Experimental study of longshore currents on a plane beach

R 64·13 0 \ 1 I :_, 2

EXPERIMENTAL STUDY OF

LONGSHORE· CURRENTS ON A PLANE BEACH

by C. J. Galvin Jr. P. S. Eagleson

HYDRODYNAMICS LABORATORY

Report No. 63

Prepared Under

Contract No. DA-49-055-eng-62-9 COASTAL ENGINEERING RESEARCH CENTER

U.S. Department of the Army Corps of Engineers

Washington, D.C.

and

NR 083-157 Contract Nonr 1841 (74)-4 OFFICE OF NAVAL RESEARCII

Earth Sciences Division Geophysics Branch Oceanography Section

R 64-13

.

; ~ ~

,

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r

HYDRODYNAMI CS LABaRA'IORY

Department of ,Civil Engineering

Massachusetts Institute of Technology

EXPERIMENTAL

STUDY

OF

LONGSHORE CURRENTS ON A PLANE BEACH

by

C.J. Galvin, Jr. and P.S. Eagleson

April 1964

Report No. 63

Prepared Under

Contract No. DA-49-055-eng-62-9

COASTAL ENGINEERING RESEARCH CEN'lER

D.S. Department of the Army

Corps of Engineers

Washington, D.C.

NR 083-157

Contract Nonr 1841 (74)-4

OFFICE OF NAVAL RESEARCH

Earth Sciences Division

Geophysics Branch

Oceanography Section

,

, I ,

'.J

i

ACKNOWLEDGEMENTS

This study of the mechanics of longshore current generation on

straight beaches was sponsored jointly by the Coastal Engineering

Research Center (formerly the Beach Erosion Board) of the Department

of the

Army,

Corps of Engineers under Contract Number

DA-49-055-eng-62-9 and by the Office of Naval Research, Earth Sciences Division,

Geophysics Branch, Oceanography Section under Contract

Nor~

1841 (74)-4.

Administration of these contracts was provided by the Division of

Sponsored Research of

MIT

under DSR 9266 and DSR 8840 respectively.

The work was performed in the Hydrodynamics Laboratory of the

Department of Civil Engineering at the Massachusetts Institute of

Technology by Cyril J. Galvin, Jr., Research Assistant in Geology and

Geophysics under the supervision of Dr. Peter S. Eagleson, Associate

Professor of Civil Engineering.

R.L. Bernstein and R.M. Males, undergraduate part-time assistants,

aided in taking the data and did much of the data reduction. G.A. Tlapa,

Research Assistant in Civil Engineering, assisted with the machine

computation which was performed on the IBM 1620 in the Civil Engineering

Computer Laboratory.

ii

ABSTRACT

Measurements are made of the characteristics of breaking

wa'les

and the resulting longshore currents for 34 combinations of wave height

(up to 0.22 feet), period (0.90 to 1.50 seconds), and breaker angle

(up to 32

0) ,

along a 20 foot test section of a 30 foot plane, smooth

concrete beach with a 0.104 slope.

Techniques are developed to measure the distribution of longshore

current velocity and of mean water level in the surf zone, and the

measurement of breaker point and angle for plunging waves on a laboratory

beach is standardized.

The nature of the growth of the longshore current in the lee of an

impermeable obstacle is studied. In addition to the expected increase

of the current velocity downstream of such an obstacle the mean water

level is found to increase and the breaker position and runup limit to

move shoreward. It is not clear to what extent these latter effects

are influenced by the scale of the apparatus used.

V

i i i

TABLE OF CONTENTJ

Page No.

ACK NOWI,ED GEMENTS

i

l\J3~-> 'LRll.C

'r

ii

'k{ E ut, l:m\j']Ir';N'I'~)

iii

LIS~e

OF

JPIGURES

iv

LIST OF TABLES

vi

LIS T OF SYMBOLS

vii

ry

I.

INTRODUCTION

1

AoProblel'! Jtatemerrt

1

BoScope of this Investigation

2

110

PREVIOUS INVESTIGATIONS

2

Ao Field Studies

2

B. Laboratory Studies

3

Co Analytical Studies

3

III.

EXPERIMENTAL PROGR.M1

5

IV.

EXPERU'1ENTAL EQUIPMENT AND PROCEDURES

7

A. Run Conditions

7

B. Wave Profile Gage

7

C. Measurement of Wave Height, Speed and Shape

12

Do Measurement of Breaker Point, Breaker Angle

and Runup Limit

14

E. Change in Mean Water Level

18

F .. Velocity Measurement

19

G. General Basin Conditions

23

H.

Coordinate Systems and Definition

₂₄

V.

EXPERIMENTAL RESULTS

26

A,. Wave Height, Shape and Speed

26

B. Breah:er and Runup

31

C. Mean lrvater Level

₃₂

D. Longshore Current Velocity

₃₃

E. Breaker Height and Depth

36

F. General Longitudinal Nonuniformity

₃₉

VI.

ANALYTICAL CONSIDERATIONS

42

A. Qualitative Description of Longshore Current

Formation

₄₂

B .. Approximate Energy Budget of Typical Test

₄₄

Co Effect of External Circuit

48

D. Momentum and

Enerl:~Y

Analysis of Putnam et ale

(12)

50

E. Revised Momentum Analysis

₅₂

F. Empirical Correlation

56

VII ..

S1JllllJ~AI{Y

AND

CONCLUSION~3

61

A. Summary

61

B ..

Conclusions

₆₁

VIII ..

RFJI'miENCES

62

Figure No.

1.

2.

,3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

1,3.

14.

I

r;

~ !.CJ •

17.

18.

19.

20.

21. 22.

2,3 •

24.

25.

26.

27.

28.

,30.

,31.

32.

33.

I,IST

OF Fl(}llfiK;

Title

Wave Basin

Plan View of Basin

Cross-Section of Beach and Basin

Platinum Wire Resistance Wa're Gage

Wave Gage Calibratioll Curve

Test Section with IrmtrLUnent Frame

Phase Lag Measurement for Celerity

Determination

Breaker Point Definition

Breaker Locator

Definition Sketch

Location of Taps for Damped Piezometers

Piezometer Well

Velocity Probes

Calibration of Veloci t;y Probes with

Surface Floats

Definition Sketch - Coordinate System

Definition Sketch

Definition Sketch

Wave Height Erwelope Through Surf Zone

Definition Sketch - Wave Shape

Wave Speed in Surf Zone

Wave Speed at Breaking

Mean Water Level in ,'jurf Zone

Frequency Distribution of Set-Dp in MWL

Velocity Distribution in Longshore Current

Longshore Variations for Conditions of

Test

4

Breaker Height and Breaker Depth

Location of Maximum and Minimum Longshore

Current Velocity

Location of Maximum and Minimum Mean

Water Level

Location of Maximum and Minimum Breaker

Distance

Location of Maximum and Minimum Hunup

Distance

Location of Maxim1Jll1 and Minimum Breaker

Angle

Shape

0 f

Shaa]

:iYlF~ Wav f?

Near

B:l'paJd 11[;

Mean Water Level in

~;ur I'

!:al1e for Hun

111-2

iv

Page No.

8

9

9

11

11

12

1,3

13

15

18

20

20

22

22

25

25

25

28

28

30

3(1

34

.34

35

.35

38

40

40

41

4l

~3

h3

117

"

Figure No.

34.

35.

36.

37.

38.

Title

Control Volume for Momentum Analysis

Variation in Ratio of Longshore Velocity

at Breaker to Mean Longshore Velocity

Variation of Mean Longshore Current

Velocity with Distance

Idealized Distribution of Longshore

Current Velocity

Empirical Correlation of Field and

Laboratory Data

v

Page No.

53

57

57

58

&J

Table No.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

LIST OF TABLES

Title

Types of Experimental Data

Run Conditions

Repeatability and Operator Variation for G

b

Measurement (Test IV-2)

Operator Variation in Average Breaker Angle

Dye and Float Velocity in Longshore Currents

Shape Factor vs. Position on Beach

Breaker Angle from Small Amplitude Theory

and From Observation

Net Particle Motion in Shoaling

Zone

(Test

rv-4)

Estimates of Breaker Depth-Breaker Height

Ratios

vi

Page No.

6

7

17

17

21

27

32

Energy Budget for Uniform Longshore Current

Friction Factor, Reynolds Number and Relative

Roughness for Data from Putnam, et ale (12)

51

Comparison of C

a

1\

A w b C d e

.

E

E.

1

.

E P

.

E r LIST OF SYMffiLS

Wave amplitude, 1/2 H

Vertical distance between mean water

level and trough elevation

Area of longshore current channel

Cross-sectional area of breaker carried

into surf zone

Cross-sectional area of triangular

breaker

~

high and Lb cos G

b

long

Breaker distance, horizontal distance

between SWLine and breaker position

Wave speed

Water depth, mean water level to beach

surface

Mean water depth at breaking, defined as

mb

Mean water depth between toe of beach

and plunger

Constants in revised momentum analysis

Elevation of mean water level above

vii

ft.

ft.

ft.2

ft.

ft/sec.

ft.

ft.

ft.

still water level

ft •

Energy flux

ft-lbs/sec.

Rate of energy dissipation in wave

breaking

ft-lbs/sec.ft.

Rate of energy dissipation by

long-shore current per foot length of beach

ft-lbs/sec.ft.

