough developed. During this period of greatest profile develop- 
ment, Kp rose sharply, reaching a maximum at 25 hours. As a result of 
the high reflection, a significantly large standing wave developed, with 
antinodes at the foreshore and station 18, over the steepest part of the 
profile just seaward of the flat shelf. Between the first two antinodes 
of the standing wave, over the flat shelf of the inner offshore, a clock- 
wise circulation pattern developed, apparently driven by the counterclock- 
wise circulation in the foreshore zone. Apparently, the circulation over 
the inner offshore moved the sand to the edge of the shelf, but the lack 
of current movement through the antinode prevented further transport and 
thus increased the steepness. 


Between 25 and 70 hours, while the profile changed 3 feet (0.9 meter) 
in the length of the shelf between the two reflecting zones (foreshore 
zone and submerged offshore slope), K, did not increase or decrease 
Significantly, but fluctuated over a range of 0.05. Part of this varia- 
tion, which was greater than the 0.02 maximum variation in the fixed-bed 
tank, may have been caused by the 90° change in phase difference between 
the waves reflected from the two slopes as they separated. 


After 70 hours the seaward edge of the shelf began eroding, moving 
landward, even though the foreshore was still retreating and the off- 
shore was still prograding. Simultaneously, the clockwise circulation 
pattern over the inner offshore began disintegrating and Kp began 
decreasing. By 100 hours the bar had eroded and the trough had almost 
filled completely. From 15 to 100 hours the outer offshore steepened, 
with deposition at the upper elevations and erosion at -2.0- and 
-2.1-foot elevations. The eroded material was moved seaward to form 
a bar over part of the concrete bottom. 


40 


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Between 100 and 135 hours the foreshore continued to retreat, the 
inner offshore became a gently sloping region, the outer offshore slope 
steepness decreased, and Kp continued to drop. 


The movement of the -1.2-foot (36.6 centimeters) contour in Figure 
9(a) is an indication of some of these profile adjustments and correlates 
well with Kp variations. The -1.2-foot contour moved seaward at 15 
hours and Kp began rising. After 70 hours the -1.2-foot contour began 
moving shoreward, as the inner offshore eroded and the outer offshore 
slope became less steep, and Kp began to decrease. 


(2) Experiment 72A-10. The average Kp for three ranges versus 
time for experiment 72A-10 is shown in Figure 9(b). The Kp dropped 
initially to 0.24 and then began a gradual long-term increase, reaching 
a maximum of 0.37 at 55 hours. Between 60 and 80 hours, Kp varied 
between 0.31 and 0.35. 


During the first 1.5 hours the foreshore developed a steep slope and 
within the first 10 hours an almost flat shelf developed in the inner 
offshore region (Table 12). From 1.5 to 25 hours the foreshore prograded 
0.5 foot (15.2 centimeters), beginning first along the outside ranges. 
For the first 20 hours sand was deposited in the outer offshore at depths 
from 1.2 to 1.5 feet; from 20 to 25 hours sand was eroded at depths of 
1.6 and 1.7 feet (48.8 and 51.8 centimeters), thus forming a slightly 
steeper slope on the upper part of the outer offshore. During this 
initial profile development, Kp rose sharply. 


After 25 hours the only profile changes were a slight general in- 
crease in the foreshore slope and a gradual increase in the foreshore 
berm-crest elevation. The Kp continued to increase, but at a slower 
rate. The short-term variations in Kp after 35 hours was +0.03, on 
the order of the +0.025 variation in the fixed-bed tank. 


Throughout the experiment the foreshore slope was slightly flatter 
along the outside ranges and Kp was significantly lower along the 
outside ranges. 


The movements of the +1.0-, +0.9-, and +0.8-foot contours in Figure 
9(b) indicate the gradual increase in the foreshore berm-crest elevation 
which apparently caused the increase in Kp. The distance between the 
foreshore and offshore did not vary. 


(3) Summary of the Two Experiments. The average Kp in experi- 
ment 72A-06 was 0.26 and in experiment 72A-10 was 0.30 (Table 2). The 


elevation of the top of the submerged offshore slope appeared to be the 
primary source of long-term Kp variability in experiment 72A-06. The 
gradually increasing berm-crest elevation appeared to be the source of 
increasing Kp in experiment 72A-10. The development of a steeper slope 
and higher crest in the foreshore in experiment 72A-10 explains the higher 
Kp in that experiment. More details on the 3.75-second experiments are 
in Volume VI. 


42 


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43 


f. Summary. The Kp results from the 10 experiments are summarized 
in Table 3. For the two experiments with a wave period of 3.75 seconds 
on an initial slope of 0.10 the average Kp was 0.28; the difference 
between the two experiments was caused by a current pattern which devel- 
oped only in experiment 72A-06. For the two experiments with a wave 
period of 2.35 seconds on an initial slope of 0.10 the average Kp was 
0.125; the difference between the two experiments was caused by a trans- 
verse wave which occurred only in experiment 72B-10. In the four experi- 
ments with a wave period of 1.90 seconds on an initial slope of 0.10 the 
average Kp was 0.08 for each experiment. In the one experiment with 
a wave period of 1.50 seconds on an initial slope of 0.10, the average 
Kp was 0.05. These results support the following hypothesis: as the 
wavelength decreases (or the wave steepness increases) on a given initial 
profile slope, Kp decreases. 


The Kp would then be expected to decrease if the initial profile 
steepness were decreased for a given wavelength. However, the average 
Kp in the experiment with a wave period 1.90 seconds on an initial 
slope of 0.05 was 0.12, higher than the four experiments with a wave 
period of 1.90 seconds on an initial slope of 0.10. 


The effect of the different reflecting processes does not appear to 
correlate with any change in wave period (or wavelength). The effect of 
the steepness of submerged slopes may have been important in all of the 
experiments, but the correlation between Kp and the offshore slope was 
much better in the 6-foot tank (Fig. 10). A predominant cause of the 
variability in experiments 71Y-06. (1.90-second wave), 72D-06 (1.90-second 
wave; 0.05 initial slope), and 72A-06 (3.75-second wave) was the effect 
of the elevation at the top of the submerged slope. In all experiments 
except 72A-10, the foreshore remained fairly stable in shape and the Kp 
from the foreshore appeared to have been fairly constant, but in 72A-10 
the changing foreshore was the predominant cause of Kp variability. 
The effect of reflection from a plunging breaker appeared to be small 
and difficult to measure. The increasing width of the inshore shelf 
(increasing distance between foreshore and offshore) appears to have 
been a cause of long-term Kp variability in the experiments with the 
1.90-second wave and the predominant cause of K, variability in the 
experiments with the 1.50-second wave (Fig. 11). In the other experi- 
Ments the distance between the foreshore and offshore changed relatively 
little and Kp variability was shown to be related to other sources. 


3. Variations in Incident Wave Height. 


In the 10 experiments, the measured incident wave (Table 13) was com- 
posed of the nominal (generated) wave, the re-reflected wave, and, in 
experiment 72B-10, the transverse wave. Secondary and cross waves were 
also observed, but they did not affect the measurement of the incident 
wave height. 


Barnard and Pritchard (1972) state that ''Cross waves are standing 
waves whose crests are at right angles to a wavemaker; they oscillate 


44 


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at half the frequency of the wavemaker.'' Normally, cross waves occur at 
the generator and result from critical combinations of generated wave- 
length and tank width. In movable-bed tests with gradual bottom slopes, 
cross waves have been observed by the author at isolated sections over 
the profile where the wavelength, as it decreased in shoaling, passed 
through a critical value with respect to the tank width and remained at 
that value for sufficient distance to generate a cross wave. Cross waves 
are a spatial variation in the lateral direction. Cross waves were 
observed over a short segment of the movable-bed profile in experiment 
72B-06; however, the waves lasted only a brief period of time and were 
not measured. 


Secondary waves (or solitons) result from the breakdown of a finite- 
amplitude wave of nonpermanent form into a primary and one or more 
secondary waves traveling at different speeds dependent on depth. 
Secondary waves can be generated by a sinusoidally moving generator 
blade or by a wave as it passes a slope onto a shelf of smaller but 
constant depth (see Madsen and Mei, 1969 and Galvin, 1972) and are a 
spatial variation in the longitudinal direction. Secondary waves caused 
by waves passing onto a shelf probably occurred, but were not recorded. 
Secondary waves caused by sinusoidal generator blade motion occurred, 
but (as pointed out in Volume VI for the experiments where secondary 
waves were most pronounced) the wave height variation due to secondary 
waves was at least an order-of-magnitude less than the variation due to 
wave reflection from the profile. Because the incident wave height 
Measurement was an average of wave heights all along the tanks, the 
measured incident wave height was not affected by any spatial variation 
in height due to secondary waves. 


Transverse waves, generated by a gap at the side of the blade and a 
critical combination of wavelength and tank width, have an amplitude that 
varies across the tank, but since the transverse wave has the same period 
as the plane progressive wave, the combined wave motion causes the wave 
height at one point to increase from right to left and at another point, 
farther down the tank, to increase from left to right. (See Madsen, 
1974.) Transverse waves are spatial variations in both the lateral and 
longitudinal directions. Transverse waves were observed and recorded 
in only experiment 72B-10; a complete discussion of the wave height 
variability resulting from transverse waves is given in Volume VII. 


Re-reflection was the primary source of incident wave height varia- 
bility in these experiments. The effect of re-reflection on incident 
wave height variability in an experiment can be determined by comparing 
the difference in the range of wave heights between the fixed- and movable- 
bed tanks. The wave height variation in the fixed-bed tank is a measure 
of the wave height measurement accuracy in the movable-bed tank, and sub- 
tracting the measurement accuracy from the total variation in the movable- 
bed tank gives a measure of the incident wave height variation due to 
re-reflection in the movable-bed tank. 


a. 1.50-Second Wave. The nominal (generated) wave height for the 
1.50-second wave period was 0.41 foot (12.5 centimeters). In the 


48 


fixed-bed tank the average incident wave height was 0.44 foot (13.4 
centimeters), 0.03 foot (0.9 centimeter) above the nominal (generated) 
height, and the range of heights was only 0.03 foot. 


In the movable-bed tank the range of values was 0.09 foot (2.7 centi- 
meters), so that 0.06 foot (1.8 centimeters) is assumed due to varying 
profile reflectivity. The average incident wave height was 0.43 foot 
(13.1 centimeters), just over the nominal (generated) height by 0.02 
foot (0.6 centimeter). 


b. 1.90-Second Wave. The nominal (generated) wave height for the 
1.90-second wave period was 0.36 foot (11.0 centimeters). In the fixed- 
bed tanks the average incident wave heights for the five 1.90-second tests 
were all within 0.02 foot of the nominal (generated) height. In the 10- 
foot tank, initial test length of 61.7 feet (18.8 meters), the average was 
0.36 foot, the same as the nominal (generated) height; in the 6-foot tank, 
initial test length of 100 feet (30.5 meters), the average was 0.37 or 
0.38 foot (11.3 or 11.6 centimeters). In four of the five experiments 
the range of variation in incident wave height was 0.03 foot and in 
experiment 71Y-06 the range was 0.04 foot (1.2 centimeters). 


In the movable-bed tank in experiment 70X-06 the range of values was 
0.06 foot, 0.03 foot due to varying reflectivity; in experiment 70X-10 
the range was 0.05 foot (1.5 centimeters), 0.02 foot due to varying 
reflectivity; in experiment 71Y-06 the range was 0.07 foot (2.1 centi- 
meters), 0.03 foot due to varying reflectivity, and in experiment 72D-06 
the range was 0.06 foot, 0.03 foot due to varying reflectivity. 


The average incident wave height in the movable-bed tanks was less 
than the nominal (generated) height in experiment 70X-06, equal to the 
nominal (generated) height in experiment 71Y-10, and greater than the 
nominal (generated) height in experiments 70X-10, 71Y-06, and 72D-06. 


c. 2.35-Second Wave. The nominal (generated) wave height for the 
2.35-second wave period was 0.34 foot (10.4 centimeters). In the fixed- 
bed tanks the average incident wave height was 0.02 foot above the nominal 
(generated) height in experiment 72B-06 and equal to the nominal (generated) 
wave height in experiment 72B-10. The difference was likely due to the 
difference in initial test length. The range of incident heights was 0.05 
foot in experiment 72B-06 and 0.04 foot in experiment 72B-10. 


