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CHAPTER

216

VERTICALSTRUCTUREOFTHENEARSHORECURRENTAT

DELILAH:

MEASURED

AND

MODELED

Jane

McKeeSmith

1

,

lb

A.

Svendsen

2

,

and

Uday

Putrevu

3

ABSTRACT:

omprehensiveield

easurements

ereadefhe

vertical

current

structureona

barredbeach

profile

atth eDELILAH

project

duriiigctober

f

990.

he

urrentas

easured

ith

ive

electromagnetic

urrent

etersountedn obileledhichas

stationedatthree

to

eightcross-shorepositions.

he

incidentdirectional

wave

spectra,

bathymetry,

tide,

wind,

andcross-shorewave

transformation

were

also

measured.numerical

model

wasdeveloped

to

calculatethe

random

wave

ransformation

basedonhemodelf

Dally,

ean,nd

Dalrymple

(1985)

Larson

and

Kraus

1991)

and

th e

local

vertical

current

structure

(Putrevu

and

Svendsen

1991).

he

model

predictedth eshape

of

th e

currentprofileswell

witharoot-mean-squareerrorinvelocityof5.9

cm/sec.

hemodeltended

to

underpredict

th e

velocity

over

th e

barcrest.

INTRODUCTION

Predicting

he

vertical

tructure

of

th e

cross-shore

current

s

a

critical

tep

o

advancingth emodeling

ofbeachevolution,especially

th eresponseofth ebeach

profile

to

storms,

the

post-storm

profile

recovery,

and

th e

development

and

movement

of

bars.

he

cross-shore

currents

havealsobeen

shown

to

be

mportant

in

describing

the

mixing

for

longshore

currents

(Putrevu

and

Svendsen

1992,

Svendsen

and

Putrevu

1992b).he

lack

of

high-qualityfield

measurements

of

th evertical

current

structure

has

been

a

hinderance

toth e

development

and

validationof cross-shore

current

models.

In

October

of

1990,

a

comprehensive

field

experimentwas

performed

at

th e

U.S.

ArmyEngineerWaterwaysExperiment

tation,

oastal

ngineering

Research

enter

'Res.

Hyd.

Engr.,

US

Army

Engr.

Waterways

Exp.

Sta.,

Coast.

Engrg.

Res.

Center,

3909

Halls

Ferry

Rd.,

Vicksburg,

MS9180-6199,

USA.

2

Prof.,

Dept.

ofCivilEngrg.,

Univ.

ofDelaware,Newark,

DE

19716,

USA.

3

Res.

Assoc,Dept.

of

Civil

Engrg.,

Univ.

ofDelaware,

Newark,

DE 19716,USA.

2825

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2826

OASTAL

ENGINEERING

1992

(CERC),

FieldResearch

Facility

FRF)

n

Duck,NC,

o

measurethewind-

and

wave-

forced

three-dimensional

nearshorehydrodynamics.heDELILAH(Duck

Experiment

on

Low-frequency

and

Incident-band

LongshoreandAcross-shore Hydrodynamics)experiment

wasa

cooperative

projectinvolving

researchersfromCERC,Naval

Postgraduate

School,

Naval

Research

Lab,

Oregon

State

University,

Quest

Integrated,

Inc.,

Scripps

Institution

of

Oceanography,

Universityof

California

atSanta

Cruz,andWashingtonState

University.

The

hydrodynamic

data

collectedat

DELILAH

were

used

to

efine

and

verify

a

numerical

model

developed

tocalculate

the

vertical

variation

of

thecross-shore

current.

Thepurpose

of

thispaperisto

describetheDELILAH

field

measurementsandto

describe

the

applicationof

these

data

to

evaluate

the

numericalmodel.

DELILAHFIELDPROJECT

The

core

of

the

DELILAH

field

project

was

a

fixed

array

of

19

electromagnetic

current

meters

deployed

in

one

cross-shore

array

and

twolongshore

arrays

to

th e

north

of

the

FRF

pier.

he

cross-shore

array

consisted

of

nine

sensor

positions,extendingfromthe

shoreline

to350moffshore4-m

depth).

pressuregage

wasdeployed

alongwith

a

current

metert

ach

position

n

heross-shorearray.he

ongshore

arraysere

positionedapproximatelyon

hebarcrest

andnthe

trough

ofthebeach

profile.he

longshore

arrays

were

approximately

200

m

long.

The

bathymetry

adjacenttoth ecurrentmeter

arrays

340

mby

600

m

area)

was

surveyeddailyduring

the

experiment.

ccuratesurveying

was

accomplished

with

a

special

self-contained

vehicle,

th e

CRAB(Coastal

Research

Amphibious

Buggy),

that

drove

along

surveytransects

(Birkemeier

andMason

1984).

he

position

andelevation

oftheCRAB

wasdeterminedwith

a

Geodimeterauto-trackingelectronic

totalstation.ig .

hows

an

exampleof

th e

bathymetry

surveyed

on

19

October1990.

he

bathymetrywasgenerally

homogeneous

in

the

longshoredirectionduring

th e

cross-shore

current

measurements,

with

a

inear

bar

pproximately

00

offshore.

ffshore

directional

wave

pectra

were

measuredwithan

arrayof

sixteen

pressure

gagesat

th e8-m

depthcontour.pectra

were

measured

every3hours

during

th eexperimentand

provide

offshore

boundaryconditions

fo rwaveorcingof

heurrentmodel.ig .howshewo-dimensionalpectrum

measuredon

19October

1990

at

1300.

n

Fig.2 ,th e

x-axis

is

th e

frequency,/,

the

y-axis

is

the

wave

direction

(measured

counter-clockwise

from

shore

normal),

6,

nd

the

z-axis

istheenergy

density,S.

ver-waterwinds

andtidalelevationweremeasured

at

th e

FRF

pier.