Rate of energy brought to beach per

foot of beach length

ft-lbs/sec.ft •

Rate of energy dissipation in runup

and backwash

ft-lbs/sec.ft •

energy flux off test beach in reflected

wave per foot of test beach

ft-lbs/sec.ft.

Darcy-Weisbach friction factor

Acceleration due to gravity

Head loss due to friction

ft/sec

2

"

h H k k x L m MWL p P r R JR S

SWL

SWLine

t T u

v

LIST OF SYMPOLS (cont Id)

Mean water level at breaking from solitary

wave theory

Trough elevation above beach

Wave height, crest elevation minus trough

elevation

absolute roughness

Local horizontal distance between top of

beach and SWLine

Proportionality constant in empirical

correlation

Wave length

Beach slope

Mean water level, average water surface

elevation

proportionality constant

Energy

flux

from plunger per foot of crest

length

viii

ft.

ft.

ft.

ft.

ft.

ft.

ft/ft.

ft.

ft-lbs/sec .ft.

Mass

flux

in longshore current

ft

3

_/sec.

~/~

Hypothetical mass

flux

through wave

ft

3

_/sec.

Runup distance, horizontal distance between

SWLine and runup limit

ft •

Hydraulic radius of longshore current channel:

~/2

ft.

Reynolds number of longshore current,

4

VR/v

Surface force 'in breaking

Still water level. Free surface of fluid

at rest

Ibs.

ft.

Intersection of SWL with beach, the x-coordinate

axis

Time

Wave period

Particle velocity in head of bore

Average longshore current velocity

sec.

sec.

ft/sec.

ft/sec.

.,.

;; c· LJ b cJ f L o r

w

w

{3

y

p a

L I S T OF SYMBOLS ( c o n t ' d ) Vj_^p Longshore c w r e n t v e l o c i t y i n d i c a t e d by p r o b e a t b r e a k e r p o s i t i o n f t / _{s e c .} L o n g s h o r e component o f v e l o c i t y i n r e t i i r n f l o w o u t o f s u r f zone f t / s e c . V ,V Average v e l o c i t y o f f l o a t s a t x = 10 and l 6 f t , f t / s e c .

^10 ^16

V '

v^A

x H o r i z o n t a l c o o r d i n a t e d i s t a n c e measured p o s i t i v e l y a l o n g beach f r o m upstream t r a i n i n g w a l l f t . y D i s t a n c e measured p o s i t i v e l y o f f s h o r e f r o m SWLine f t , y ' H o r i z o n t a l c o o r d i n a t e , measured f r o m t o p o f beach f t . z V e r t i c a l c o o r d i n a t e measured p o s i t i v e l y up f r o m SWL f t . s u b s c r i p t s b L o c a t i o n a t b r e a k e r

d L o c a t i o n between beach t o e and wave g e n e r a t o r f R e f e r s t o f l o a t , o r f r i c t i o n L R e f e r s t o l o n g s h o r e c u r r e n t o Deep w a t e r c o n d i t i o n s r R e f e r s t o r u n u p l i m i t W Wave a t b r e a k i n g i n e m p i r i c a l c o r r e l a t i o n w Wave a t b r e a k i n g i n momentum a n a l y s i s Y S p e c i f i c w e i g h t o f f l u i d l b s / f t ^ p Mass d e n s i t y o f f l u i d s l u g s / f t ^ CT Wave shape f a c t o r ^.^A^^

I INTRODUCTION A . Problem S t a t e m e n t

Longshore c u r r e n t s f l o w p a r a l l e l t o t h e s h o r e l i n e and r e a c h t h e i r h i g h e s t v e l o c i t i e s between t h e p o i n t o f wave b r e a k i n g and t h e s h o r e -l i n e . They a r e d r i v e n b y t h e -l o n g s h o r e component o f m o t i o n a s s o c i a t e d w i t h waves w h i c h approach t h e s h o r e l i n e o b l i q u e l y .

L o n g s h o r e c u r r e n t s a r e o f i n t e r e s t t o e n g i n e e r s and g e o l o g i s t s because t h e y e r o d e , t r a n s p o r t and d e p o s i t s e d i m e n t . A l o n g beaches b o r d e r i n g oceans and l a r g e l a k e s t h e s e c u r r e n t s a r e c a p a b l e o f t r a n s -p o r t i n g hundreds o f thousands o f c u b i c y a r d s o f sand -p a s t a g i v e n -p o i n t d u r i n g an average y e a r (see Johnson (1)", Brebner and Kennedy ( 2 ) ) . T h i s i s an a n n u a l l a y e r one s q u a r e m i l e i n a r e a and s e v e r a l i n c h e s t h i c k .

On n a t x j r a l beaches a q u a s i - e q u i l i b r i u m o f t e n e x i s t s b e t w e e n t h e r a t e a t w h i c h sediment i s s u p p l i e d f r o m r i v e r s and c l i f f s and t h e r a t e a t w h i c h i t i s t r a n s p o r t e d away b y l o n g s h o r e c u r r e n t s , so t h a t n e t e r o s i o n o f t h e beach f a c e i s s l i g h t . An example o f t h i s e q i o i l i b r i u m i s t h e w e l l s t u d i e d c o a s t o f S o u t h e r n C a l i f o r n i a , H e r e , a l l o f t h e beaches s t u d i e d b y H a n d i n (3, p.5U) w i t h t h e e x c e p t i o n o f one l 5 m i l e s t r e t c h , "had been i n e q u i l i b r i a d u r i n g h i s t o r i c t i m e p r i o r t o c o n s t r u c t i o n o f a r t i f i c i a l b a r r i e r s " . Sand r e a c h e s t h e s e beaches " c h i e f l y f r o m streams and t o a much l e s s e r e x t e n t f r o m e r o s i o n o f sea c l i f f s and t h e sea f l o o r " (U, p . 2 ^ ) . P o s s i b l y t h i s i s t y p i c a l o f most c o a s t s f o r i t has been e s t i m a t e d t h a t c l i f f e d s h o r e l i n e s o f t h e w o r l d erode back a t an average r a t e o f o n l y 1 cm p e r y e a r and c o n t r i

-b u t e o n a w o r l d w i d e -b a s i s a-bout 1/8 km^ per y e a r t o t h e sea ( 5 ) . R i v e r s , on t h e o t h e r h a n d , b r i n g t o t h e sea 5 t o 10 km^ o f s e d i m e n t each y e a r .

C o a s t a l e n g i n e e r i n g works ( b r e a k w a t e r , g r o i n s , j e l t i e s , p i e r s , d r e d g e d c h a n n e l s , e t c . ) d i s t u r b t h e e q u i l i b r i u m , a c c e l e r a t i n g l o c a l

e r o s i o n and d e p o s i t i o n a l o n g beaches and i n h a r b o r e n t r a n c e s . E n g i n e e r s a r e t h e r e f o r e i n t e r e s t e d i n t h e mechanics o f l o n g s h o r e c u r r e n t s i n o r d e r t o p r e d i c t a n d , i f p o s s i b l e , e l i m i n a t e t h e unwanted e f f e c t s o f t h e i r s t r u c t u r e s on t h e e n v i r o n m e n t . Beach E r o s i o n Board T e c h n i c a l R e p o r t N o . I4 ( 6 ) summarizes and e v a l u a t e s t h e l i t e r a t u r e on t h e e n g i n e e r i n g i m p o r t a n c e o f l o n g s h o r e c u r r e n t s . C o a s t a l p r o c e s s e s i m p a r t d i s t i n c t i v e c h a r a c t e r i s t i c s t o t h e s i z e d i s t r i b u t i o n o f beach sand ( 7 ) as w e l l as t o t h e m o r p h o l o g y o f t h e b o d i e s i n w h i c h t h i s sand o c c u r s . Because t h e sand i n some s a n d s t o n e s has l a i n , o f t e n more t h a n o n c e , on beaches d u r i n g p a s t g e o l o g i c t i m e , knowledge o f l o n g s h o r e c u r r e n t s i s v a l u a b l e i n i n t e r p r e t i n g t h e r o c k r e c o r d o f t h e p a s t . The l a n d f o r m s p r o d u c e d b y l o n g s h o r e cTJirents -s p i t -s , h o o k -s , b a r -s , and -s t r a i g h t beache-s •- a r e -sometime-s, a-s f o -s -s i l f o r m s , i m p o r t a n t p e t r o l e u m r e s e r v o i r s ( 8 ) .

"Numbers i n p a r e n t h e s i s r e f e r t o l i s t o f r e f e r e n c e s a t t h e end o f t h e r e p o r t .