In the movable-bed tank in experiment 72B-06 the range of heights 
was 0.06 foot, only 0.01 foot (0.3 centimeter) due to varying reflec- 
tivity, and in experiment 72B-10 the range was 0.03 foot, which was . 
within the accuracy of the wave height measurement; thus, the effect 
of re-reflection in each experiment was not measurable. 


d. 3.75-Second Wave. The nominal (generated) wave height for the 
3.75-second wave period was 0.31 foot (9.4 centimeters). In the fixed- 
bed tanks the average incident wave heights were within 0.01 foot of one 
another and both were greater than the nominal (generated) height. The 
range of incident height variation was 0.07 foot in experiment 72A-06 
and 0.04 foot in experiment 72A-10. 


49 


In the movable-bed tank in experiment 72A-06 the range of values was 
0.10 foot (3.0 centimeters), 0.03 foot due to varying reflectivity, and 
in experiment 72-10 the range was 0.12 foot (3.7 centimeters), 0.08 foot 
(2.4 centimeters) due to varying reflectivity. The average incident 
heights in the movable-bed tanks were 0.07 foot and 0.04 foot, both 
greater than the nominal (generated) height. 


e. Comparison of the Ten Experiments. Varying profile reflectivity 


caused no measurable change in the incident height in experiment 72B-10 
(2.35 seconds), a moderate change (0.01 to 0.03 foot) in experiments 
70X-06, 70X-10 (1.90 seconds), 71Y-06, 72D-06, 72A-06, and 72B-06, and 
a Significant change (0.06 to 0.08 foot) in experiments 71Y-10 (1.90 
seconds), 72C-10 (1.50 seconds), and 72A-10 (3.75 seconds). The effect 
in the 6-foot-wide tank was in the moderate range for all five experi- 
ments and in the 10-foot-wide tank ranged from no change to 0.08 foot, 
and the effect was not a function of wave period. It appears then that 
the wider tank may have amplified this effect. 


III. EQUILIBRIUM PROFILES 


1. Definitions and Importance of Equilibrium Profiles. 


The term "equilibrium profile" implies a profile whose mean position 
is fixed in space for the given wave and sediment conditions, with the 
expectation that the actual profile at any given time will deviate some- 
what from the mean profile. It has been assumed that equilibrium is a 
state which can be reached on a model profile with a constant wave action 
impinging on it for a sufficiently long time. 


Laboratory studies of longshore transport often depend on having an 
equilibrium profile to determine the longshore transport rate without 
having an onshore-offshore transport component (Savage, 1959, 1962; 
Fairchild, 1970a). Coastal engineering models are frequently based on 
simulating the equilibrium profile. However, Savage (1962) and Fairchild 
(1970a) found that equilibrium profiles are not always easily attained. 
Collins and Chesnutt (1975, 1976) showed that the final unchanging pro- 
file for the same wave and sediment conditions was not always repeatable 
and that the initial slope could affect the final profile shape. 


Swart (1974) found that for a single periodic wave impinging on a 
profile, 1,500 hours of wave action was required to reach equilibrium 
for some wave and sediment conditions. However, 1,500 hours is not a 
practical test duration for most models or experiments. 


J.W. Kamphuis (Professor of Civil Engineering, Queen's University, 
Kingston, Ontario, personal communication, 1978) used a series of wave 
conditions replicating a year's seasonal variations and found that 
when using a wave in the transition region in place of either the winter 
or summer waves the profile reached equilibrium much less readily than 
when using only winter and summer waves. Kamphuis further compared two- 
dimensional tests with three-dimensional tests, and found that 9 to 11 
yearly cycles were required to reach equilibrium with the two-dimensional 
setup and only 1 to 2 cycles with the three-dimensional setup. 


50 


The LEBS experiments were planned to be run until the profile devel- 
oped an equilibrium shape because it was assumed that if the profile 
reached equilibrium, the primary source of temporal wave height varia- 
bility, the changing profile reflectivity, would be eliminated or sig- 
nificantly reduced. 


The effects of varying initial slope and wave period are discussed 
below. The effect of tank width on profile development is discussed in 
Section IV. 


7c EEeCts Ore ini ti alg hcorilepoloper. 


Two experiments were conducted in which the only variable was the 
initial profile slope--0.10 in experiment 71Y-06 and 0.05 in experiment 
72D-06. 


The steeper initial slope in experiment 71Y-06 (Fig. 12) adjusted 
slowly to the waves and did not appear to have reached equilibrium along 
any segment of the profile after 375 hours. The foreshore retreated at 
a rate of 0.113 foot (3.44 centimeters) per hour between 1 and 15 hours 
and at a rate of 0.025 foot (0.76 centimeter) per hour thereafter. The 
flat shelf in the inshore zone and the steeper slope in the offshore zone 
developed between 200 and 220 hours. 


The flatter initial slope in experiment 72D-06 (Fig. 13) adjusted 
more quickly to the wave attack, but also did not appear to have reached 
equilibrium. The foreshore retreated at a rate of 0.05 foot per hour 
between 5 and 125 hours, prograded seaward between 125 and 135 hours, 
and then stabilized for the remainder of the experiment. The inshore 
zone slowly grew in width and the offshore slope remained mild during 
the first 100 hours. After 100 hours the flat shelf in the inshore zone 
and the steeper slope in the offshore zone rapidly developed. Once the 
foreshore stabilized, the inshore zone began eroding, creating a signifi- 
cant depression in the profile belaw the forshore zone, while the off- 
shore zone continued to prograde seaward. The Kp stopped varying 
during the last 25 hours (Fig. 7), indicating that equilibrium may have 
been near. 


Although neither profile reached equilibrium, the profiles developed 
somewhat different shapes (Fig. 14). The differences in rates and types 
of profile adjustments verify the conclusions of Collins and Chesnutt 
(1975, 1976) that the initial profile slope can affect the final profile 
shape. 


3. Effect of Wave Period. 


Nine experiments were conducted with an initial profile slope of 
0.10 and four different wave periods; the experiments are analyzed below 
to determine the effect of wave steepness on profile equilibrium. The 
deepwater wave steepness was 0.039 for the 1.50-second wave, 0.021 for 
the 1.90-second wave, 0.013 for the 2.35-second wave, and 0.004 for the 
3.75-second wave. 


5| 


} Foreshore 
Inshore 


NOM 


ee NG 


oy | / 


ae 


‘ 


= N 
(45) 4JdaosajuT MS [DUIIIQ Woy souDIsiG 


eZ 


[00 150 L000 250) HOO. BD) 0) 
Cumulative Time (hr) 


50 


3 x . 
: 0 


nge of experiment 71Y-06. 


Distance from Original SWL Intercept (ft) 


= Aw 9 9 tt 


15 Inshore 


1.0 
|G Offshore 
Se oe Se 
40h aE ES 118 
a -2.0ft 
45 
50 


@) 5OmanlO Ow SO a 20 0250 
Cumulative Time (hr ) 


Figure 13. Contour movements along center 
range of experiment 72D-06. 


‘sodo[TS [@I}IUT JUILOFFIP PUL DAEM PUODDS-0G"[T & YIIM SaTTjord TeutzZ Fo uostaedwoy 


(45) }dads9jUT TMS JOUIb14Q wos} adUD\SIG 
9G 8b Ov Ge v¢ 9| 8 @) 8- 


2|!JO1q 10141] 99-22 ——:— 
a[tJOld |DIyIU) 9O—A} 2 — - — 
(14 081 18440) 90-Gzz ------ 
(4U GJE 42440) 990-A1Z ——— 


a[1jOld yooeg 


‘pl oan3sty 


(13) IMS 9A0QD: UON}DAa/Z 


54 


a. 1.50-Second Wave. The profile in the one experiment (72C-10) 
conducted with a wave period of 1.50 seconds appeared to be near equi- 
librium, as indicated by horizontal contours in the foreshore zone and 
most of the inshore zone in Figure 15. Erosion of the foreshore was con- 
tinuing but slowing along the range 1 side of the tank and some erosion 
was occurring in parts of the inshore zone. Deposition continued in the 
offshore zone, but at a slower rate. The breaker type and position had 
stabilized and the Kp and its variability had decreased to small values. 
If this experiment had been continued, presumably it would have soon 
reached equilibrium. The final profile is shown in Figure 16. 


b. 1.90-Second Wave. Four experiments were conducted with a wave 
period of 1.90 seconds and an initial slope of 0.10. 


(1) Experiments 70X-06 and 70X-10. These experiments had a 


7-foot longer initial test length than the other experiments in their 
respective tanks. Because the shoreline was stabilized by the renourish- 
ment of the backshore after 54 and 62 hours in experiments 70X-06 and 
70X-10, the final profile shapes for those experiments may not have been 
characteristic of profiles for the 1.90-second wave. The final profiles 
could not have been at equilibrium because sand was still being eroded 
from the backshore when the experiments were stopped (see Table 10 in 
Vol. II). However, the nearly horizontal contour lines near the end of 
the experiment in the offshore in Figure 17 indicate that parts of the 
profile in experiment 70X-06 may have been approaching equilibrium. It 
is difficult to determine from Figure 18 if the profile in experiment 
70X-10 was approaching equilibrium. Several of the offshore contours 

had stopped moving in the seaward direction and had begun to move in the 
shoreward direction, indicating the possible approach to some dynamic 
equilibrium, but the lateral variations in the shape and development of 
the profiles (see Vol. II and Section IV,5 in this volume) made it diffi- 
cult to determine equilibrium. 


Figure 19 compares the center profiles from the two experiments at 
50, 100, and 175 hours, indicating that the profiles at 50 and 100 hours 
were nearly the same, but that at 175 hours the profile in experiment 
70X-10 had built farther seaward while maintaining a similar shape. The 
profile development after 175 hours in experiment 70X-10 is shown in 
Figure 20. 


(2) Experiments 71Y-06 and 71Y-10. These experiments had a 
shorter initial test length than the two experiments discussed above. 


There is no indication that either experiment 71Y-06 or 71Y-10 was near 
equilibrium at the end of the experiments, as shown in Figures 12 and 21; 
both experiments showed slow, steady development throughout. 


Figure 22 compares the center profiles from the two experiments at 
100, 200, and 300 hours, indicating that at 100 hours the profiles had 
nearly the same shape; at 200 hours the profile in experiment 71Y-10 had 
already developed a flat inshore shelf while the profile in experiment 
71Y-6 had not, and at 300 hours the profile in experiment 71Y-06 had 


55 


Distance from Original SWL Intercept (ft) 


|| ft 


} Foreshore 


Inshore 


Offshore 


-30 
0) 


50 100 150 200 250 
Cumulative Time (hr ) 


Figure 15. Contour movements along center range of 
experiment 72C-10. 


Elevation above SWL (ft) 


Beach Profile 


— -— - — 72C-10 Initial Profile 
72C-10 (after 140 hr) 


-8 0 8 16 24 32 
Distance from Original SWL Intercept (ft) 


Figure 16. Equilibrium profile in experiment 72C-10, 
with steep ''winter"' wave. 


57 


Distance from Original SWL Intercept (ft) 


7 Foreshore 
Inshore 
Offshore 
25) 
30 
0) 50 100 150 200 290 


Cumulative Time (hr) 


Figure 17. Contour movements along center 
range of experiment 70X-06. 


58 


Distance from Original SWL Intercept (ft) 


20 


29 


30 


50 


Figure 18. 


PSs a —& 


fi\N} 
(est ee nL 


100 150 200 
Cumulative Time (hr ) 


Contour movements along center 
range of experiment 70X-10. 


COMR NM O 


290 


Foreshore 


Inshore 


Offshore 


Figure 


0. Beach Profiles after 50 hr 


Elevation above SWL (ft) 


-14 -7 (0) Uv 14 2! 28 
Distonce from Original SWL Intercept (ft) 


b. Beach Profiles after 100 hr 


Elevation above SWL (ft) 
fe) © 


' 
n 


-14 -7 ie) 7 14 2l 28 
Distance from Original SWL Intercept (ft) 


c. Beach Profiles ofter 175 hr 


Elevation obove SWL (ft) 
° n 


' 
~ 


-4 
“14 -7 0 7 14 2l 28 
Distance from Originol SWL Intercept (ft) 


19. Greater seaward development of profile in 
experiment 70X-10 than in experiment 70X-06. 


60 


Elevation above SWL (ft) 


oi 


Beach Profile 


—-— Initial Profile 
After | 75 hr 
Seen = After 210 hr 


0 T 14 2| 28 


Distance from Original SWL Intercept (ft) 


Figure 20. 