B , Scope o f t h i s I n v e s t i g a t i o n The u l t i m a t e aim o f s t u d i e s o f l o n g s h o r e c u r r e n t s b y e n g i n e e r s o r g e o l o g i s t s i s t h e q u a n t i t a t i v e p r e d i c t i o n o f s e d i m e n t t r a n s p o r t b y l o n g s h o r e c u r r e n t s . Because s e d i m e n t t r a n s p o r t i s p r i m a r i l y r e l a t e d t o t h e v e l o c i t y o f t h e t r a n s p o r t i n g c u r r e n t , i t i s f i r s t n e c e s s a r y t o p r e d i c t t h i s f l u i d v e l o c i t y b e f o r e a p p r o a c h i n g t h e more d i f f i c i a l t t a s k o f p r e d i c t i n g sediment t r a n s p o r t . T h i s p r e d i c t i o n o f v e l o c i t y s h o u l d be c o n s i s t e n t w i t h t h e b a s i c e q u a t i o n s o f m o t i o n , energy and c o n s e r v a t i o n o f mass. S o l u t i o n o f t h e s e e q u a t i o n s f o r such a complex p r o b l e m r e q u i r e s t h e i r c o n s i d e r a b l e b u t j u d i c i o u s s i m p l i f i c a t i o n . T h e r e f o r e , t h e l o g i c a l approach t o u n d e r s t a n d i n g sediment t r a n s p o r t b y l o n g s h o r e c u r r e n t s i n ¬ v o l v e s f i r s t t h e a c c u r a t e d e s c r i p t i o n o f t h e phenomena g e n e r a t i n g t h e s e c u r r e n t s , t h e n t h e p r o p e r f o r m u l a t i o n o f s i m p l i f i e d eqxiations o f m o t i o n t o p r e d i c t t h e v e l o c i t y o f t h e c u r r e n t s and an e x p e r i m e n t a l v e r i f i c a t i o n o f t h i s p r e d i c t i o n , and f i n a l l y t h e i n v e s t i g a t i o n o f r e l a t i o n b e t w e e n l o n g s h o r e c u r r e n t v e l o c i t y and s e d i m e n t t r a n s p o r t . T h i s i n v e s t i g a t i o n d e a l s w i t h t h e i n i t i a l s t e p s o f e x p e r i m e n t a l d e s c r i p t i o n o f l o n g s h o r e c u r r e n t s and t h e a n a l y t i c a l p r e d i c t i o n o f l o n g s h o r e c u r r e n t v e l o c i t y . Sediment m o t i o n i s n o t t r e a t e d . The e x p e r i -m e n t a l phase i n c l u d e s -measure-ments under c o n t r o l l e d l a b o r a t o r y c o n d i t i o n s o f phenomena a s s o c i a t e d w i t h l o n g s h o r e c u r r e n t s f l o w i n g o n a p a r t i c \ 3 l a r p l a n e , smooth c o n c r e t e b e a c h . The a n a l y b i c a l phase i n c l u d e s an e m p i r i c a l r e l a t i o n between l o n g s h o r e c u r r e n t v e l o c i t y and wave c o n d i t i o n s a t

b r e a k i n g on l a b o r a t o r y and n a t u r a l b e a c h e s , and a p r e l i m i n a r y e x a m i n a t i o n o f t h e e q u a t i o n s o f m o t i o n f o r l o n g s h o r e c u r r e n t s .

I I PREVIOUS INVESTEGATIONS

A. F i e l d S t u d i e s

Johnson ( 9 ) stmimarizes t h e e a r l y w o r k p r i o r t o I919 i n w h i c h some i n v e s t i g a t o r s r e c o g n i z e d t h e f u n d a m e n t a l i m p o r t a n c e o f b r e a k e r a n g l e and wave h e i g h t . C o r r e l a t i o n o f l o n g s h o r e c u r r e n t v e l o c i t y w i t h t h e s e v a r i a b l e s f o r o v e r a t h o u s a n d q u a l i t a t i v e o b s e r v a t i o n s a l o n g t h e c o a s t o f S o u t h e r n C a l i f o r n i a was l a t e r d e m o n s t r a t e d b y Shepard ( 1 0 ) . Of p a r t i c u l a r I n t e r e s t and i m p o r t a n c e i s t h e r e p e a t e d o b s e r v a t i o n t h a t mean l o n g s h o r e c u r r e n t s a r e u n s t e a d y and n o n - u n i f o r m on n a t u r a l b e a c h e s , ( 1 1 ) , ( 1 2 ) . The u n s t e a d i n e s s i s u s u a l l y a t t r i b u t e d t o t h e s t o c h a s t i c n a t v i r e o f t h e i n c i d e n t wave t r a i n . N o n - u n i f o r m i t y w i l l o f c o u r s e resu3.t f r o m c o a s t a l s t r u c t u r e s o r f r o m v a r i a t i o n s i n t h e n e a r -s h o r e h y d r o g r a p h y . Shepard (10) a t t r i b u t e -s n o n - u n i f o r m i t y t o t h e p r e s e n c e o f r i p c u r r e n t s , s t a t i n g " . . . . most l o n g s h o r e c u r r e n t s can be shown t o be r e l a t e d t o r i p s because i n v a r i a b l y t h e y can be t r a c e d t o a l o c a l i t y where t h e c u r r e n t t u r n s seawai-d i n t o a r i p " . D u r i n g h i s

l o n g s h o r e c t t r r e n t measiirements on S o u t h e r n C a l i f o r n i a b e a c h e s , r i p s p a c i n g v a r i e d f r o m s e v e r a l hvmdred t o a f e w t h o u s a n d f e e t .

Q u a n t i t a t i v e o b s e r v a t i o n s were made b y Putnam, Kxxnk and T r a y l o r (12) and b y Inman and Quinn ( I 3 ) , B o t h groups o f i n v e s t i g a t o r s g i v e meastirements o f b r e a k e r a n g l e , wave h e i g h t and p e r i o d , beach s l o p e and l o n g s h o r e c u r r e n t v e l o c i t y f o r c e r t a i n C a l i f o r n i a b e a c h e s . T h e i r e x p e r i m e n t a l t e c h n i q u e s w i l l be d i s c u s s e d l a t e r .

Inman and Quinn (I3) f o u n d t h e v a r i a b i l i t y i n l o n g s h o r e c u r r e n t v e l o c i t y t o be such t h a t t h e s t a n d a r d d e v i a t i o n o f t h i s v a r i a b l e

(measured a t 15 s t a t i o n s r o t i g h l y 3OO f e e t a p a r t ) u s u a l l y e q u a l e d o r exceeded t h e mean o f t h e measurements. I n o t h e r words i t was n o t uncommon on some r e l a t i v e l y p l a n e n a t i a r a l beaches ( T o r r e y P i n e s and P a c i f i c Beach, C a l i f o r n i a ) f o r l o n g s h o r e c u r r e n t v e l o c i t y t o oppose t h e l o n g s h o r e component o f m o t i o n i n t h e b r e a k i n g w a v e s .

B . L a b o r a t o r y S t u d i e s

E a r l y l a b o r a t o r y work was concerned w i t h l i t t o r a l d r i f t , t h e m a t e r i a l moved b y l o n g s h o r e c u r r e n t s . The l i t e r a t u r e abounds w i t h d e s c r i p t i o n s o f model s t u d i e s t o d e v e l o p s o l u t i o n s f o r l i t t o r a l d r i f t p r o b l e m s on p a r t i c u l a r s h o r e l i n e s however t h e s e o f f e r l i t t l e t o w a r d a f u n d a m e n t a l u n d e r s t a n d i n g o f t h e p r o b l e m . Savage (ih) summarizes p r e s e n t f i e l d and l a b o r a t o r y knowledge o f t h e r a t e o f t h e l i t t o r a l d r i f t t r a n s p o r t r a t e and d i s c u s s e s t e c h n i q u e s u s e f u l i n l a b o r a t o r y s t u d i e s o f l o n g s h o r e c u r r e n t s .

One o f t h e f i r s t f i x e d - b e d s t u d i e s o f t h e l o n g s h o r e c u r r e n t s t h e m s e l y e s i s t h a t o f Putnam e t a l (12) i n w h i c h beach s l o p e and roughness w e r e v a r i e d i n a d d i t i o n t o a l l t h e wave p a r a m e t e r s a t b r e a k i n g .

More r e c e n t l y Brebner and Kamphuis (l5) have made a s e r i e s o f f i x e d - b e d s t u d i e s on smooth p l a n e beaches b u t • u n f o r t u n a t e l y t h e wave c h a r a c t e r i s t i c s were n o t measured a t b r e a k i n g , o n l y i n deep w a t e r ,

C. A n a l y t i c a l Approaches

P r o b a b l y t h e f i r s t a n a l y t i c a l a t t a c k on any a s p e c t o f t h e l o n g s h o r e c u r r e n t p r o b l e m was an a t t e m p t t o r e l a t e t h e l i t t o r a l d r i f t t r a n s p o r t r a t e t o t h e l o n g s h o r e component o f power s u p p l i e d b y t h e w a v e s . The i d e a was i n i t i a l l y advanced b y Munch-P e t e r son ( i n I91J4 a c c o r d i n g t o Svendson

( 1 6 ) ) .

S i n c e t h a t t i m e , E a t o n

(1?),

C a l d w e l l ( 1 8 ) , and o t h e r s have c o n t r i b u t e d t o i t s e v a l u a t i o n . Savage (I9) g i v e s a c o m p i l a t i o n o f f i e l d and l a b o r a t o r y d a t a w h i c h shows an o r d e r o f m a g n i t u d e s c a t t e r i n t h e l a b o r a t o r y d a t a b u t good agreement among t h e two a v a i l a b l e s e t s o f f i e l d measurements (18) , F i e l d meastirements o f Johnson (20) i n c l u d e a l l b u t

t h e a n g l e s needed b y t h i s m e t h o d , b u t even assuming t h e most f a v o r a b l e v a l u e f o r t h e m i s s i n g a n g l e s , t h e d a t a do n o t come w x t h x n an o r d e r o f magnitude o f t h e r e l a t i o n d e f i n e d p r e v i o u s l y ( 1 8 ) .

Putnam e t a l (12) c o n s i d e r t h e f l u x o f mass, momentum and e n e r g y i n t o a c o n t r o l volume o f d i f f e r e n t i a l l e n g t h a l o n g t h e s h o r e bounded b y t h e beach and t h e b r e a k e r l i n e . They d e v e l o p two e x p r e s s x o n s , b o t h f o r c o n d i t i o n s w h i c h a r e s t e a d y and u n i f o r m i n t h e mean: 1 . From e n e r g y f l u x : i n w h i c h V mean l o n g s h o r e c u r r e n t v e l o c i t y m " beach s l o p e C^=» wave g r o u p v e l o c i t y a t b r e a k i n g wave energy p e r u n i t o f s u r f a c e a r e a a t b r e a k i n g 0^= a n g l e o f wave i n c i d e n c e a t b r e a k i n g p = f l u i d mass d e n s i t y d^= mean w a t e r l e v e l a t b r e a k i n g f = D a r c y - W i e s b a c h r e s i s t a n c e c o e f f i c i e n t s - f r a c t i o n o f b r e a k i n g wave energy a v a i l a b l e f o r l o n g s h o r e c u r r e n t g e n e r a t i o n . 2. Prom momentum f l u x : h V. i n w h i c h

V - I [ ( 1 . s i n e J ^ / 2 „ 13 [ 2 ]

V •= wave p a r t i c l e v e l o c i t y a t b r e a k i n g b 8 m cos 9^ volume r a t e o f i n f l o w a c r o s s b r e a k e r l i n e T wave p e r i o d

The m a j o r assumptions i n v o l v e d i n t h e d e r i v a t i o n o f E q . [2] a r e : i •- momentxam e q u a t i o n can be w r i t t e n i n t e r m s o f t i m e average

q u a n t i t i e s i i - f l o w i s u n i f o r m i n t h e l o n g s h o r e d i r e c t i o n i i i - no shear e x i s t s o n t h e c o n t r o l volume f a c e a t t h e b r e a k e r l i n e i v - 0 e x i t s t h e c o n t r o l voltmie a c r o s s t h e b r e a k e r l i n e w i t h v e l o c i t y v . Putnam e t a l t h e n a p p l y s o l i t a r y wave r e l a t i o n s h i p s f o r Q^, v ^ , and use t h e f i e l d and l a b o r a t o r y measurements m e n t i o n e d p r e v i o u s l y t o e v a l u a t e s and f .

Inman and Quinn ( 1 3 ) c a l c i a a t e d t h e D a r c y f f r o m E q . [ 2 ] u s i n g t h e i r f i e l d measurements as w e l l as t h e f i e l d and l a b o r a t o r y d a t a o f Putnam e t a l ( 1 2 ] ' , Assuming an e x p o n e n t i a l r e l a t i o n between f and v t h e y o b t a i n e d t h e l e a s t squares f i t :

f = 0.38k V •^•^-^ [3]

Brebner and Kamphuis (l5) measured o n l y deep w a t e r wave c h a r a c t e r i s t i c s and p e r f o r m e d m t a t i p l e r e g r e s s i o n a n a l y s e s w h i c h y i e l d e d :

H

V - m s i n ^ / ^ ( m ) [ s i n (1.65 e^) + a i s i n (3.30 6 ^ ) J [k]

Most o f Ikh s e p a r a t e o b s e r v a t i o n s l i e w i t h i n + 10 ° / o o f t h i s r e l a t i o n . No a t t e m p t was made t o check i t a g a i n s t t h e d a t a o f o t h e r i n v e s t i g a t o r s . .

I n a r e v i e w o f t h e o r i e s o f l o n g s h o r e c u r r e n t m o t i o n Bruxin ( 2 1 ) c o n -c l u d e s t h a t t h e momentum approa-ch i s t h e b e s t a v a i l a b l e f o r p l a n e bea-ches b u t s u g g e s t s t h a t f o r beaches b o r d e r e d b y b a r s , a c o n t i n u i t y r e l a t i o n between t h e f l u i d b r o u g h t i n b y t h e b r e a k i n g waves and t h a t c a r r i e d o u t b y t h e r i p s m i g h t be u s e f u l . I l l EXPERIMENTAL PROGRAM A... As was s t a t e d e a r l i e r , t h e u l t i m a t e o b j e c t i v e o f t h e r e s e a r c h program o f w h i c h t h i s i s a p r e l i m i n a r y r e p o r t , i s t o f o r m u l a t e a

5

m a t h m a t i c a l .nodel g o v f c r r i n g t h e g e n e r a t i o n o f l o n g s h o r e c u r r e n t s w h i c h i s c o n s i s t e n t w i t h t h f f x f i d a m e n t a l l a w s o f f l u x d mechanics and xs hence i n d e p e n d e n t o f s c a l e .

I n o r d e r t o dete>-mine t h e p h y s i c a l l y i m p o r t a n t ïeat^es t h i s complex phenomena and t o add t o t h e body o f d a t a ^ ^ ^ f ^ ^ ^ ^ J ' ^ ^ J ? ^ ! ^ a s e t o f e x p e r i m e n t s were p e r f o r m e d on a l a b o r a t o r ; / beac I n t h e Hydro dynamics L a b o r a t o r y o f t h e Department o f C : r / i l l ^ ^ ' g - ^ ^ ' ^ ^ ^ ^ y ' \ , , / ; 3 \ , , e a r T e x t e n s i v e p r e l i m i n a r y i n v e s t i g a t i o n , .nethods were ' f ^ ^ ^ ^ ' " ^ ^ ^ f ' f o u r t v o e s o f d a t a , c l a s s i f i e d f o r convenience as t y p e s A , B, b a a u {^B S i e 1 ) , E n ^ g y d i s s i p a t i o n i n t h e b r e a k i n g wave, p e r h a p s t h e l o ^ t i m p o r t a n ; d e p e x S n t v a r i a b l e i n t h i s s t u d y , cotiLd r,ot be d x r e c t l y measured, f o r a p p r o p r i a t e i n s t r u m e n t s do n o t e x x s t . One o r more o f t h e f o u r t y p e s o f d a t a a r e i n c l u d e d i n UU r u n s , i d e n S f i e d f o r c o n v e n i e n c e b y a u n i q u e c o m b i n a t i o n o f t h r e e i n d e p e n d e n t i ï ï a b l e s : 9 , , H . , and T . Four v a l u e s o f 9 ^ , f « - " g ^ % X ' ? ï a o ° ) g e n e r a t o r anS s h o r e l i n e , d i v i d e t h e r u n s i n t o S e r i e s I ( 0 ° ) * / ^ ^ ! ° ^> 1 1 1 ( 2 7 ° ) , and I V ( 5 1 ° ) . Each s e r i e s , e x c e p t I , i n c l u d e s a b o u t a dozen t e s t s i d e n t i f i e d b y a u n i q u e c o m b i n a t i o n o f wave p e r i o d ( T ) a n d wave h e i g h t i n f r o n t o f g e n e r a t o r ( H ^ ) ,

TABLE 1 TYPES OF EXPERIMENTAL DATA

P r i n c i p a l measuring d e v i c e p a r a l l e l w i r e r e s i s t a n c e gage Q u a n t i t y measm^ed wave h e i g h t wave speed wave f o r m Symbol H G o b r e a k e r l o c a t o r t a p e b r e a k e r p o s i t i o n b r e a k e r a n g l e r u n u p l i m i t b damped p i e z o m e t e r s change i n MWI. due t o waves D m i n i a t u r e c u r r e n t m e t e r , f l o a t s l o n g s h o r p - - ' i i r r e j i t v e l o c i t y

Tables A l and A 2 o f t h e A p p e n d i x summai^ize t h e d a t a a v a x l a b l e i r o m t h e s e e x p e r i m e n t s a c c o r d i n g t o d a t a t y p e , s e r i e s , and t e s t number. ^or.-i«<. T ro « 0 ° ! was done o n l y t o check a few cases when no l o n g i i h o r c Jierxes I ( 9 « 0 ° ) was done o n l y

I V EXPERIMENTAL EQUIPMENT AND PROCEDURES A . Rvn C o n d i t i o n s

The e x p e r i m e n t s were conducted i n a model b a s i n k'? f t . b y 22 f t . by l,k f t , c o n t a i n i n g a m o v a b l e , p l u n g e r - t y p e wave g e n e r a t o r 20 f t . l o n g and a smooth p l a n e c o n c r e t e beach .30 f t , l o n g and 13 f t . w i d e w i t h a 1 on 10 s l o p e (see F i g u r e s 1 , 2, and 3 ) . O f f s h o r e w a t e r d e p t h was k e p t a t I . l 5 f t . Waves, g e n e r a t e d a t known a n g l e s t o t h e b e a c h ,

advanced i n t o t h e beach between t r a i n i n g w a l l s c u r v e d t o match t h e r e f r a c t i o n p a t t e r n o f a wave o f i n t e r m e d i a t e p e r i o d i n each s e r i e s .

The upstream t r a i n i n g w a l l extended up t h e beach beyond t h e swash l i n e c o m p l e t e l y b l o c k i n g l o n g s h o r e m o t i o n s i n t h e s u r f z o n e . The downstream t r a i n i n g w a l l t e r m i n a t e d s h o r t o f t h e s h o r e l i n e t o p r o v i d e an e x i t f r o m t h e t e s t s e c t i o n f o r t h e l o n g s h o r e c u r r e n t . The f l o w e v e n t u a l l y r e t u r n e d t o t h e beach b y p a s s i n g under t h e p l u n g e r .