Profile changes in experiment 70X-10 
during the last 35 hours. 


6 


35 


Olt 
NIE a } Foreshore 
GL J 0.2 
0.4 
0.6 


Inshore 


Distance from Original SWL Intercept ( ft) 


Offshore 


3 l 
2 0 50 100 0) 400) 250) sss Ss) I) 


Cumulative Time (hr ) 


Figure 21. Contour movements along center range of experiment 71Y-10. 


Elevation above SWL (ft) Elevation above SWL (ft) 


Elevation above SWL (ft) 


a. Beach Profiles after 100 hr 


2 
{o} 
-2 
-4 
-14 7 (0) 7 14 2 28 
Distance from Original SWL Intercept (ft) 
4 


b. Beach Profiles after 200 hr 


-14 -7 0 7 14 2l 28 
Distance from Original SWL Intercept (ft) 


c. Beach Profiles ofter 300 hr 


-14 -7 {¢) 7 14 2l 268 
Distonce from Original SWL Intercept (ft) 


Figure 22. Greater seaward development of the profile 


in experiment 71Y-06 than in 71Y-10. 


63 


developed the flat inshore shelf and had surpassed experiment 71Y-10 in 
the progradation of the offshore zone. The comparison of the final pro- 
files for the two experiments in Figure 23 indicates that the experiments 
had roughly the same shape, but that in experiment 71Y-06 the foreshore 
had eroded farther landward and the offshore had prograded farther sea- 
ward. 


(3) Comparison of the Four Experiments. The final profiles in 


the experiments with the 1.90-second waves are compared in Figure 24, 
showing that the profile shape was similar in all four experiments, but 
that the longer the experiment, the farther landward the foreshore and 
the farther seaward the offshore. The Kp variability increased with 
time during each test (Figs. 3 to 6). This indicates that if an equi- 
librium slope can be attained for the 1.90-second period on an initial 
0.10 sand slope, it is probably shaped like these four profiles with an 
even longer inshore zone. 


c. 2.35-Second Wave. The profile in experiment 72B-06 adjusted 
slowly to the waves and appeared to be near equilibrium at the end of 
the experiment (150 hours) (Fig. 25); the profile in experiment 72B-10 
adjusted more rapidly and did not appear to be near equilibrium at the 
end of the experiment (150 hours) (Fig. 26). 


The differences in rate of profile adjustment and the differences in 
the shape of the offshore zone between the two experiments are shown in 
Figure 27. These differences may have been caused by differences in 
tank width and initial test length or by the transverse wave which was 
only generated in experiment 72B-10. 


d. 3.75-Second Wave. Two experiments were conducted with a 3.75- 
second wave. Although the profile in the narrower tank (experiment 
72A-06) did not appear close to equilibrium, the profile in the wider 
tank (experiment 72A-10) did, as shown by comparing Figures 28 and 29. 
The development and disintegration of circulation cells between antinodes 
of the standing wave envelope evidently prevented the profile from reach- 
ing equilibrium in experiment 72A-06 (discussed in Vol. VI). The absence 
of any horizontal contours in Figure 28 (narrower tank) shows this lack 
of equilibrium. However, in the wider tank, nearly all contours are 
horizontal after only 25 hours (Fig. 29). 


Figure 30 compares the center profiles from the two experiments at 
25, 50, and 80 hours, indicating that throughout the experiments the 
profile shapes were quite different in the two tanks, probably as a 
result of the circulation pattern in experiment 72A-06. Profile changes 
during the final 55 hours of experiment 72A-06 are shown in Figure 31. 
The offshore zone changed to a more gently sloping region. 


e. Comparison of the Profiles. Although the profile in experiment 


71Y-06 was not at equilibrium, it appears to well represent the shape 
of profile adjustment for a 1.90-second wave. The profile in experiment 
72C-10 (1.50-second wave) was close to equilibrium and is assumed to be 


64 


Elevation above SWL (ft) 


Elevation above SWL (ft) 


-/ 


Figure 23. 


af 


Figure 24. 


_ Beach Profile _ 
— 7IY-06 (after 375 hr) 
Ee 7IY- 10 (after 335 hr) 
—v-— 71Y Initial Profile 


0 a 14 2l 28 


Distance from Original SWL Intercept (ft) 


Final profiles in experiments 71Y-06 and 71Y-10 
with the longest test durations in the series. 


Beach Profile 


70X-06 (after 175 hr) 
—-—— 70X-1[0 (after 210hr) 
SUE al 71Y-06 (after 375hr) 
noone 71Y-10 (after 335 hr) 
—-— Initial Profile 


0) 1 14 2| 28 
Distance from Original SWL Intercept (ft) 


Comparison of final profiles with a wave period 
of 1.90 seconds and an initial slope of 0.10. 


65 


35 


2 


D0) 


Distance from Original SWL Intercept (ft) 


i ae 
0.6 ft 
Ni eats 0.4 
OR 0.2 Foreshore 
0.0 
- 0.2 
5 i “ae ito 
aS aE NNR ING 
--0.8 
- 1.0 
= 152 
0 | asian - 1.4 
- 1.6 
IS 5 
Se Offshore 
20 
25 -2.0 
Tenentt 
30 
O 50 100 150 200 250 
Cumulative Time (hr) 
Figure 25. Contour movements along center 


range of experiment 72B-06. 


66 


Distance from Original SWL Intercept (ft) 


Foreshore 


i pe a Inshore 
10 Uk -0.8 
Oe {1,0 
ame ee = 
Ae NE “18 
0 SE ZS = 
; AT eae Off 
yee shore 
a ee J 16 
20 Sn a) a a aS = at |.8 
TE Oc ee ay 
-2.2 ft 
ZS) 
30 
0) 50 100 150 200 250 
Cumulative Time (hr) 
Figure 26. Contour movement along center range of 


experiment 72B-10. 


67 


0. Beach Profiles ofter 50 hr 


Elevation above SWL (f1) 


-16 -8 {¢) 8 16 24 32 
Distance from Original SWL Intercept (ft) 


b. Beach Profiles ofter 100 hr 


Elevation above SWL (ft) 


-16 -8 (0) 8 16 24 32 
Distance from Original SWL Intercept (ft) 


c. Beach Profiles ofter 150 hr 


Elevation above SWL (ft) 


-16 -8 {e) 8 16 24 32 
Distance from Original SWL Intercept (ft) 


Figure 27. Development of different offshore shapes: 


concave upward in experiment 72B-06 and 
convex upward in experiment 72B-10. 


68 


=02 
: LL 0,2 (¢ Momsen 


Distance from Original SWL Intercept ( ft ) 
) 


é 
2B Offshore 
6) 


ZS 
-2.2 ft 
30 
39 
0 50 100 150 200 290 


Cumulative Time (hr ) 


Figure 28. Contour movements along center 
range of experiment 72A-06. 


69 


Distance from Original SWL Intercept (ft) 


RORit 

RI NS 08 
Ree 0G 
Sea «04 
SSeS 

6 —— oe Foreshore 
SVE 20.2 
INS 33 
IRAE -0.6 

5 [ \ = 10 

lOF 
Ve ine Offshore 
ia ag ee i 
Ri te ee tO 
eee SSS 
keer onal i = 1.8 

20, VAR 
|—__—_—___~-—_- - 2.2 ft 

29 

30 
0) 50 100 150 200 250 


Cumulative Time (hr ) 


Figure 29. Contour movements along center range of 
experiment 72A-10. 


70 


0. Beach Profiles ofter 25 hr 


Elevation above SWL (ft) 
° 


‘ 
Nn 


-4 
-16 -8 (0) 8 16 24 32 
Distance from Original SWL Intercept (ft) 
4 
b. Beoch Profiles after 50 hr 
2 ——_ 724-06 


sacesso 72A-10 
os 72A Initial Profile 


Elevation above SWL (ft) 


-16 -8 (0) 8 16 24 32 
Distonce from Original SWL Intercept (ft) 
4 
c. Beach Profiles after 80 hr 
2 —— 72A-06 
72A-10 
a 72A Initial Profile 


Elevation above SWL (ft) 


-16 -8 0 & 16 24 32 
Distance from Original SWL Intercept (ft) 


Figure 30. Development of a higher foreshore in 


experiment 72A-10 and a steeper off- 
shore in experiment 72A-06. 


7 


Beach Frofile 


—— - —— Initial Profile 
Fl eewn  N After 80 hr 
After 135 hr 


Elevation above SWL (ft) 


4 
-16 -8 O 8 16 24 Se 
Distance from Original SWL Intercept (ft) 


Figure 31. Profile change in experiment 72A-06 during 
the last 55 hours. 


72 


representative of a profile adjustment for a 1.50-second wave. The pro- 
files in experiments 72A-10 and 72B-06 were close to or at equilibrium 
and are assumed to typify profile adjustment for 3.75- and 2.35-second 
waves. These four profiles are compared in Figure 32. 


The profile from experiment 72A-10 (Hj/Lo = 0.004 at 80 hours) is 
typical of the step-type or summer (prograding shoreline) profile, with 
a high berm and a step at the toe of the foreshore zone. The profile 
from experiment 72B-06 (H,/Lo = 0.013 at 150 hours) is also somewhat 
typical of the summer profile, except that the berm crest is lower and 
the lower foreshore appears to be half-bar and half-step. On both of 
these two profiles, some deposition occurred in the offshore zone, more 
in the H,/Lo = 0.013 experiment than in the H o/Lo = 0.004 experiment. 
The profile from experiment 71Y-06 (Ho/Lo = 0. 021 at 375 hours) is cer- 
tainly an eroding profile consisting Of Beco foreshore and offshore zones 
separated by a long shelf with several shallow bars and troughs. The pro- 
file from experiment 72C-10 (Hj/L5 = 0.039 at 140 hours) is typical of 
the bar-type or winter (rodane Bhoreltine) profile with a vertical scarp, 
a steep foreshore, a longshore bar, and offshore deposition. 


The transition zone between the two types of profiles is normally 
accepted to be between H,/L, = 0.020 and 0.025 and the profiles from the 
five experiments with H,/L, = 0.021 could certainly not be classified as 
either winter or summer. In fact, this was the least stable of the four 
conditions, with none of the five profiles close to equilibrium. With 
the other three wave steepnesses, at least one of the profiles appeared 
to be near a stable shape. This agrees with the findings of Kamphuis 
(personal communication, 1978) that waves in the transition region tend 
to take longer to develop an equilibrium profile. 


The final profiles from experiments 72C-10, 71Y-10, 72B-10, and 
72A-10 were averaged to develop a standard initial profile (Fig. 33) 
to be used in longshore transport experiments in CERC's Shore Processes 
Test Basin (SPTB) (P. Vitale, hydraulic engineer, CERC, personal communi- 
cation, 1976). This standard profile will also be used in a study of 
wier jetties in the SPTB (J.R. Weggel, Chief, Evaluation Branch, CERC, 
personal communication, 1977). 


f. Discussion of Results. The four experiments with the 1.90-second 
wave verify the findings of Savage (1962) and Fairchild (1970a) that an 
equilibrium profile is not always easily attained, even with the wave 
direction normal to the shoreline. The four experiments with the 3.75- 
and 2.35-second waves verify the findings of Collins and Chesnutt (1975, 
1976) that profiles for the same wave conditions do not always have the 
same shape. In particular, the experiments with 3.75- and 2.35-second 
waves point out that the physical constraints of the laboratory facilities 
can affect the final profile shape. The currents in experiment 72A-06 
(3.75 seconds) and the transverse wave in experiment 72B-10 (2.35 seconds) 
kept those from reaching equilibrium. 


In judging the evidence presented here, profile equilibrium in basi- 
cally two-dimensional tests does not appear to be an easily definable, 


US 


Elevation above SWL (ft) 


Figure 32. 


4 


Elevation above SWL (ft) 
(@) ine) 


' 
ine) 


Falourens Sy. 


Experiments Ho/Lo 


—-— Initial 0.1 Slope . 

----- 72A-10 (after 8Ohr) 0.004 

—--— 72B-06 (after |50hr) 0.013 

—— 7lY-06 (after 375 hr) 0.021 
es —-— 72C-10 (after 140hr) 0.039 


-8 6) 8 16 24 32 40 
Distance from Original SWL Intercept (ft) 


Comparison of the equilibrium or representative profile 
for each wave steepness. 


-8 0 8 16 24 32 40 
Distance from Original SWL. Intercept (ft) 
Preliminary beach profile of Vitale (personal communication, 


1976), developed from the final profiles of experiments 
72C-10, 71Y-10, 72B-10, and 72A-10. 


74 


attainable, or a useful state to be trying to reach in experiments of 
practical duration. Coastal engineering might be better advanced if 
researchers were more concerned with trying to reach some constant rate 
of profile change or a rate of profile change small in comparison to 
other variables. 


IV. LABORATORY EFFECTS 


1. Definitions of Terms. 


Laboratory effects are the undesired differences between laboratory 
and prototype conditions caused by the physical constraints which exist 
in the laboratory, but not in the field. For example, the variations in 
incident wave height discussed in Section II, 3 are laboratory effects; 
i.e., the mechanical generator at one end of the wave tank caused a re- 
reflection of the wave energy propagating away from the profile that 
would not have occurred in nature. This project evolved from an investi- 
gation of wave height variability and equilibrium profiles into a more 
comprehensive examination of all laboratory effects. 


This section analyzes five laboratory effects based on results from 
the 10 experiments. Other known laboratory effects are also identified. 


2. Test Length and Initial Slope Effects. 


a. Processes. Two physical processes are known to be affected by 
changes in initial test length: re-reflection of waves from the wave 
generator and secondary waves. 


(1) Re-Reflection. The height of the incident wave is a func- 
tion of the height of the nominal (generated) and re-reflected waves and 
the phase difference between the re-reflected wave and the wave generator 
motion. The height and phase of the re-reflected wave are functions of 
the height and phase of the reflected wave. The height of the reflected 
wave is a function of the profile reflectivity. The phase of the reflec- 
ted wave with respect to the generator motion is a function of the dis- 
tance between the profile and the generator. The effect of initial test 
length on re-reflection and incident wave height variability is discussed 
in Section II, 3. The effect of incident wave height variability on the 
profile is discussed in this section. 


(2) Secondary Waves. Secondary waves cause a spatial (longi- 
tudinal) variation in wave height and a variation in the asymmetry of the 
velocity distribution under a wave. The degree of asymmetry obviously 
depends on the position along the tank. In this case the distance to the 
toe of the initial profile from the generator is the controlling distance. 


b. Initial Test Length Effect. Four pairs of experiments are ex- 
amined here. In two pairs (experiments 70X-06 and 71Y-06 and experiments 


UD 


70X-10 and 71Y-10) the initial test length was the only variable; in the 
other two pairs (experiments 72B-06 and 72B-10 and experiments 72A-06 and 
72A-10) both initial test length and tank width varied, but the effects 
of initial test length are distinguishable from the tank width effects. 


(1) Experiments 70X-06 and 71Y-06 (1.90-Second Wave). In each 
experiment the effect of re-reflection on the incident wave height was 
the same, 0.03 foot (Table 13). However, the average incident wave 
height was 0.34 foot in experiment 70X-06 and 0.37 foot in experiment 
71Y-06, and the difference in incident height is likely due to the dif- 
ference in the phase difference as a result of the 7-foot difference in 
initial test length. 


The profiles in the two experiments developed similar shapes (Fig. 
24), with the length of the inshore shelf the only difference, due pri- 
marily to the 200-hour difference in the duration of the experiments. 
However, the rate of shoreline recession was quite different (Fig. 34). 
In experiment 70X-06 the shoreline recession rate was 0.06 foot per hour 
between 1 and 22 hours, 0.14 foot (4.2 centimeters) per hour between 22 
and 30 hours, 0.10 foot per hour between 30 and 44 hours, and 0 there- 
after. The backshore was artificially nourished after 54 hours, thus 
maintaining the stable shoreline after that time. In experiment 71Y-06 
the rate was 0.113 foot per hour between 1 and 15 hours and 0.025 foot 
per hour thereafter (for 360 hours). 


The differences in profile adjustment rates may have been caused by 
the difference in initial test length; if so, the difference was not due 
to re-reflection effects, since the higher recession rate was associated 
with the lower incident wave height. It is unlikely that secondary waves 
would have caused the difference in shoreline recession rates without 
also affecting the profile shape and such profile shape differences were 
not observed. 


(2) Experiments 70X-10 and 71Y-10 (1.90-Second Wave). In each 


of these experiments the effect of re-reflection on the incident wave 
height was different, 0.02 foot in experiment 70X-10 and 0.06 foot in 
experiment 71Y-10 (Table 13). However, the average incident wave height 
was almost the same, 0.37 foot in experiment 70X-10 and 0.36 foot in 
experiment 71Y-10, even though the initial test length had a difference 
of 7 feet in the two experiments. 


The profiles in the two experiments developed similar shapes (Fig. 
24), with the length of the inshore shelf the only difference, due pri- 
marily to the 125-hour difference in the duration of the experiments. 
However, the rate of shoreline recession was quite different (Fig. 34). 
In experiment 70X-10 the shoreline recession rate was 0.08 foot per hour 
between 12 and 62 hours, and 0 thereafter because the backshore was re- 
nourished to maintain a stable shoreline position. In experiment 71Y-10 
the rate was 0.133 foot (4.05 centimeters) per hour (uniform laterally) 
between 1 and 15 hours, 0.016 foot per hour (uniform laterally) between 


76 


Distance from Original SWL Intercept (ft) 


0 


Figure 34. 


50 100 150 200 250 300 350 400 
Cumulative Time (hr) 


Comparison of shoreline movement in four experiments with 
a 1.90-second wave and a 0.10 initial slope. 


Cana 


15 and 205 hours, and varied from 0.016 foot per hour along the center 
of the tank to 0.025 foot per hour along the tank walls thereafter (for 
130 hours). 


Re-reflection is not the likely explanation for the difference in 
shoreline recession rates, since there was little difference in average 
incident wave heights and the slower recession rate was associated with 
the higher range of re-reflection effect within an experiment. Secondary 
waves are not a likely cause because there was no difference in profile 
shape. 


(3) Experiments 72B-06 and 72B-10 (2.35-Second Wave). In these 


two experiments the effect of re-reflection on the incident wave height 
variability was slight. In experiment 72B-06 the range of incident wave 
heights in the movable-bed tank was only 0.01 foot greater than in the 
fixed-bed tank; in experiment 72B-10 the range in the movable-bed tank 
was less than in the fixed-bed tank (Table 13). However, there was a 
0.07-foot difference in average incident wave height. The average Kp 
was lower in experiment 72B-06 than in experiment 72B-10, indicating that 
Hp and Hpp would have been lower in experiment 72B-06. The higher Hy 
in experiment 72B-06 must then have been the result of the difference in 
phase difference between H; and Hpp as a result of the 38.3-foot 
(11.7 meters) difference in initial test length. Secondary waves were 
also present. 


The profiles in the two experiments developed different profile 
shapes. Some of those differences were due to the differences in tank 
width and the presence of the transverse wave in experiment 72B-10 
(discussed in the following subsection). In experiment 72B-06 the off- 
shore zone had a concave-upward shape; in experiment 72B-10 the offshore 
zone had a convex-upward shape (Fig. 27,c). This significant difference 
could have been caused by either secondary waves or re-reflection effects, 
as a result of the difference in initial test length. This difference in 
offshore profile shape may have been a contributing cause to the lack of 
equilibrium in experiment 72B-10. 


(4) Experiments 72A-06 and 72A-10. In each of these experiments 


the effect of re-reflection on the incident wave height variability was 
different, 0.03 foot in experiment 72A-06 and 0.08 foot in experiment 
72A-10; the difference in average incident wave height between the two 
experiments (0.03 foot) was significant (Table 13). Thus, varying re- 
flectivity within an experiment caused variations in H;; and the 38.3- 
foot difference in initial test length affected the average Hy. 
Secondary waves were the most pronounced in these experiments. 


The profiles in the two experiments developed different shapes (Fig. 
31). Some of the \differences were due to tank width effects, which are 
discussed in the following subsection. The differences in the shape of 
the outer offshore were probably due to re-reflection or secondary wave 
effects. In experiment 72A-06 the outer offshore had a steep segment 
between stations 16 and 20 and a bar at station 28. In experiment 72A-10 


78 


the outer offshore below -1.9 feet remained unchanged throughout the 
experiment. The differences in foreshore berm-crest elevation may have 
resulted from the differences in the outer offshore, but these cannot be 
determined. 


c. Initial Slope Effect. The effect of varying the initial slope 
can be seen by comparing experiment 71Y-06 with an initial slope of 0.10 


and experiment 72D-06 with an initial slope of 0.05. All other parameters 


were equal in these two experiments. 


In each of these experiments the effect of re-reflection on the inci- 
dent wave height variability was the same (0.03 foot), but there was a 
0.02-foot difference in average incident wave height (Table 13). Re- 
reflection caused a higher average incident wave height in the experi- 
ment with the flatter initial slope. 


The distance from the generator to the toe of the initial slope was 
23 feet greater in experiment 71Y-06 (0.10 slope); thus, the velocity 
distribution at the toe of the slope may have been different in the two 
experiments. 


The offshore profiles in these two experiments developed similar 
shapes (Fig. 14), but the inshore zone developed somewhat differently. 
In experiment 72D-06 (0.05 initial slope) the flat shelf in the inshore 
zone developed during the first 100 hours and a trough was scoured in 
the zone after the foreshore stabilized at 135 hours. In experiment 
71Y-06 (0.10 initial slope) the flat shelf in the inshore zone developed 
between 200 and 220 hours and then continued to widen as the foreshore 
and offshore separated. 


It is not possible to ascertain whether re-reflection, secondary 
waves, or some other phenomena caused the profiles to develop such 
different inshores, but it was probably the result of the difference 
in initial slope. 


3. Tank Width Effects. 


When the wavelength, L, is much larger than the tank width, W, 
then the wave tank is 'narrow'' and the result of wave action on the sand 
bed is expected to be two dimensional; i.e., without lateral variations 
in profile shape. When L is much smaller than W, then the wave tank 
is essentially a "basin" and the result of wave action on the sand bed, 
even when wave direction is normal to the initial shoreline, is expected 
to be three dimensional; i.e., with lateral variations in profile shape. 
In the intermediate case, when the tank width and wavelength are nearly 
the same (L/W = 1), the wave tank is wide enough for the lateral varia- 
tions to begin to occur, but the tank walls confine the third dimension 
of current patterns and sediment movement to an unknown extent. In the 
10 LEBS experiments, L had values that ranged from equal to W to 
several times larger than W, so the point at which a wave tank becomes 
Narrow can be examined. 


(69 


The confining effect of the tank walls on flow in the longshore di- 
rection is complicated by other tank width effects. There are critical 
wavelengths for each tank width which can generate tank oscillations or 
unique circulation patterns (see Sec. II). Cross waves were observed 
over a limited segment of the profile for a short period of time in ex- 
periment 72B-06 (Vol. VII), but neither the cross waves nor their effect 
on the profile were measured. Transverse waves were observed and meas- 
ured throughout experiment 72B-10 (Vol. VII) and their effect on the 
profile determined. Circulation currents between the antinodes of the 
standing wave, along with their effects, were measured in experiment 
72A-06 (Vol. VI). These three special cases of tank width effects are 
assumed to produce special effects on the sand beds. Tank width effects 
in all 10 experiments from lowest to highest wave period tested are 
discussed below. 


a. 1.50-Second Wave (L/W = 1.03, Experiment 72C-10). The foreshore 


and inshore zones had significant lateral variations. The shoreline sta- 
tion along the five ranges varied as much as 2.5 feet (0.76 meter) at any 
given time (Fig. 35). Specific instances of this variation are illustra- 
ted by the two photos in Figure 36. At 50 hours (Fig. 36,a) the shore- 
line and scarp on the near side (ranges 1 and 3) are farther landward 
than the shoreline along the far side (ranges 7 and 9). At this time 

the backshore, was apparently eroding along ranges 1 and 3, and the sand 
moved alongshore to range 7 where it caused the shoreline to protrude 
into the inshore zone. At 85 hours (Fig. 36,b) the scarp was uniform in 
position across the tank, but the position of the shoreline was seaward- 
most on the near side (range 1) and landwardmost in the middle (range 5). 
At this time the backshore was apparently eroding in the middle of the 
tank, and the sand moved alongshore to range 1 where it moved out into 
the inshore zone. At other times the erosion of the backshore occurred 
only along ranges 7 and 9 and the sand was transported alongshore to 
range 1 before moving into the inshore. 