Table 2 l i s t s t h e r a n g e o f t h e i n d e p e n d e n t v a r i a b l e s i n t h e s e

e x p e r i m e n t s . The v a l u e s were l a r g e l y d e t e r m i n e d b y a v a i l a b l e space and e q u i p m e n t .

B . Wave P r o f i l e Gage ( l y p e A Equipment)

"Wave h e i g h t , speed, and f o r m were o b t a i n e d u s i n g a p l a t i n u m w i r e r e s i s t a n c e wave gage and Sanborn r e c o r d i n g o s c i l l o g r a p h . Model 1^0. The wave gages (see F i g u r e 3) d i f f e r f r o m p r e v i o u s models (Dean, ( 2 2 ) j W i e g e l , (23)) p r i n c i p a l l y i n t h e a d d i t i o n o f c o n n e c t o r s between t h e

s e n s i n g w i r e s and t h e c a b l e l e a d i n g t o t h e r e c o r d e r . For use i n and near t h e s u r f z o n e , t h i s c o n n e c t i o n i s made b y s o l d e r i n g t h e

0,036

i n c h d i a m e t e r p l a t i n v m i w i r e

TABLE 2 RUN CONDITIONS Wave g e n e r a t o r a n g l e Wave p e r i o d Wave h e i g h t a t g e n e r a t o r Beach s l o p e ( H , ) im) Beach s u r f a c e Water d e p t h a t g e n e r a t o r Water t e m p e r a t u r e L e n g t h o f t e s t beach (between t r a i n i n g w a l l s )

Opening between downstream t r a i n i n g w a l l and SW L i n e Mean e l e v a t i o n o f p l u n g e r base above f l o o r T r a i n i n g w a l l c u r v a t u r e S e r i e s I I I I I I I V

0 ° , 1 0 ° , 27°,

51°

0.90

t o

1.50

s e c ,

0,05

t o

0.21

f t . O.lOU f t . / f t . o v e r a l l average 0.109 f t . / f t . n e a r s h o r e average smooth c o n c r e t e

1.15

f t .

1U°

t o

23°

^ 2 2

f t .

2.2

f t . o.ho f t . C w v a t u r e n o t needed f o r r e f r a c t i o n o f 1.25 sec.wave none f o r r e f r a c t i o n o f 1,50 sec.wave

7

Basin Wolll F i g , 2 P l a n View o f B a s i n P L U N G E R A T M E A N E L E V A T I O N X 2 V E R T I C A L E X A G G E R A T I O N F i g , 3 C r o s ; : . - o e c t i o n o f Beach and B a s i n 9

i n an Amphinol f e m a l e j a c k (80 M C 2 F) w h i c h f i t s a male p l t i g (80 M G 2M) on t h e c a b l e . The base o f t h e f e m a l e j a c k was c o v e r e d w i t h a smooth convex c o a t o f beeswax. These m o d i f i c a t i o n s p r e v e n t t h e c a l i b r a t i o n f r o m d r i f t i n g due t o t h e c o l l e c t i o n o f s p r a y f r o m b r e a k i n g waves a t t h e c o n n e c t i o n , and t h e y a l s o make t h e w i r e s e a s i l y d e t a c h a b l e f r o m t h e l o n g l e n g t h s o f c a b l e . The p a r a l l e l , O.O36 i n c h d i a m e t e r w i r e s o f t h e s e gages c a n t i l e v e r 5-1/2 i n c h e s beyond t h e c o n n e c t o r and a r e h e l d p a r a l l e l and 3/16 i n c h a p a r t b y two l u c i t e s p a c e r s (see F i g u r e h) >

C a l i b r a t i o n . Gages were c a l i b r a t e d b y l o w e r i n g them i n t o s t i l l w a t e r i n one c e n t i m e t e r i n c r e m e n t s over a r a n g e o f 6 or 7 c m . , and r e

-c o r d i n g on Sanborn paper t h e -change i n r e s i s t a n -c e between t h e w i r e s . A p l o t o f gage e l e v a t i o n ( i n cm. above an a r b i t r a r y datum) a g a i n s t r e c o r d e r d e f l e c t i o n ( i n mm.) i s r e a s o n a b l y l i n e a r and c o n s t a n t f o r t i m e i n t e r v a l s on t h e o r d e r o f 10 hours (see F i g v i r e 5) • The s l o p e o f t h i s c u r v e , i n f e e t o f w a t e r p e r mm. o f Sanborn p a p e r , i s t h e c a l i b r a t i o n c o n s t a n t used t o o b t a i n wave h e i g h t .

This s t a t i c c a l i b r a t i o n was checked b y h a r m o n i c a l l y o s c i l l a t i n g t h e gage a known v e r t i c a l d i s t a n c e i n s t i l l w a t e r , f o l l o w i n g t h e p r o -cedure o f Dean (22). I n s i x t e s t s , d i f f e r e n c e s between s t a t i c and

dynamic c a l i b r a t i o n s were 2 p e r c e n t o r l e s s , w h i c h approaches t h e o r d e r t o w h i c h t h e a m p l i t u d e o f t h e v e r t i c a l o s c i l l a t i o n can be r e a d .

—Gage p e r f o r m a n c e . Because t h e gages were used i n s h a l l o w w a t e r on a c o n c r e t e beach c o n t a i n i n g aliominum channels i n t h e beach s u r f a c e , t h e e f f e c t s o f t h e s e s u r f a c e s on t h e c a l i b r a t i o n were d e t e r m i n e d .

L i n e a r i t y o f c a l i b r a t i o n was n o t a f f e c t e d b y t h e f r e e s \ i r f a c e i n s h a l l o w w a t e r as l o n g as t h e p r o b e was 3 mm. below t h e f r e e s t i r f a c e . The c a l i -b r a t i o n c u r v e o -b t a i n e d w i t h t h e ends o f t h e two w i r e s i n c o n t a c t w i t h t h e same c o n c r e t e s u r f a c e was i n d i s t i n g u i s h a b l e f r o m a n o r m a l c a l i b r a t i o n c u r v e . C a l i b r a t i o n made i n s h a l l o w w a t e r was a f f e c t e d b y t h e aluminum channels a t d i s t a n c e s o f l e s s t h a n 2 i n c h e s , and t h e r e f o r e , gages were n o t used o v e r t h e c h a n n e l s . The l u c i t e s p a c e r s , as l o n g as t h e y were e n t i r e l y below o r above t h e f r e e s u r f a c e , d i d n o t a f f e c t t h e s l o p e o f t h e c a l i b r a t i o n c u r v e , b u t p o s i t i o n o f t h i s c t i r v e was t r a n s l a t e d s l i g h t -l y i f s p r a y wet t h e upper s p a c e r . D u r i n g a f e w r u n s , t h e p l a t i n v m i w i r e s were a c c i d e n t l y b e n t , b u t a f t e r s t r a i g h t e n i n g , a r e c a l i b r a t i o n showed no more t h a n n o r m a l v a r i a t i o n f r o m t h e o r i g i n a l c a l i b r a t i o n . U n p u b l i s h e d e x p e r i m e n t s b y J . A . Hoopes showed t h e r e t o be l i t t l e v a r i a t i o n i n s e n s i t i v i t y f o r l a r g e changes i n w i r e s p a c i n g . A 100 p e r c e n t i n c r e a s e i n s p a c i n g ( f r o m l / U t o l / 2 i n c h ) d e c r e a s e d t h e s e n s i t i v i t y o n l y 15 per c e n t . I n normal u s e , s p a c i n g does n o t change. The w i r e s o f t h e gages a r e r e l a t i v e l y s h o r t and s t i f f j no v i b r a t i o n or s e v e r e b e n d i n g under t h e a c t i o n o f t h e waves o c c u r s .

Gages were never w i p e d w h i l e i n use s i n c e c a l i b r a t i o n s made b e f o r e and a f t e r a t e s t w i p i n g were i n d i s t i n g u i s h a b l e , one f r o m t h e o t h e r . Water s u r f a c e d u r i n g t h e s e r i i n s was c l e a n , and t h e gages were i n w a t e r o n l y

M)

5 1/2 inch

3 / l 6 inch

i _ i

' 1

Connection Lucite spacers 0.036 inch diameter platinum

F i g . k P l a t i n u r n W i r e R e s i s t a n c e Wave Gage xon s 37 5 37,0 >-< t 3 6 0 cr < UJ > O CD 35,0 < z 34,0 o > Ui 3 3 0 32 0 O 10 0 5 A M , • 12 18 P.M. A 5 3 0 R M . I 10 2 0 3 0 4 0 5 0 DISPLACEMENT OhJ SANBORN PAPER (mm)

F i g . 5 Wave Gage C a l i b r a t i o n Curve

I n f ' e n e r a l , t h e s e t e s t s o f t h e p e r f o r m a n c e o f p a r a l l e l w i r e

r e s i s t a n c e gages r e p e a t and e x t e n d t e s t s r e p o r t e d b y W i e g e l and Dean, and s u b s t a n t i a t e Dean's c o n c l u s i o n t h a t a c t u a l wave h e i g h t w i l l n o t d i f f e r b y more t h a n 3 t o 5 per c e n t f r o m measured wave h e i g h t .