Considerable lateral variation also occurred in the inshore zone of 
this experiment (Fig. 37 compares movements of the -0.3-, -0.4-, -0.5-, 
-0.7-, and -0.8-foot (-9.1, -12.2, -15.2, -21.3, and -24.4 centimeters) 
contours). The lateral variations were particularly great just below the 
foreshore (elevation -0.3 foot) and the amount of variation decreased 
moving in the seaward direction. No lateral variation occurred in the 
offshore zone (Fig. 38 compares movements of the -0.9-, -1.4-, and 
-1.9-foot (-27.4, -42.7, and -57.9 centimeters) contours). Erosion of 
a trough near station 10 started first along the tank walls and pro- 
' gressed toward the center (discussed in Vol. V). 


The three dimensionality of the profile shape is shown in Figure 39, 
which is a contour map of the sand bed at the end of the experiment. 
The foreshore and offshore topographies are skewed in the same direction 
and the inshore topography is approximately symmetric about the tank 
centerlines. The symmetric development of the inshore is illustrated by 
the depressions along the tank walls near stations 3 and 13. The tank 
walls obviously constrained the shape that did develop, but that shape 
does have a significant variation in the third (longshore) dimension. 


80 


Distance from Original SWL Intercept (ft) 


0 50 100 150 200 


Cumulative Time (hr) 


Figure 35. Shoreline movement of five ranges in 
experiment 72C-10 (L/W = 1.03). 


8| 


a : oo a a S ae i 
b. At 8S hr Figure 36. Foreshore variability over 35-hour period 
in experiment 72C-10 (L/W = 1.03). 


82 


-0.5-ft Contour 


0.0 


Distance from Original SWL Intercept (ft) 


-0.8-ft Contour 


150 


100 
Cumulative Time (hr) 


Figure 37. Lateral variations in movement 
of inshore zone contours in 
experiment 72C-10 (L/W = 1.03). 


83 


5.0 


-0.9-ff Contour 
20.0 


-|.4-ff Contour 


Distance from Original SWL Intercept (ft) 


oO: 50 100 150 
Cumulative Time (hr) 
Figure 38. Lack of lateral variations in movement of offshore 
zone contours in experiment 72C-10 (L/W = 1.03). 


84 


Seawardmost position 

of each contour 

Other more landward 
positions of a given 
contour SSS => 


Distance from Original SWL Intercept (ft) 


Figure 39. Profile shape at end (140 hours) of 
experiment 72C-10 (L/W = 1.03). 


85 


b. 1.90-Second Wave. 


(1) L/W = 1.43 (Experiments 70X-10 and 71Y-10). Although the 


foreshore had some lateral variations, the inshore zones had greater 
lateral variations, particularly in the development of the flat shelf in 
the inshore in experiments 70X-10 and 71Y-10, the experiments with the 
next highest value of L/W. 


In both experiments with L/W = 1.43, the slope of the foreshore and 
position of the shoreline varied with range at any one time and with time 
at any one range. The slope varied from 0.04 to 0.60 in experiment 70X-10 
and from 0.08 to 0.56 in experiment 71Y-10. The shoreline position at any 
one time varied up to 1.6 feet (48.8 centimeters) in experiment 70X-10 and 
2.0 feet in experiment 71Y-10 (Fig. 40) (compared to up to 2.5 feet with 
L/W = 1.03). The most important profile change in all of the experiments 
with the 1.90-second wave was the development of the long flat shelf with- 
in the inshore zone. In experiment 70X-10 the shelf development began at 
15 hours along range 1 and at 95 hours along range 9, as indicated by the 
initial upward movements of the -0.6-foot contour positions in Figure 41. 
In experiment 71Y-10 (Fig. 41) the shelf development began at 210 hours 
along range 1 and 110 hours along range 9. The 80-hour difference in 
experiment 70X-10 and the 100-hour difference in experiment 71Y-10 are 
significant--that this variation occurred in both experiments in the 
same tank and that the development started on one side in one experiment 
and on the other side in the other experiment indicates that the varia- 
tion was not due to a unique external influence or some misalinement in 
the tank. 


The three dimensionality of the profile shape at the end of the ex- 
periments is shown in Figure 42. The offshore zones are skewed seaward 
along ranges 7 and 9 in both experiments, just as in experiment 72C-10. 


(2) L/W = 2.38 (Experiments 70X-06, 71Y-06, and 72D-06). In 


three experiments with a 1.90-second wave conducted in the narrower tank, 
the profile shape usually had less lateral variation, as would be expected 
from the higher value of L/W. 


In these experiments, lateral variations in slope and position oc- 
curred on the foreshore. The foreshore slope varied from 0.10 to 0.36 
in experiment 70X-06, from 0.08 to 0.52 in experiment 71Y-06, and from 
0.02 to 0.50 in experiment 72D-06 (the experiment with a 0.05 initial 
slope). The shoreline position varied as much as 2.0 feet in experiment 
70X-06, 2.3 feet (70.1 centimeters) in experiment 71Y-06, and 1.9 feet in 
experiment 72D-06 (Fig. 43). The foreshore variations are not less than 
those with L/W = 1.43 (compare Fig. 43 with Fig. 40), especially since 
the tank was narrower. 


The inshore in experiment 70X-06 developed the flat shelf with little 
lateral variation in time of development, but after the shelf developed 
lateral variations occurred, as indicated by the -0.6-foot contour move- 
ments in Figure 44. The same holds for experiment 71Y-06 (Fig. 44). In 


86 


\ 
oO 


Distance from Original SWL Intercept ( ft ) 


) 


Figure 40. 


50 


100 


0.0 Contour 


150 200 
Cumulative Time (hr) 


250 


Shoreline movement in experiments 
(L/W = 1.43). 


87 


300 350 


70X-10 and 71Y-10 


-0.6-ft Contour 


Range 


mo (o) wo 1S) 
(44) sdaosajyuT TMS jOUIH14Q wos 


a2UD}SIQ 


10 


OM 


15 


300 350 


250 


50 


Cumulative Time(hr) 


Comparison of the movements of the -0.6-foot contour in 


experiments 70X-10 and 71Y-10 (L/W 
Figure 37. 


Figure 41. 


Compare with 


LAS) 6 


88 


70x-10 71 Y-10 
(after 335 hr) 
eenfashee ent 


(after 210 hr) 
1 \ 


=||Ornmy =|| (0) 


0.2 ft 
0.0 


-0.2 
-0.4 


-0.6 
=(0),7/ 


Distance from Original SWL Intercept (ft) 
Distance from Original SWL Intercept (ft) 


Seawardmost position 


of each contour 
Other more landward 
positions of a given 
contour SRSo => 


I 1 1 ' 1 
ae JS 1D Tighe) I So 08 


Figure 42. Profile shape at end of experiments 70X-10 and 71Y-10 
(L/W = 1.43). Compare with Figure 39. 


89 


Distance from Original SWL Intercept (ft) 


So u 


fe) 


( 
ao om 


(0) 50 100 150 200 250 300 350 400 
Cumulative Time (hr) 


Figure 43. Shoreline movement in experiments 70X-06, 71Y-06, 
and 72D-06 (L/W = 2.38). Compare with Figure 40. 


90 


—0.6-ft Contour 


Range 
1 
3—: — 
—— 


Distance from Original SWL Intercept (ft) 


(0) 50 100 150 200 250 300 350 400 
Cumulative Time (hr) 


Figure 44. Comparison of the -0.6-foot contour 
movements in experiments 70X-06, 71Y-06, 
and 72D-06 (L/W = 2.38). Compare with 
Figure 41. 


9I 


experiment 72D-06 the flat inshore developed quickly and then a large 
trough was scoured at the shoreward end of the inshore. In contrast to 
experiments 70X-06 and 71Y-06, the lateral variations in the position of 
the -0.6-foot contour in experiment 72D-06 (Fig. 44) occurred while the 
inshore was a flat shelf, perhaps because of the differences in initial 
slope. 


Contour maps of the final profile shape for the three experiments are 
in Figure 45, The profile shape obviously varied laterally, particularly 
in the foreshore and inshore, but in the offshore zone the variations 
were less than in the wider tank. 


c. 2.35-Second Wave. 


(1) L/W = 1.86 (Experiment 72B-10). In experiment 72B-10, the 


L/W ratio was less than the three experiments in the 6-foot tank with 
the shorter 1.90-second wave. The profile in this experiment was affec- 
ted by the transverse wave, generated by the gap at the end of the gene- 
rator blade. Thus, the width effects identified here are the result of 
the "generator gap effect," which is another special case of width 
effects. 


The foreshore slope and position varied laterally and with time, as 
a result of the three-dimensional swash movement. The slope varied from 
0.10 to 0.54. During the first 100 hours and between 130 and 150 hours, 
the shoreline position was skewed across the tank, with up to a 1.2-foot 
difference in shoreline position between range 1 (seawardmost) and range 
9 (landwardmost) (Fig. 46). Between 100 and 130 hours the shoreline 
position was not skewed. 


In the inshore a longshore bar developed near station 2 and later 
eroded, and a flat area developed near station 5 and later developed into 
a bar. The above changes occurred at different times along each range, 
as shown by the variation in movement of the different contours in Figure 
47, and as discussed in Volume VII. 


Flat areas developed in the offshore zone near stations 8 and 16, but 
in each case the elevation of this flat area increased from the range 1 
side to the range 9 side. Sand deposited at the toe of the slope along 
ranges 1 and 3, but not along ranges 5, 7, and 9. The lateral variation 
of contours in each of the three areas is shown in Figure 48. 


The final profile shape is shown in Figure 49 with lateral variations 
in the areas discussed above. 


(2) L/W = 3.10 (Experiment 72B-06). In experiment 72B-06 the 
lateral variations in profile shape were minimal. The foreshore slope 
varied from 0.10 to 0.46 as a result of lateral variations in swash move- 
ment, but the shoreline position varied as much as 0.5 foot only once and 
was generally uniform (Fig. 50). 


Je 


70X-06 71 Y-06 72D-06 
(after 175 hr) (after 375 hr) (after 180 hr) 
-20;-, I | -20 


-5 
Ltt | ort 
——— | 00 


Seawardmost position a -0.2 
of each contour Sie eeess -03 
= Other more landward Cee aE 
Irs) positions of a given 0 fesreeesy |L gig 
contour SS SR eEe -0.6 
©-0.7 
*~---2 -0.8 
=| -10 Ss) Se pene ay 
e nee ~2 ||-).2 
Spee 
SS oS oes Sees - 1.3 
oa = STOR. eins 
o~ SA fe) 
_— ~S a NS 
SS = @ ee = 3 
oO o L ee) 
uu — > od 
@ ® = = [ke 
c c SSeS hee ME 
= ae ee 
a) =I Sem—ale| 
= — 
a a 2 aS.) - 1.0 
S S ° 55 | 1.0 
e c e 207. 
ic. > el hay Sees (ae 
S 3 S ~0.9 
E E We aca 
S S Sys 5 Eee 
= = os if “> |-0.8 
@ @ @ va 
c c = ~~~ 
S) 2 2 
2 2 © 30 
a ron) (an) 
i -0.8 
oe = 1.0 aaa 
—>— ]-1.2 ees 
OEE ae 
Se | 4 
20; aes |= 16 39 pee CO 
o—_-——- |- 1.8 —__, Bike 
—-— |-2.0Ft Ceaeain| i 
ToS o—-——- |- 1.4 
See |G 
o—-—_ 
— —~ |-2.0ft 
C= as 
I I I I i 4 \ I I 
Som 3.5 eae esis ale os 
Range Range Range 


Figure 45. Profile shape at end of experiments 70X-06, 71Y-06, and 
72D-06 (L/W = 2.38). Compare with Figure 42. 


93 


oO 50 100 150 
Cumulative Time (hr) 


Distance from Original SWL Intercept (ft) 


Figure 46. Shoreline movement in experiment 72B-10 
(L/W = 1.86). Compare with Figure 40. 


94 


Range 


-0.5-ft Contour rer 


Distance from Original SWL Intercept (ft) 


re) 50 100 150 
Cumulative Time (hr) 


Figure 47. Lateral variations in the movements of 
inshore zone contours in experiment 72B-10 
(L/W = 1.86). Compare with Figure 41. 


95 


-|.0-ft Contour 


-|,5-ft Contour 


Distance from Original SWL Intercept (ft) 
oO 


O 50 100 150 
Cumulative Time (hr) 


Figure 48. Lateral variations in the movements of off- 
shore zone contours in experiment 72B-10 
(L/W = 1.86). Compare with Figure 38. 


96 


Distance from Original SWL Intercept (ft) 


25 Seawardmost position 
of each contour 
Other more landward 
positions of a given 
contour SS 


Range 


Figure 49. Profile shape at end (150 hours) of experiment 
72B-10 (L/W = 1.86). Compare with Figure 42. 


Sil 


Distance from Original SWL Intercept (ft) 


Figure 50. 


50 100 150 
Cumulative Time (hr) 


Shoreline movement in experiment 
72B-06 (L/W = 3.10). Compare 
with Figure 43. 


98 


In the inshore, little significant lateral variation occurred at 
elevations -0.4, -0.5, and -0.6 foot; only a random variation in the 
times at which the longshore bar crest reached elevation -0.3 foot 
(aig, Sil). 


Large lateral variations occurred in position of particular contours 
in the offshore (Fig. 52), indicating that the crest elevation of the 
seaward bar reached -2.0 feet at different times, but the variations had 
no pattern. 


At the end of the experiment the only significant lateral variation 
was the slope of the foreshore (Fig. 53). 


d. 3.75-Second Wave. 


(1) L/W = 3.14 (Experiment 72A-10). Experiment 72A-10 had a 


longer wavelength in a wider tank than experiment 72B-06 discussed above, 
with the result that the L/W ratio was nearly the same (3.14 versus 
3.10). As expected, this experiment also had little significant lateral 
variation. 


The foreshore slope was steeper along the middle ranges (3, 5, and 
7), varying from 0.14 to 0.36 with an average of 0.20, and flatter along 
the outside ranges (1 and 9), varying from 0.12 to 0.30 with an average 
of 0.18. The shoreline position varied laterally during the first 25 
hours as it prograded first along the outside ranges (Fig. 54). Between 
30 and 50 hours the shoreline position also varied laterally. At other 
times the shoreline position was quite uniform. 


The only lateral variations in the offshore zone were differences in 
the bar-crest elevation along the different ranges (Fig. 55), but this 
was a fairly minor variation in elevation. 


A contour map of the profile at the end of the experiment in Figure 
56 shows how little the lateral variations were. 


(2) L/W = 5.23 (Experiment 72A-06). In experiment 72A-06, with 


the highest L/W value, the lateral variations in profile shape were 
quite large, contrary to what was expected. 


In the foreshore, a strong counterclockwise circulation caused the 
foreshore slope to be steeper (0.20) along range 5 and flatter (0.12) 
along range 1, but only at 115 hours was there a large (1.3 feet) lateral 
difference in shoreline position (Fig. 57). 


In the inner offshore zone, a clockwise circulation developed between 
the antinodes in the foreshore and near station 18 during the first 70 
hours, and then began disintegrating. The wavelength in this area was 
approximately 24 feet (7.3 meters), or four times the tank width, which 
suggests that the circulation was the result of some resonance unique to 
a laboratory wave tank. This is apparently another special tank width 


99 


Distance from Original SWL Intercept (ft) 


—0.3-ft Contour 


—0.4-ft Contour —— 


=O." Comrour 


Cc 
Figure 51. 


—0.6-Contour 


50 100 150 
umulative Time (hr) 


Comparison of the movements of inshore 
zone contours in experiment 72B-06 
(L/W = 3.10). Compare with Figure 44. 


100 


Distance from Original SWL Intercept (ff) 


—2.0-ft Contour 


r) 50 100 150 
Cumulative Time (hn 


Figure 52. Comparison of the movements of offshore 
zone contours in experiment 72B-06 
(L/W = 3.10). Compare with Figure 48. 


101 


Distance from Original SWL Intercept ( ft) 
S) 


20 


25 


30 


Figure 53. 


eo———_.—___ 
cot henner cece), OJ6itt 
Ne co || OG 
Ei eee 0.6 
—— 0.4 
Ee 0.2 
o—__.,— 
— 0.0 
SSS 
Le -0.2 
ae SSS 
oa lll ees - 0.4 
eZ - 0.6 
—__._ 
a ee 
Sess 116 
o—___.— ~*~ 
or - 1.2 
Ce ee 
o_o 1.4 
— 
~ 1.8 
——___ 
Verne -2.0 
ae (ors |e Bw 
{ 
Re 
oN [= 2.0 
+- [-2.0 
— -2.0 
~ |-2.2 ft 


Seawardmost position 
of each contour 

! Other more landward 
| 3 2) positions of a given 
Range contour 


Profile shape at end (150 hours ) 
of experiment 72B-06 (L/W = 3.10). 
Compare with Figure 45. 


102 


(9) 50 100 150 
Cumulative Time (hr) 


Distance from Original SWL Intercept { ft) 


Figure 54. Shoreline movement in experiment 
72A-10 (L/W = 3.14). Compare 
with Figure 50. 


103 


Figure 55. 


Distance from Original SWL Intercept (ft) 


—|.0-ft Contour 


ao 
(one) 


10.0 


15.0 — |.l- ft Contour 
LE Poe ee A ee ee oe Se 
0) 50 100 150 


Cumulative Time (hr) 


Comparison of the movements of offshore zone contours in 
experiment 72A-10 (L/W = 3.14). Compare with Figure, 51. 


104 


Seawardmost position 

of each contour 

Other more landward 
positions of a given 
contour SSCS 


\ 
oO 
° 


SF 
— aS SSS ned 
= ey I Oe 
= eT 
a 
ee) pe 
c “TT en sue, MOI 
3j i agape EEOC -0.4 
= -0.6 
a -0.8 
So fs) === ——— Soe =/.0 
c ©“ Saas Sr eeea Ste -1.1 
rs Cpe ee ee ey -1.2 
= -1.4 %/ =O —}55) 

Ee ae -@-~~~e----2 =| - 1.3 

) 2) 

E Woe alee 
e Oran Gage eS 1S lel 
o 10 _o-8---- 
c ti 
° oO — (<0) 
@ wv 
(an) fe ee ee = || 


2Of ee 


Range 
Figure 56. Profile shape at end (80 hours) of experiment 
72A-10 (L/W =*3.14). Compare with Figure 51. 


105 


Q 
n 


Nn 
(eo) 


50 100 150 
Cumulative Time (hr) 


Distance from Original SWL Intercept ( ft) 
eo} 


Figure 57. Shoreline movement in experiment 
72A-06 (L/W = 5.23). Compare 
with Figure 54. 


106 


effect, since this effect was not seen for this wavelength in the wider 
tank. Lateral variations in the position of contours in the inner off- 
shore are shown in Figure 58. 


Lateral variations at the toe of the profile are shown in Figure 59, 
which compares the movement of selected contours, and in Figure 60, which 
is a contour map of the final profile. 


4. Water Temperature Effects. 


a. Processes. Since the 10 LEBS experiments were conducted in an 
outdoor basin, water temperature was an uncontrolled variable, varyin 
from 4° to 31° Celsius, the dynamic viscosity varying from 3.30 x 107 
to 1.64 x 107° pounds-second per square foot (1.61 x 10°23 go O80 8 107° 
grams-second per square centimeter) (Daily and Harleman, 1966). Vis- 
cosity is known to affect the fall velocity of sediment particles in 
settling tubes: as the viscosity of water increases, the fall velocity 
decreases (see Fig. 4-31 in U.S. Army, Corps of Engineers, Coastal Engi- 
neering Research Center, 1977). Since viscosity has been shown to have 
several effects on sediment transport in unidirectional flow (American 
Society of Civil Engineers, 1975), it is likely that water temperature 
and viscosity would affect sediment suspension and transport in oscilla- 
tory flow. For example, the erosion of beaches in the winter months may 
not be the result of increased wave steepness alone, but perhaps due to 
the decrease in water temperature as well. 


A greater knowledge of temperature-viscosity effects on sediment 
transport in oscillatory flow is needed for at least three purposes: 
(a) to understand the effects of temperature on erosion and accretion 
in nature, (b) to understand the scale effects in the laboratory when 
relating laboratory results obtained with one temperature history to _ 
prototype localities with another temperature history, and (c) to under- 
stand the laboratory effects when attempting to compare results from a 
series of research experiments with one another when the water tempera- 
ture was not controlled. The lack of knowledge on this last point has 
made it difficult to prove that the lack of profile equilibrium in 
several of these experiments was not due to a constantly decreasing 
water temperature. 


The important effects of temperature-viscosity on sediment transport in 
unidirectional flow and the results on the effect of temperature-viscosity 
on shoreline recession and profile development in the LEBS experiments are 
discussed below. 


b. Literature Review--Unidirectional Flow. Colby and Scott (1965) 
found three effects of water temperature on sediment discharge: (a) Vis- 
cosity changes cause changes in the thickness of the laminar sublayer 
which affect the relationship between mean velocity and effective bed 
shear. (b) The vertical distribution of suspended sediment depends on 
the ratio between the fall velocity of sediment particles in a turbulent 
sediment-water mixture and the effective turbulence of the flow for sus- 


107 


6.0 


10.0 


15.0 


15.0 


200 -I.l-ft Contour 


Distance from Original SWL Intercept (ft) 


20.0 =|,.2- ft Contour 


-1.3—ft Contour 


0 60 100 150 
Cumulotive Time (hr) 
Figure 58. Comparison of the movements of 
upper offshore zone contours in 
experiment 72A-06 (L/W = 5.23). 
Compare with Figure 55. 


108 


20 


ine) 
(6) 


~ 
fe) 


SWL Intercept (ft) 


25 


—2.2-ft Contour 


Os 
(o) 


i) 
(2) 


Distance from Original 


—2.3- ft Contour 


O 50 100 150 
Cumulative Time (hr) 


Figure 59. Comparison of the movements of lower off- 
shore zone contours in experiment 72A-06 
(L/W = 5.23). Compare with Figure 52. 


109 


“15 I | i 


1.0 ft 


9 
@ 


i] 
29 S999000 
QP aAaNONSA 


= fa 

= = 

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iy 

4 

w 

io. 

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ae 

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— 

o -1.4 

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ee 

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25 ; 
AA -. -2.2 
Sess -2.2 ft 
- _»” 


Seawardmost pesition 
— of each contour 


30 Other more landward 
positions of a given 
contour PROS = 

351 \ I 

Pos) 78 
Range 


Figure 60. Profile shape at end (135 hours) of experiment 
72A-06 (L/W = 5.23). Compare with Figure 56. 


110 


pending sediment. The effective turbulence of the flow is evidently not 
affected by viscosity changes, but the fall velocity of sand in turbulent 
water (nearly the same as the fall velocity in still water) is directly 
related to viscosity. The temperature effect is greatest for particle 
sizes between 0.25 and 0.5 millimeter and next greatest for the 0.125- 

to 0.25-millimeter range, and the effect increased with increasing depth. 
(The sediment used in the LEBS experiments had a ds5g of 0.22 to 0.23 
millimeter.) (c) Changes in viscosity affected the fall velocity which 
changed the ds5q of the bedload and thus the bed forms. (The size dis- 
tribution of the SPTB sand was narrow, so this effect would be negligible. 
Changes in bed form change the resistance to flow and thus the sediment 
discharge. Temperature effects in both directions were found; i.e., 
sediment discharge both increased and decreased with increasing tempera- 
ture. 


Taylor and Vanoni (1972a, 1972b) examined temperature effects in both 
low- and high-transport flows, and they also found temperature effects in 
both directions in each case. 