O s c i l l o g r a p h . D u r i n g t h e t e s t s o f t h e wave gage, an i m p o r t a n t p o s s i b l e s o u r c e o f e x p e r i m e n t a l e r r o r was n o t e d . The s t y l u s o f t h e r e -c o r d e r i s h e l d b y a s p r i n g a g a i n s t t h e r e -c o r d i n g p a p e r , and i f t h e s p r i n g t e n s i o n i s t o o h i g h , f r i c t i o n between s t y l u s and p a p e r can cause l a r g e e r r o r s , p a r t i c u l a r l y when l o w paper speeds and s m a l l d e f l e c t i o n s o f t h e s t y l u s p e r m i t s t i c k i n g t o o c c u r . For t h i s r e a s o n , most wave gage d a t a were t a k e n a t h i g h e s t paper speed (100 mm./sec.) and about two t h i r d s o f f u l l s c a l e d e f l e c t i o n , under w h i c h c o n d i t i o n s t h e r a p i d r e l a t i v e m o t i o n between s t y l u s and paper m i n i m i z e s t h e f r i c t i o n e f f e c t . Whenever r e -c o r d i n g s were made a t low speeds, t e n s i o n on t h e s t y l u s was -c h e -c k e d . R e c o r d i n g d a t a near t h e edges o f t h e Sanborn paper was a v o i d e d when p o s s i b l e because t h e r e s p o n s e o f t h e s t y l u s i n t h i s r e g i o n i s s l i g h t l y n o n l i n e a r ,

C. Measurement o f Wave H e i g h t , Speed and Shape ( I > p e A P r o c e d u r e ) I n u s e , wave gages were suspended f r o m a p o i n t gage mounted on a r o l l i n g c r o s s b a r w h i c h t r a v e l e d on an aluminum f r a m e e x t e n d i n g o v e r a 6 f t . b y 20 f t , area o f t h e t e s t beach (see F i g u r e 6 ) . Wave h e i g h t w&s o b t a i n e d b y a v e r a g i n g t h e r e c o r d e d wave h e i g h t o f t w e n t y s u c c e s s i v e waves p a s s i n g one c a l i b r a t e d wave g a g e . Wave shape ( t e m p o r a l v a r i a t i o n o f w a t e r s u r f a c e e l e v a t i o n a t t h e gage p o s i . t i o n ) c o u l d be o b t a i n e d f r o m t h e s e same

r e c o r d i n g s . Envelopes o f wave h e i g h t were o b t a i n e d by moving ^he c a l i -b r a S d S g e s l o w l y f r o m o f f s h o r e , throiogh t h e -b r e a k e r z o n e , and i n t o t h e T u S u r r e g L n . Wave speed was o b t a i n e d b y a v e r a g i n g t h e r e c o r d e d phase l a g (As i n F i g u r e 7) o f 20 waves p a s s i n g two gages f i x e d 0.25 f t . a p a r t on a l i n e p a r a l l e l t o t h e d i r e c t i o n o f wave t r a v e l .

These d a t a were always t a k e n a t a s t a t i o n i n t h e m i d d l e o f t h e t e s t b e a c h and u s u a l l y a l s o a t t h e u p s t r e a m and downstream ends ^ ^ J ^ beach (see A p p e n d i x , T a b l e A U ) . A t t h e s e s t a t i o n s , wave speed and h e i g h t were measured a t b e t w e e n s i x and t e n l o c a t i o n s a l o n g a l i n e e x t e n d i n g

ïrom t h e t o p o f t h e r u n u p r e g i o n t o o f f s h o r e o f t h e b r e a k e r .

A S

F i g u r e 7. Phase Lag M e a s u r é d b y 2 Wave Gages, Gages Spaced 0.25 f e e t A p a r t i n P l a n e Normal t o D i r e c t i o n o f Wave P r o p a g a t i o n . Shape Shown i s t h a t o f a Bore Forming f r o m t h e Hroken Wave.

L ^1' OF

F i g u r e 8 . Breaker P o i n t D e f i n i t i o n , P o s i t i o n o f t h e F i r s t Appearance o f Dark L i n e i n t h e S h o a l i n g Wave i s D e f i n e d as t h e Breaker P o s i t i o n .

D . Meastrement o f Breaker P o i n t . B r e a k e r _ A n g l e _ j i n ^ ^ jTyye B Eqviipment and P r o c e d ü r e J

D e f i n i t i o n s . As t h e b r e a k e r b e g i n s t o p l u n g e , t h e c r e s t o v e r r e a c h e s t h e concave f r o n t o f t h e w a v e . When v i e w e d f r o m a b o v e , t h i s c o n c a v i t y f o r m s a g r a y i s h , t r a n s l u c e n t band a l o n g t h e wave f r o n t and i s s e p a r a t e d f r o m t h e c l e a r w a t e r t o t h e back o f t h e wave b y a d a r k l i n e m a r k i n g t h e v e r t i c a l segment o f t h e wave f a c e (see F i g u r e 8 ) . The p o s i t i o n w h e r e t h i s d a r k l i n e f i r s t appears i n t h e shoreward moving wave i s d e f i n e d as t h e b r e a k e r p o i n t ( y ' } . The b r e a k e r a n g l e (9^^) i s d e f i n e d as t h e a n g l e b e t w e e n t h e w a v e ^ c r e s t a t t h e b r e a k e r p o i n t and t h e mean s h o r e l i n e .

The average maximum p o s i t i o n a t t a i n e d b y t h e b o r e w h i c h f o r m s a f t e r t h e wave b r e a k s i s d e f i n e d as t h e r u n u p l i m i t ( y ' ) . The c o o r d i n a t e , y ' , i s

h o r i z o n t a l , p e r p e n d i c u l a r t o t h e s t i l l w a t e r l i n e , has i t s o r i g i n a t t h e t o p o f t h e beach and i s p o s i t i v e g o i n g o f f s h o r e (see F i g u r e 3) .

B r e a k e r l o c a t o r . Breaker p o i n t and b r e a k e r a n g l e were measured v i s u a l l y w i t h a b r e a k e r l o c a t o r c o n s i s t i n g o f two h o r i z o n t a l p l a t e s whose f r o n t edges had been f i x e d i n t h e same v e r t i c a l p l a n e . The l o w e r

o f t h o s e two p l a t e s i s opaque l u c i t e and p i v o t s f r o m a p r o t r a c t o r w h i c h can-move a l o n g t h e t r a v e l i n g c r o s s bar (see F i g u r e 9 ) . A second l u c i t e p l a t e i s f i x e d on dowels 0.25 f e e t above t h e f i r s t .

W i t h t h e p l a t e s p a r a l l e l t o t h e s h o r e l i n e ( 9 = 0 ) , b r e a k e r p o i n t was measured b y s l i d i n g t h e b r e a k e r l o c a t o r o f f s h o r e u n t i l t h e d a r k l i n e

d e f i n i n g t h e b r e a k e r p o i n t j u s t d i s a p p e a r e d b e n e a t h t h e opaque p l a t e . The p o s i t i o n o f t h e b r e a k e r was t h e n r e a d f r o m a t a p e on t h e c r o s s b a r . The measurement was r e p e a t e d b y s l i d i n g t h e l o c a t o r i n f r o m o f f s h o r e and n o t i n g t h e f i r s t appearance o f t h e d a r k l i n e . The average o f t h e s e two r e a d i n g s was r e c o r d e d as t h e b r e a k e r p o s i t i o n ( y ^ ' ) «

W i t h t h e b r e a k e r l o c a t o r a t t h e b r e a k e r p o i n t , b r e a k e r a n g l e ( 9 ^ ) was measured by p i v o t i n g t h e p l a t e s u n t i l t h e i r f r o n t edges f e l l i n t h e

same v e r t i c a l p l a n e as t h e wave c r e s t a t b r e a k i n g . The a n g l e was t h e n r e a d d i r e c t l y f r o m t h e p r o t r a c t o r on t h e b r e a k e r l o c a t o r .

I n measurements o f b o t h y ' and 9 , t h e o b s e r v e r ' s l i n e of s i g h t

was

k e p t v e r t i c a l b y l o o k i n g

Sown

p a s t t h e l o c a t o r i n such a way t h a t t h e f r o n t edges o f t h e two p l a t e s c o i n c i d e d . 9 and, y ' were m e a s u r é d b y two o b s e r v e r s at each o f 5 s t a t i o n s a l o n g t h e t e s t s e c t i o n o f t h e b e a c h .

Runup l i m i t . The d i s t a n c e between t h e beach t o p and r u n u p l i m i t ( v ' ) was measured w i t h a t a p e b y two o b s e r v e r s a t t h e 5 s t a t i o n s w h e r e yi'^and 9^ were measured. The c o n v e r s i o n o f y ' and y ^ , d i s t a n c e s measured f r o m t h e % e a c h t o p , t o r and b , d i s t a n c e s measured f r o m s t i l l w a t e r l e v e l , i s o u t l i n e d l a t e r .

R e p e a t a b i l i t y and o p e r a t o r v a r i a t i o n . The p o s i t i o n o f t h e b r e a k e r p o i n t and r u n u p l i m i t and t h e m a g n i t u d e Of t h e b r e a k e r a n g l e a r e v i s i b l e o v e r o n l y a s m a l l f r a c t i o n o f t h e wave c y c l e , and t h e q u a n t i t i e s t h e m s e l v e s

f l u c t u a t e f r o m wave t o w a v e . The average p o s i t i o n o f t h e s e q u a n t i t i e s was meastired v i s u a l l y i n a s t a n d a r d manner b y two o b s e r v e r s , b u t i n s p i t e o f t h e s t a n d a r d i z a t i o n , t h e o b s e r v a t i o n s a r e s t i l l somewhat s u b j e c t i v e .

I n e v a l u a t i . n g t h e s e measurements i t i s n e c e s s a r y t o know what i s t h e agreement c"^ong r e p e a t e d measurements o f t h e same q u a n t i t y b y one o b -s e r v e r ( r e p e a t a b l l j l y ) and what i -s t h e d i f f e r e n c e between mea-surement-s o f t h e same q u a n t i t y t y d i f f e r e n t o b s e r v e r s ( o p e r a t o r v a r i a t i o n ) . I f i t can be assumed t h a t t h e average v a l u e s o f t h e q u a n t i t i e s can be measured i n t h e i n t e r v a l o f o b s e r v a t i o n ( a b o u t 1 m i n u t e ) , t h e n t h e r e p e a t a b i l i t y and o p e r a t o r v a r i a t i o n g i v e measur-es o f t h e a c c u r a c y o f t h e m e t h o d .

Over a s i x week i n t e r v a l , y ' , y ' , and 9 were measured 3 t i m e s b y one o b s e r v e r f o r t h e c o n d i t i o n s o f lest I V 2. I n Table B , t h e r e p e a t a b i -l i t y o f y ' and y ' seems a b o u t t h e same, and t h e maximum r a n g e i n any o f t h e 9 s e t s o f r e p e a t e d y ' and y ' r e a d i n g s i s 0 , l 6 f e e t . The i m p o r t a n t q u a n t i t y here i s y ' - y ' , t h e d i s t a n c e between b r e a k e r p o i n t and r u n u p l i m i t w h i c h i s on t h e o r d e r o f 2 f e e t i n t h e s e t e s t s . I f i t i s assumed t h a t any measurement i s w i t h i n 0.08 f e e t o f t h e mean, t h e n t h e 'most p r o b a b l e ' e r r o r i n y ^ - y ^ ( T o p p i n g ,

(2I4))

i s

(0.08^ + 0.082)1/2

o r 0.11 f e e t o r about 5 per c e n t o f y ^

-I n a l l b u t k o f t h e 38 t e s t s i n v o l v i n g t y p e B d a t a t h e measurements were r e p e a t e d by a second o b s e r v e r . The o p e r a t o r v a r i a t i o n , i n d i -c a t e d b y Table 3, haa-maximum r a n g e s o f 0.23 f e e t f o r measurements o f y ' and 0,09 f e e t f o r y ' . I n t e s t s I I 2, I I I 2 , I V 2, t h e a b s o l u t e v a l u e o r o p e r a t o r v a r i a t i o n averages 0,12 f e e t f o r y ^ and O.O3 f e e t f o r y ^ , b u t t h e d i f f e r e n c e s betweem t h e average y ' and y ' o f each o b s e r v e r m t h e s e 3 t e s t s i s o n l y O.Oi; f e e t and 0.02 f e e t . T h i s i n d i c a t e s t h a t y ^ i s s u b j e c t t o g r e a t e r i m c e r t a i n t y t h a n y ^ , b u t t h a t s y s t e m a t i c d i f f e -r e n c e s between o b s e -r v e -r s a -r e s m a l l . The e x p e -r i m e n t a l d a t a p -r e s e n t e d i n t h i s r e p o r t (see Appendix) i s based on t h e average j.^ and y ^ o f t h e two o b s e r v e r s .

I n Table 3, t h e r e p e a t a b i l i t y o f measurements o f 9^ i s shown t o be w i t h i n 8.5 d e g r e e s , o r 3.5 degrees i f one measurement i s e l i m i n a t e d ,

f o r 5 s e t s o f 3 r e a d i n g s . For t h e same d a t a , t h e o p e r a t o r v a r i a t i o n ranges up t o 6 d e g r e e s . U n l i k e measurements o f y ^ and y ' , t h e r e i s a s y s t e m a t i c d i f f e r e n c e between t h e measurements o f t h e two o b s e r v e r s

(see Table k ) , b u t s i m i l a r t o t h e t r e a t m e n t o f y ^ and y ^ d a t a , t h e v a l u e s o f t h e a n g l e p r e s e n t e d i n t h i s r e p o r t a r e t h e average 9^ o f t h e two o b s e r v e r s . T h i s c h o i c e o f 9 ^ , a c r i t i c a l v a r i a b l e i n t h i s s t u d y , i s e x p l a i n e d l a t e r .

T A B L E 3

R E P E A T A B I L I T T A N D OPERATOR V A R I A T I O N POR 9^ MEASUREMENT ( T E S T I V 2)

Measurement y ' ( i n f t , ) y ^ ( i n f t . ) 9^ ( i n d e g . ) Observer C J G • R L B " ' * ' C J G R L B C J G R L B D i s t a n c e a l o n g Beach i n f e e t k 2.82

0.5U 23.5

2.76 3.0U,2.79 0.52 0.50 32 26

2,91 O.Iió 28.5 7 2.73 O.iió 27

2.86 2.73 0.li2 0.39 30 30.5

2.86 0.37 29

11 2.68 26

2.7h

2.70 28 31

2.66

26

15 2.U2 0.32 26.5

2.ii9 2.71,2.62 0.31 0.29 29 33.5

2.i;9 0.17 28

18 2.31 0.35 29

2.32 2.29 0.3^,0.19 0.25,0.2130.5 32.5

2.33 0.31 29

'"Measurements t a k e n on 8/3I/63, 9 / 6 / 6 2 , I O / I I / 6 2 Average d i f f e r e n c e y ^ -- y ^ - ' 2 , 2 5 f t . Measixrements t a k e n on

9/6/62

TABLE h

OPERATOR VARIATION I N AVERAGE BREAJ<ER ANai.,E

S e r i e s D a t e A 9^ 9, AVE xn degrees m degrees _ _ _ _ _ - ^ ^ ^ y - j ^ 2 2 . 6 U ~ ~ "T^ I I I March I 9 6 3 2 . 3 9 8 I V S e p t . 1962 3 . 8 7 17 b " b AV ( R L B ) ' b AV ( C J G ) 17

E . Change i n Mean Water Level^^jJT^j^^e J J ^ J k ^ ^

D e f i n i t i o n s . The eleA^ation o f t h e s u r f a c e o f a motionl^ess body o f w a t ë F T s ~ d ë f I n e t i as t h e s t i l l w a t e r l e v e l (oWI,) . The i n t e r s e c t i o n

o f t h e s t i l l w a t e r l e v e l with a } i l a n e boaoh i s c a l l e d t h e s t i l l water

l i n e (wSWIAne) , a terin approxlin-itely e q u i v a l e n t t o s h o r e l i n e . The time average e l e v a t i o n o f a movjng w a t e r jna^face i s d e f i n e d as t h e mean water l e v e l (MWL) . The e l e v a t i o n oJ' t h o mean w a t e r l e v e l measured p o s i t i v e l y upward f r o m t h e r r b i l l w a t e r l e v e l i d e f i n e d as t h e s e t u p e l e v a t i o n , e,

(see F i g i i r e 10) .

e = m\. ~ GWl. [51

L i t t l e i s known o f e , e x c e p t t l i a t i t depends on wave energy b r o u g h t t o t h e beach and i s d i r ; t i n g u i : ï h e d f r o m w i n d or t i d a l s e t u p . V a r i a t i o n i n t h e energy s u p p l i e r ! b y wave" t o n a t u r s l beaches causes t h e

F i g u r e 1 0 . D e f i n i t i o n S k e t c h

MWL t o f l u c t u a t e . Because wave s e t u p i s a meas\ire o f one mechanism o f e n e r g y d i s s i p a t i o n i n t h e s u r f zone, njeasurements were made t o e v a l u a t e i t s i m p o r t a n c e .

Piezometer c o n d u i t s and w e l l s . E i g h t 10 f e e t l o n g p i e z o m e t e r c o n d u i t s were imbedded f l u s h w i t h t h e s u r f a c e o f the smooth c o n c r e t e b e a c h , and

e x t e n d i n a d i r e c t i o n p e r p e n d i c u l a r t o t h e s h o r e l i n e a t h f o o t i n t e r v a l s a l o n g t h e beach (see F i g u r e 2 ) . The c o n d u i t s , c o n s i s t i n g o f n e s t e d aluminum c h a n n e l s , c o n t a i n 6 smootlxLy p o l i s h e d l / l 6 - i n c h p i e z o m e t e r t a p s so t h a t h o f t h e s e t a p s l i e i n or near t h e s u r f zone (see F i g u r e 11) , Three e i g h t h i n c h I D l y g o n t u b i n g l e a d s f r o m each p r e s s u r e t a p t i i r o u g h t h e p i e z o m e t e r c o n d u i t and a m a n i f o l d t o a p i e z o m e t e r w e l l , w h i c h i s a U~inch ID t u b e w i t h a hook gage t o measure w a t e r l e v e l (see F i g u r e 12) . The l a r g e r a t i o o f w e l l - t o - t u b i n g d i a m e t e r and t h e highl^y v i s c o u s f l o w i n t h e t u b i n g (]F( 10) so damps t h e f l u c t u a t i o n o f t h e w a t e r l e v e l i n t h e p i e z o m e t e r w e l l t h a t c a r e f u l o b s e r v a t i o n w i t h a hook gage and f l a s h l i g h t i s r e q u i r e d t o see any p e r i o d i c r e s p o n s e t o wave m o t i o n i n t h e b a s i n . The ^/iscous damping and d i a m e t e r r a t i o a r e such t h a t 5

m i n u t e s a r e r e q u i r e d f o r t h e w a t e r l e v e l i n t h e t u b e t o a d j u s t t o a change o f one mm. i n t h e SWL o f t h e b a s i n .