For low-transport flow, Taylor and Vanoni found that the direction of 
the effect was related to position on the Shields curve (Fig. 2.45 in 
American Society of Civil Engineers, 1975; shear stress versus boundary 
Reynolds number) where the Shields curve slopes down, increasing tempera- 
ture caused increasing sediment discharge; where the Shields curve slopes 
up, increasing temperature caused decreasing sediment discharge; and where 
the Shields curve is flat, increasing temperature caused no change in 
discharge. 


For high-transport flows, they found that the effect was related to 
particle size: for the particles finer than 0.135 millimeter, suspended- 
sediment concentrations at all depths increased with increasing tempera- 
ture; for particles coarser than 0.135 millimeter, the concentrations at 
all depths decreased with increasing temperature; but for particles with 
a ds59 of 0.135 millimeter, concentrations at the higher elevations 
increased with increasing temperature and at the lower elevations 
decreased with increasing temperature. 


c. LEBS Results--Oscillatory Flow. Those results for unidirectional 
flow point out the complexity of the temperature effect, so it is not un- 
reasonable to expect a complex temperature-viscosity effect on sediment 
transport in oscillatory flow. These experiments were obviously not 
designed to study temperature effects since temperature was uncontrolled, 
but they do indicate the potential for temperature effects. Temperature 
changes are compared to the shoreline recession rate and volume erosion 
rate in the discussions that follow. Because the backshore slope was 
not flat the volume erosion and profile development rates were propor- 
tional to the square of the shoreline recession rate in these tests. 


(1) 1.50-Second Wave. In experiment 72C-10 (Fig. 61) the shore- 
line recession rate was decreasing, which means that the volume erosion 
rate was decreasing or near constant, while the temperature was gradually 
falling. 


A 


Distance from original SWL intercept (f+) 


Figure 61. 


20 


ecco 


Range Water )) 
Temperature 


50 100 150 
Cumulative Time (hr) 


Comparison of daily mean water 
temperatures and shoreline 
positions in experiment 72C-10. 


ll2 


Temperature (°C) 


(2) 1.90-Second Wave. The most dramatic evidence for a tempera- 
ture effect was in experiment 70X-06. At 22 hours the water temperature 
dropped from 28° to 18° Celsius and the shoreline recession rate increas- 
ed from 0.06 to 0.14 foot per hour (Fig. 62,a). (After sand feeding was 
begun the experiments had little value to this analysis.) In experiment 
70X-10 (Fig. 62,b) temperature data collection did not begin until 38 
hours and the comparison of shoreline recession and temperature between 
38 and 62 hours is not very conclusive. The temperature was fairly high 
(25° to 30° Celsius) and the shoreline recession rate was 0.08 foot per 
hour. 


In experiments 71Y-06 and 71Y-10 (Fig. 63) the shoreline recession 
rates were high during the first few hours (0.113 foot per hour in ex- 
periment 71Y-06 and 0.133 foot per hour in experiment 71Y-10). However, 
the shoreline recession rate soon decreased to 0.025 foot per hour in 
experiment 71Y-06 and 0.016 foot per hour in experiment 71Y-10, although 
the temperature remained at a high value. The recession rate remained 
constant throughout the remainder of the experiments, even though the 
temperature dropped sharply several times, which tends to disprove the 
effect suggested by experiment 70X-06. However, the mutual agreement 
between experiments 70X-06 and 71Y-06 is important. Between 10 and 50 
hours the recession rate was quite high in experiment 70X-06 while the 
temperature dropped and the recession rate was much lower in experiment 
71Y-06 while the temperature remained high. 


In experiment 72D-06 the shoreline retreated at a rate of 0.05 foot 
per hour, which means that the volume rate of erosion was continually 
increasing, while the temperature decreased from 20° to 6° Celsius (Fig. 
64). The erosion of the trough in the inshore zone after the shoreline 
recession stopped occurred when the temperature was at its lowest values. 


(3) 2.35-Second Wave. In experiment 72B-06 (Fig. 65,a) the 
shoreline was stable and the profile was at equilibrium, even though the 
temperature took two 8° drops. In experiment 72B-10 (Eig; (65), b)) the 
shoreline retreated at a very slow rate, which varied between 0.004 and 
0.018 foot (0.12 and 0.55 centimeter) per hour, while the temperature 
varied between 30° and 20° Celsius, with drops of 5° and 9°. Compared 
to the 1.90-second experiments (Figs. 62, 63, and 64), the temperature 
remained fairly high and the recession rate was small. 


(4) 3.75-Second Wave. In experiment 72A-06 (Fig. 66,a) the 
shoreline recession rate was constant, meaning that the volume erosion 
rate was increasing, while the water temperature increased. In experi- 
ment 72A-10 (Fig. 66,b) the shoreline was stable as the profile was at 
or near equilibrium and the temperature rose initially and then remained 
fairly constant. 


(5) Discussion. Experiment 70X-06 supports the hypothesis that 
decreasing water temperature causes increasing erosion. Although the 
shoreline recession rate did not respond to sharp drops in temperature 
in experiments 71Y-06, 71Y-10, 72D-06, 72B-06, and 72B-10, the comparison 
of those experiments with 70X-06 supports the general hypothesis that the 


113 


Distance from Original SWL Intercept (ft) 


1 


Sand feeding 
begun 


fan 
/ | Water Temperature 


50 100 


Cumulative Time (hr) 


a. Experiment 7OX—06 


50 100 
b. Experiment 7O0X—10 


Figure 62. 


150 


150 


30 
RANGE 
— 
03—-— 


(See 
? 20 


0 
200 290 


200 250 


Comparison of daily mean water temperatures and 
shoreline positions in experiments 70X-06 and 70X-10. 


114 


Temperature (°C) 


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Water Temperature 


ZN 
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Shoreline Position 


Distance from Original SWL Intercept (ft) 
ro) 


(6) 50 100 150 200 
Cumulative Time (hr) 


Figure 64. Comparison of daily mean water temperatures 


Temperature (°C) 


and shoreline positions in experiment 72D-06. 


116 


35 


T 
(43) 4dadsaju} 


(O-) eunyosedwa, 
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100 


50 
Cumulative Time (hr) 


a. Experiment 72B—-06 


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b. Experiment 72B—10 


Comparison of daily mean water tempera- 


tures and shoreline positions in 
experiments 72B-06 and 72B-10. 


Figure 65. 


UI 


a i Temperature 
(So) 9 | 
2 |:72A-06 © 
S 8 ~— 
= (One 
2 10 50 100 150 2 
S Cumulative Time (hr) = 
= a 
ic E 
5 30° 
E ® 
= 3 
= = 
@ 
[S) 
(= 
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w 20 
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10 
O 50 100 150 


Cumulative Time (hr) 


Figure 66. Comparison of daily mean water tempera- 
tures and shoreline positions in 
experiments 72A-06 and 72A-10. 


118 


higher the temperature the lower the recession rate. Too little useful 
data are available in experiment 70X-10 to be of any value to the com- 
parison. 


Experiment 72A-06 supports the opposite hypothesis that an increasing 
water temperature causes an increasing erosion. Experiment 72C-10 sup- 
ports this hypothesis or perhaps tends to disprove the other hypothesis 
in that a decreasing water temperature coincided with a decreasing ero- 
sion rate. 


Experiment 72A-10 supports either hypothesis since the temperature 
and the shoreline were both stable. 


5. Other Laboratory Effects. 


The known causes of laboratory effects are summarized in Table 14, 
classified by physical constraint and by phenomena or parameter affected. 
The effects of re-reflection, wavelength-to-tank width ratio, transverse 
waves, and circulation between antinodes were discussed earlier in this 
section. Secondary waves were observed on the wave records and their 
effect in a few of the experiments was discussed. Hulsbergen (1974) 
provides a detailed description of the effects of secondary waves on 
profile shape. Water temperature was measured and some of the possible 
effects of changing viscosity were measured, but the results are incon- 
clusive. Cross waves were observed for a short period of time but their 
effect could not be measured. 


Four other phenomena can cause laboratory effects, depending on the 
physical constraints of the individual experiment or facility designs. 


When conducting experiments in a wave basin with training walls and 
with the waves approaching the shoreline obliquely, the waves reflected 
from the profile can re-reflect from the down-drift sidewall, then from 
the generator, from the up-drift sidewall, and then reattack the profile 
from an entirely different angle. In similar experiments without train- 
ing walls, re-reflection problems are minimal but diffraction effects 
and basin resonance become significant sources of variations. Fairchild 
(1970b) discussed these three interrelated phenomena and their effects. 


Another effect is the difference between a profile shaped by mono- 
chromatic waves and a profile shaped by irregular waves. Watts (1954) 
and Watts and Dearduff (1954) examined the effect of varying wave period 
and water level. The effect of periodic waves could be examined by 
repeating these experiments with a set of irregular waves having the 
same energy density. 


V. CONCLUSIONS 
1. Wave Height Variability. 
(a) Variation in reflection from the profile was found to be the 


major source of wave height variability in 10 movable-bed experiments. 
The varying phase difference between the wave re-reflected from the 


119 


Table 14. 
Physical constraint 


. Tank length 


a. Distance to initial SWL 
intercept 


b. Initial profile slope 


. Tank width 


. Water temperature 


. Wave basin (waves approaching 
obliquely with training walls) 


. Wave basin (waves approaching 
obliquely without training 
walls) 


. Periodic wave 


Known laboratory effects. 


Phenomenon or parameter affected 


Ile 


Bo 


n wm SF WW 


10. 


Tate 


Secondary waves from generator 
motion! 


Re-reflection from wave 
generator? 


Wavelength-to-tank width ratio“ 


Transverse waves2 


Cross waves? 


Circulation between antinodes 
of standing wave? 


. Viscosity! 


. Sidewall re-reflection 


. Diffraction 


Basin resonance 


Simulation of real waves 


lPhenomenon observed and effects measured to a limited extent in LEBS 


study. 


2Phenomenon observed and effects measured. 


3Phenomenon observed, but effects not measured. 


generator and the generator motion caused a varying average incident 
wave height. Transverse, cross, and secondary waves also contributed 
to the spatial variability of the incident wave height. 


(b) The reflection coefficient variation ranged from moderate to 
significant in the movable-bed tanks, ranging from 0.02 to 0.12 in ex- 
periment 72C-10 and from 0.04 to 0.27 in experiment 72D-06. In the 
fixed-bed tanks, which is an indication of the measurement accuracy 
in the movable-bed tanks, Kp ranged from 0.01 to 0.02 in experiment 
72C-10 and from 0.02 to 0.09 in experiment 72B-10. 


(c) Waves are reflected by the runup on the foreshore, a plunging- 
type breaker, and any segment of the submerged profile where the depth 
change is Significant. Variations in the steepness and top elevation 
of any submerged siope can cause significant variations in Kp. The 
distance between two reflecting zones can affect the phase difference 
between waves reflected from the two zones and thus affect the Kp 
measurement seaward of the profile. The important source of Kp vari- 
ability in any one experiment did not appear to be a function of the 
wave period. The steepness of the submerged slope was an important 
source of variability in all experiments except 72A-10, and the increas- 
ing foreshore berm elevation was the primary source of variability in 
only experiment 72A-10. Variations in the elevations of the top of the 
submerged slope caused significant Kp variability in experiments 71Y-06, 
72D-06, and 72A-06. The increasing distance between the foreshore and 
submerged slopes caused some Kp variability in all experiments with the 
1.90-second wave and was the primary source in experiment 72C-10 with the 
1.50-second wave. As the shelf length varied in each experiment, the Kp 
varied correspondingly. 


(d) The average K, from profiles which developed from an initial 
0.10 slope increased with increasing wavelength (or wave period). 


(e) The average K, of the 1.90-second wave increased, rather than 
decreased, as the initial profile steepness decreased. 


(f) Reflection coefficient variation was less than 0.05 during the 
last 25 hours of the three experiments which appeared to be at or very 
near equilibrium, but this does not conclusively prove that K, varia- 


bility is eliminated on an equilibrium profile. 


(g) In all experiments except 72C-10 the K, tended to increase 
during the experiment indicating that the profile adjustment tended 
toward reflecting, rather than absorbing, energy. 


(h) Incident wave height, H;, measurements in the fixed-bed tanks 
were indicative of the measurement errors in the movable-bed tank. H 
range in the fixed-bed tanks was as little as 0.03 foot in five experi- 
ments, and as much as 0.07 foot in experiment 72A-06. 