Measurement o f e . From t h e d e f i n i t i o n o f e q u a t i o n 5, i t i s n e c e s s a r y t o measure MWL t o o b t a i n e . SWL was measured i n t h e p i e z o m e t e r w e l l b y r a i s i n g t h e hook gage t o t h e r e f l e c t i o n o f a f l a s h - l i g h t s h i n i n g o n t h e w a t e r s u r f a c e . The wave g e n e r a t o r was t h e n s t a r t e d and a l l o w e d t o r u n

f o r 2,5 m i n u t e s . Then t h e l o c a l mean p r e s s u r e a t t h e t a p s was o b t a i n e d b y c o n n e c t i n g t h e d i f f e r e n t t a p s , one a t a t i m e , t o t h e w e l l t h r o u g h t h e m a n i f o l d , and measuring t h e s t e a d y s t a t e l e v e l i n t h e w e l l w i t h hook gage and f l a s h l i g h t . Steady s t a t e l e v e l was a t t a i n e d i n t h e w e l l when s u c c e s s i v e r e a d i n g s o f t h e w a t e r s u r f a c e , t e n minutes a p a r t , had a v a r i a t i o n o f no more t h a n 0.1 mm.

A f t e r some p r a c t i c e , r e a d i n g s c o u l d be made b y d i f f e r e n t o b s e r -v e r s w i t h an o p e r a t o r -v a r i a t i o n o f no more t h a n 0.2 mm. P r e c i s i o n was 0.1 mm. The t i m e o f each measurement was always r e c o r d e d .

The f i n a l SWL measured a t t h e end o f t h e t e s t was a l m o s t always l o w e r t h a n t h e i n i t i a l SWL. This drop i n SWL was r e c o r d e d t h r o u g h t h e t e s t a t a damped p i e z o m e t e r w e l l i n a q u i e t s e c t i p n o f t h e b a s i n ( w a t e r l e v e l p o i n t gage o f F i g u r e 2 ) . From t h e r e c o r d o f t h i s p o i n t g a g e , t h e

' e v a p o r a t i o n c o r r e c t i o n ' , as much as 1.0 mm. i n a d a y ' s r u n c o u l d be computed f o r t h e d i f f e r e n t t i m e s o f p r e s s u r e t a p measurements. I n d i -c a t i o n s f r o m t h e o r y and e x p e r i m e n t are g i v e n l a t e r t h a t t h e p i e z o m e t e r t a p b e n e a t h t h e waves measures t h e mean h y d r o s t a t i c head, and t h u s i n d i c a t e s MWL.

F . V e l o c i t y Measurement ( l y p e D Equipment and P r o c e d u r e )

V e l o c i t y i n t h e l o n g s h o r e c u r r e n t was measured by j o i n t use o f f l o a t s and a v e l o c i t y probe ( p r o p e l l o r - t y p e m i n i a t u r e c u r r e n t m e t e r ) . The f l o a t s were r e c t a n g u l a r s o l i d s o f s o f t w o o d 5 / 8 - i n c h by 5 / 8 - i n c h b y 5 / l 6 - i n c h w h i c h f l o a t e d about I / I 4 above w a t e r when w e t . The v e l o c i t y p r o b e was an A r m s t r o n g M i n i f l o w m e t e r AWE

I 8 3 A

ISSUE A w h i c h c o u n t s

e l e c t r o n i c a l l y t h e r e v o l u t i o n s o f a j e w e l - m o u n t e d p r o p e l l e r i n a 5 / 8 - i n c h d i a m e t e r h o u s i n g (see F i g u r e I 3 ) . When a c t u a t e d b y u n i f o r m f l o w i n t h e d i r e c t i o n o f t h e p r o p e l l e r a x i s , t h e s e c o i m t s are c o n v e r t a b l e t o v e l o c i t y u s i n g t h e m a n u f a c t u r e r ' s c a l i b r a t i o n c u r v e . T h i s c u r v e was r e p e a t e d l y checked i n a t o w i n g t a n k and f o u n d t o be a c c u r a t e t o w i t h i n 2 p e r c e n t .

However, t h e r e s p o n s e o f t h e probe depends upon i t s o r i e n t a t i o n w i t h r e s p e c t t o t h e v e l o c i t y v e c t o r o f t h e f l u i d , and s i n c e f l u i d

v e l o c i t i e s i n t h e s u r f zone v a r y i n an unknown manner, b o t h i n m a g n i t u d e and d i r e c t i o n , t h i s i n s t r u m e n t cannot be used d i r e c t l y t o measure l o n g -s h o r e c t i r r e n t v e l o c i t y . L i n e a r r e l a t i o n -s were f o u n d t o e x i -s t between t h e a p p a r e n t v e l o c i t y g i v e n by t h e p r o b e when a l i g n e d w i t h t h e l o n g s h o r e c \ i r r e n t and t h e mean s u r f a c e v e l o c i t y o b t a i n e d b y t i m i n g t h e t r a v e l o f t h e f l o a t s . C a l i b r a t i o n s were developed f o r S e r i e s I I , I I I , and I V by comparing t h e maximum i n d i c a t e d v e l o c i t y a t a s t a t i o n w i t h l o c a l f l o a t

7 X 2 VERTICAL EXAGGERATION FEET

F i g . 1 1 L o c a t i o n o f Taps f o r Damped P i e z o m e t e r s

MOUNT FOR HOOK GAGE

C PIEZOMETER W E L L 0 FEET TO BASIN AND PIEZOMETER TAPS MANIFOLD F i g . 12 P i e z o m e t e r W e l l 20

v e l o c i t y (see F i g u r e l i ; ) . D u r i n g t h e s e t e s t s t h e p r o b e was a t m i d - d e p t h , midway between t h e b r e a k e r l i n e and t h e SWLine.

C e r t a i n c a u t i o n s must be o b s e r v e d when u s i n g t h e s e c a l i b r a t i o n c u r v e s 1 . The s c a t t e r i s n o t random b u t r e p r e s e n t s i n p a r t , a v a r i a t i o n i n %•

2 . They may be i n e r r o r when a p p l i e d t o p r o b e p o s i t i o n s ( i n t h e y d i r e c t i o n ) d i f f e r e n t f r o m t h a t used i n c a l i b r a t i o n . I n o t h e r w o r d s , i n d i c a t e d v e l o c i t y v a r i a t i o n s i n t h e y d i r e c t i o n may be a c t u a l l y due t o a c h a n g i n g c a l i b r a t i o n . This i s p a r t i c u l a r l y l i k e l y i n s h o r e o f t h e SWLine where t h e p r o b e i s o f t e n exposed d u r i n g p a r t o f t h e wave c y c l e .

I n 31 t e s t s w h i c h i n c l u d e d t h i s t y p e o f d a t a , v e l o c i t y was measured w i t h t h e probe a t l e a s t and u s u a l l y 7, s t a t i o n s a l o n g t h e beach and

a t each s t a t i o n 3, ,U, o r 5 measurements were made on a l i n e p e r p e n d i c u l a r t o t h e s h o r e l i n e i n t h e s u r f zone (see A p p e n d i x , Table A 7 ) . Each i n d i -c a t e d p r o b e v e l o -c i t y i s t h e average o f 50 se-conds o f -c o i m t i n g . Whenever p o s s i b l e , p r o b e e l e v a t i o n was a t t h e e s t i m a t e d mean d e p t h .

The d i s t a n c e t r a v e l e d b y t h e f l o a t s i n an i n t e g r a l number o f wave p e r i o d s (U o r 5) was measured w i t h a t a p e f o r two s e c t i o n s o f t h e

beach i n each o f t h e 31 t e s t s . By assuming t h e v e l o c i t y v a r i e d l i n e a r l y between t h e s e two s e c t i o n s , t h e mean f l o a t v e l o c i t i e s w e r e a d j u s t e d m a l l t h e t e s t s t o comnion p o s i t i o n s 10 f e e t and l 6 f e e t f r o m t h e u p s t r e a m t r a i n i n g w a l l . The n e c e s s a r y a d j u s t m e n t was made as s m a l l as p o s s i b l e by t h e i n i t i a l c h o i c e o f t h e s e c t i o n over w h i c h t o measure t h e f l o a t t r a v e l . Each f l o a t v e l o c i t y i s t h e average o f 10 measurements d u r i n g w h i c h measurements t h e f l o a t s d i d n o t g r o u n d on t h e b e a c h .

TAHLl!; 5

DYE Al'JD FLOAT VEI.0C1TY IN LONCSHOtdjl GUIdÜilNTS

Test Dye V e l o c i t y ' " " F l o a t V e l o c i t y f t / s e c . f t / s e c . I l l 2 l o 3 1 1.33 I I I I ; 1.'13

1.15

I I I 6 0.97

\ a c h number i s t h e average o f 5 measui'ements o v e r t h e downstream s e c t i o n o f b e a c h . M i d -p o i n t o f dye -p a t c h was t i m e d . 1.33 1.32 1.2)4 1.23 1.00 21

F i g . 13 V e l o c i t y Probes

a

FLOAT VELOCITY, Vf, IN FEET PER SECOND

F i g . Ih C a l i b r a t i o n o f V e l o c i t y Probes w i t h S u r f a c e F l o a t s