(1) The effect of varying re-reflection on the incident wave height 
in each experiment was calculated by subtracting the range of heights in 


I2| 


the fixed-bed tanks from the range of heights in the movable-bed tanks. 
In the 6-foot tank, this effect ranged from 0.01 foot in experiment 
72B-06 to 0.03 foot in the other four experiments. In the 10-foot tank, 
this effect ranged from 0 in experiment 72B-10 to 0.08 foot in experiment 
72A-10. This implies that the wider tank may amplify this re-reflection 
effect. 


(j) The importance of phase difference between the reflected wave and 
the generator motion to the incident wave height variability is seen best 
by comparing experiments 72B-06 and 72B-10. The average Kp in experi- 
ment 72B-06 was 0.08 and in experiment 72B-10 was 0.17, which means that 
the reflected wave height was greater in the 10-foot tank. However, the 
average incident wave height was 0.38 foot in 72B-06 and only 0.31 foot 
in experiment 72B-10. Since the difference in reflected wave height 
would not have caused that difference, only the phase-difference effect 
resulting from the difference in initial test length can account for the 
difference. 


2. Profile Equilibrium. 


(a) In two experiments with all parameters the same except the 
initial slope (0.05 and 0.10), the final profiles had quite different 
slopes, although neither reached equilibrium. This further verifies the 
conclusion of Collins and Chesnutt (1975, 1976) that the initial profile 
influences the final stable profile shape. 


(b) In two pairs of experiments with the same wave condition but 
different tank width and initial test length, one experiment in each 
pair reached equilibrium; the other experiment in each pair developed a 
different shape which continued to adjust. Laboratory effects are the 
apparent causes for the differences. 


(c) Profile equilibrium is not easily attained. Two of four summer 
profiles and the one winter profile reached equilibrium, but none of the 
five profiles in the transition category (0.020 < H,/L, < 0.025) reached 
equilibrium, indicating that profiles for waves in the transition region 
are more unstable. 


3. Laboratory Effects. 


(a) The initial profile slope affects the profile development at 
least partially as a result of differences in the phase of secondary 
waves at the toe of the profile. 


(b) The initial distance from the generator to the shoreline is an 
important experimental parameter. Differences in this distance affect 
the phase difference between the reflected wave and the generator motion 
and thus affect the incident wave height. The effect of varying incident 
wave height on profile shape is opposite to intuition; in experiments 
with the same wave condition and different initial distance to the shore- 
line developed, the higher erosion rate was associated with the lower 


|e 


average H,. Differences in this distance also affect the phase of 
secondary waves at the toe of the profile. The effect of secondary 
waves was shown by differences in the shape of the offshore zone in two 
pairs of experiments. 


(c) Three special and one general tank width effects were observed. 
Strong circulation currents developed over the profile between antinodes 
of the standing wave for a wavelength four times the tank width, which 
affected the profile development and reflectivity. Cross waves occurred 
over a short segment of the profile for a brief time in one experiment, 
but the effect was not measured. Transverse waves generated by the gap 
at the end of the generator blade caused significant lateral variations 
in one experiment, but were not observed in the experiment with the same 
wave period but different tank width and initial test length and without 
a gap. In general, as the wavelength-to-tank width ratio increased from 
1, the amount of lateral variation in profile development decreased. 


(d) Two different effects of water temperature variation were 
observed. Six experiments support, to varying extents, the hypothesis 
that the higher the water temperature, the lower the recession rate. 

Two experiments support the opposite effect, that the higher the water 
temperature, the higher the recession rate. Another experiment supports 
either hypothesis. 


VI. RECOMMENDATIONS FOR CONDUCTING MOVABLE-BED COASTAL EXPERIMENTS 


1. Modeling Criterion. 


Equilibrium profiles are not often found in the prototype, and thus 
they may not be necessary to replicate. Also, equilibrium profiles are 
difficult to attain in the laboratory and may not be repeatable when 
they are reached. Therefore, it is recommended that some other criteria 
be selected as the prototype condition for replication in the laboratory, 
such as constant rate of shoreline recession or volume erosion. 


2. Tank Setup and Test Conditions. 


(a) The initial distance from the generator to the shoreline must be 
held constant when attempting to perform repeatable profile experiments. 


(b) The initial slope can affect the profile development and should 
be held constant to assure test repeatability. 


(c) To eliminate lateral variations in profile shape due to too 
short a crest length, wavelengths greater than three times the tank 
width should be chosen. However, two-dimensional tests may distort a 
three-dimensional problem to an unknown extent. 


(d) The water temperature should be kept within a 5° Celsius range 
to assure test repeatability. 


123 


(e) Cross waves in the constant-depth section and transverse waves 
can be avoided by careful selection of wave period and water depth for 
each tank width (Barnard and Pritchard, 1972; Madsen, 1974). 


(f) Secondary waves in the constant depth section can be eliminated 
by programing the generator motion with elliptic functions or by the use 
of sills placed at the proper location along the tank for each wave 
period (Hulsbergen, 1974). 


(g) Variability in profile reflectivity, generation of secondary 
waves over a shelf, and generation of cross waves over profile segments 
are phenomena which cannot be avoided or eliminated, but the experi- 
menters should be aware of the potential of these phenomena to affect 
profile development. 


(h) As a minimum the experimental conditions discussed in this series 
of reports should be documented in each movable-bed coastal engineering 
experiment and model study. 


3. Future Investigation. 


(a) The hypotheses on sources of profile reflectivity variability 
should be examined one-by-one in fixed-bed experiments. 


(b) More research is needed to quantify the effect of the initial 
profile slope on the final profile shape. 


(c) More research is needed on how wide a tank must be to assure 
that the tank walls do not affect a significant part of the profile. 


(d) More basic research is needed on the effect of water tempera- 
ture on sediment transport in oscillatory flow. 


124 


LITERATURE CITED 


ALLEN, R.H., '"'A Glossary of Coastal Engineering Terms,'' MP 2-72, U.S. 
Army, Corps of Engineers, Coastal Engineering Research Center, 
Washington, D.C., Apr. 1972. 


AMERICAN SOCIETY OF CIVIL ENGINEERS, "Sedimentation Engineering,'' ASCE 
Task Committee for the Preparation of the Manual on Sedimentation, 
New York, 1975. 


BARNARD, B.J.S., and PRITCHARD, W.G., "Cross-Waves. Part 2, Experiments," 
Journal of Flutd Mechantcs, Vol. 55, Pt. 2, 1972, pp. 245-255. 


CHESNUTT, C.B., "Laboratory Effects in Coastal Movable-Bed Models," 
Proceedings of the Sympostum on Modeling Techniques, 1975, pp. 945-961. 


CHESNUTT, C.B., and GALVIN, C.J., Jr., ''Lab Profile and Reflection 
Changes for Ho/Lo = 0.02," Proceedings of the 14th Conference on 
Coastal Engineering, 1974, pp. 958-977. 


CHESNUTT, C.B., and STAFFORD, R.P., "Movable-Bed Experiments with 
Ho/Lo = 0.021 (1970)," Vol. II, MR 77-7, Laboratory Effects in Beach 
Studies, U.S. Army, Corps of Engineers, Coastal Engineering Research 
Center, Fort Belvoir, Va., Aug. 1977a. 


CHESNUTT, C.B., and STAFFORD, R.P., 'Movable-Bed Experiments with 
Ho/Lo = 0.021 (1971)," Vol. III, MR 77-7, Laboratory Effects in Beach 
Studtes, U.S. Army, Corps of Engineers, Coastal Engineering Research 
Genter ys Kort Belvoir.) Vale.) NOV LOND. 


CHESNUTT, C.B., and STAFFORD, R.P., 'Movable-Bed Experiments with 
Ho/Lo = 0.021 (1972)," Vol. IV, MR 77-7, Laboratory Effects tn Beach 
Studtes, U.S. Army, Corps of Engineers, Coastal Engineering Research 
Genter, Fort Belvoir, Va., Dec. 1977c. 


CHESNUTT, C.B., and STAFFORD, R.P., "Movable-Bed Experiments with 
H,/Lo = 0.039," Vol. V, MR 77-7, Laboratory Effects in Beach Studies, 
U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 
Rope Welkvonsen Wels 5 Dees OW 7ele 


CHESNUTT, C.B., and STAFFORD, R.P., ''Movable-Bed Experiments with 
Hj/Lo = 0.004," Vol. VI, MR 77-7, Laboratory Effects in Beach Studies, 
U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 
Fort Belvoir, Va., Mar. 1978a. 


CHESNUTT, C.B., and STAFFORD, R.P., 'Movable-Bed Experiments with 
Ho/Lo = 0.013," Vol. VII, MR 77-7, Laboratory Effects tn Beach Studies, 
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Fort Belvoir, Va., March 1978b. 


125 


CHESNUTT, C.B., et al., "Beach Profile Development on an Initial 1:10 
Slope of 0.2 Millimeter Sand," Transactions of the American Geophysical 
Unton, Vol. 53, 1972, p. 411. 


COLBY, B.R., and SCOTT, C.H., "Effects of Water Temperature on the 
Discharge ioe Bed Material, n Professtonal une 462-G, U.S. Geological 
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COLLINS, J.1., and CHESNUTT, C.B., ''Tests on the Equilibrium Profiles of 
Model Beaches and the Effects of Grain Shape and Size Distribution," 
Proceedings of the Sympostum on Modeling Techniques, 1975, pp. 907-926. 


COLLINS, J.1., and CHESNUIT, C.B., "Grain Shape and Size Distribution 
Effects in Coastal Models,'' TP 76-11, U.S. Army, Corps of Engineers, 
Coastal Engineering Research Center, Fort Belvoir, Va., July 1976. 


DAILY, J.W., and HARLEMAN, D.R.F., Flutd Dynamics, Addison Wesley, 
Reading, Mass., 1966. 


FAIRCHILD, J.C., "Laboratory Tests of Longshore Transport,'' Proceedings 
of the 12th Conference on Coastal Engineering, 1970a, pp. 867-889. 


FAIRCHILD, J.C., "Wave Diffraction in a Laboratory Movable-Bed Setup," 
Bulletin and Summary of Research Progress Fiscal Years 1967-69, 
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Center, Washington, D.C., 1970b. 


GALVIN, C.J., "Finite-Amplitude, Shallow-Water Waves of Periodically 
Recurring Form," Proceedings of the Sympostum on Long Waves, 1972, 
pp. 1-32. 


HULSBERGEN, C.H., “Origin, Effect, and Suppression of Secondary Waves," 
Proceedings of the 14th Conference on Coastal Engineering, 1974, 
pp. 392-411. 


MADSEN, 0.S., "A Three Dimensional Wave Maker, Its Theory and Applica- 
tions ," Journal of Hydraulic Research, Vol. 12, No. 2, 1974, pp. 205-222. 


MADSEN, O.S., and MEI, C.C., 'Dispersive Long Waves of Finite Amplitude 
. Over an Uneven Bottom," Report No. 117, Massachusetts Institute of 
Technology, Hydrodynamics Laboratory, Cambridge, Mass., 1969. 


SAVAGE, R.P., "Laboratory Study of the Effect of Groins on the Rate of 
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June 1959. 


SAVAGE, R.P., "Laboratory Determination of Littoral-Transport Rates," 
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1962, pp. 69-92. 


126 


STAFFORD, R.P., and CHESNUTT, C.B., ''Procedures Used in 10 Movable-Bed 
Experiments," Vol. I, MR 77-7, Laboratory Effects tn Beach Studies, 
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SWART, D.H., "A Schematization of Onshore-Offshore Transport," Proceed- 
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TAYLOR, B.D., and VANONI, V.A., "Temperature Effects in Low-Transport, 
Flat-Bed Flows," Journal of the Hydraulics Ditviston, American Society 
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U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore 
Protectton 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. 


WATTS, G.M., "Laboratory Study of the Effect of Varying Wave Periods on 
Beach Profiles,'' TM-53, U.S. Army, Corps of Engineers, Beach Erosion 
Board, Washington, D.C., Sept. 1954. 


WATTS, G.M., and DEARDUFF, R.F., "Laboratory Study of Effect of Tidal 


Action on Wave-Formed Beach Profiles,'' TM-52, U.S. Army, Corps of 
Engineers, Beach Erosion Board, Washington, D.C., Dec. 1954. 


127 


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