CROSS-SHORECURRENT

MEASUREMENTS

The

vertical

tructure

ofth e

current

wasmeasuredwith

a

vertical

array

offive

electromagneticcurrent

meters

mounted

ona

mobile

sled.

he

meters

weremountedat

elevations

0.35

m,0.6

m,1 .0

m,

1.35

m,and

1.75

m

above

th e

bed

on

a

vertically

sloping

beam.he

beamwas

parallel

to

th eshoreline,

o

the

meters

were

aligned

in

the

cross-

shore.

he

meters

were

spreadovera

longshore

distance

of

approximately3.5

m.

he

sled

was

always

deployed

so

that

the

lower

end

of

th e

beam

was

in

the

updrift

direction

of

the

longshore

current

to

reduce

interference

of

the

flow.

common

timing

pulse

was

used

forall

th ecurrent

meters

to

reduceinterference between

instruments

forthiscloseproximity

deployment. Theeters

measured

he

ongshoreand

ross-shore

componentsof

he

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DELILAHVERTICALSTRUCTURE

2827

Figure

1 .

athymetry

fo r

19October

1990.

Figure

2 . Two-dimensionalspectrumfo r19

October

1990.

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2828 COASTAL

ENGINEERING

1992

current.hesledwasalsoinstrumentedwithapressure

gage,

aresistance

wave

staff,

and

an

anemometer.

Duringtheexperiment,

he

sled

was

owed

offshore

ofth e

breaker

zone

by

the

CRAB

to

a

depth

of

approximately

3

m.

he

sled

was

thenpulledback

to

shore

with

a

fork

lift

in

steps

of

20

m.t

each

sledposition,

data

were

collected

for

34

minutes.he

collection

period

of

34minuteswas

selectedto

balance

th e

competingneeds

fo r

long

time

series

for

stablestatistics

and

short

total

time

for

the

sled

deployment

toensure

stationarity

of

the

incident

waves.

ll

currentdatapresented

are

34

minute

averages.

he

data

were

telemeteredohore

for

eal-time

dataqualitychecking.

hree

o

ight

cross-shore

positions

were

occupied

during

each

of

eight

deployments.he

position

andorientation

of

th e

sled

wererecordedusing

an

electronic

totalstation

which

sighted

two

prisms

located

on

the

sledmast.

The

sledwas

deployed

near

th e

cross-shore

array

of

current

meters

and

pressure

gages.hefixedarraygagesprovidedbackgrounddataon

the

horizontal

structure

of

the

hydrodynamicsand on

the

stationarityof

the

waves

and

currents.

ig .

3shows

an

example

ofth e

vertical

structureofthe

cross-shore

current

measuredduring

DELILAH.The

vectors

in

Fig.

epresent

ross-shorecurrentmagnitudeand

direction

measured

t

ix

led

positions

on

19October

1990.

he

solidlines

in

Fig.

3

epresent

th e

survey

datum

and

bottom

profile

d).

led

measurements

eremadeuringhe

inal

ixdaysf

he

DELILAH

experiment.

ncidentwavesduringthesedays

provided

avarietyof

conditions

with

wave

heights

of 0.5

to1.5m,

peak

spectralperiodsof5to15sec,

windspeeds

of5

to5

m/sec,and

wave

directions

bothnorth

and

outh

ofshorenormal.he

maximum

time-averagedcurrent

velocities

exceeded0.5m/secduring

measurements

with

thesled.

0.5m/s

T-

v

K)

date

=

901019

t ime

=

1200

T

100

120

140 160

180 200

220

DistanceOffshore

m)

2 40

2 60

Figure3 . Cross-shorecurrent

velocities

measured

during

DELILAH

(1 9Oct

1990).

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DELILAH

VERTICAL

STRUCTURE

829

NUMERICAL

MODEL

The

numerical

model

consistsof

twoparts,arandomwavetransformationmodel

and

amodel

of

the

cross-shoreflow.hewavetransformationmodelprovidesthecross-

shoregradient

in

wave

height

and

thecross-shore

variation

in

the

mean

water

level

which

arethe

driving

forcesof thecross-shoreflow.he

modelsassume

longshorehomogeneity,

linear

ave

heory,

nd

teady-state

aveorcing.

ave-current

nd

ave-wave

interactionsandlongwavegenerationareneglected.

WaveTransformation

Therandom

wavetransformation

models

based

onthedecay

and

eformation

model

of

Dally,Dean,andDalrymple

(1985)

as

appliedto

randomwavesby

Larson

and

Kraus(1991).heDally,Dean,

and

Dalrymplemodelhasbeenshowntobelessaccurate

than

other

models

or

predicting

wave

etup

Svendsen

and

Putrevu

992a),

he

main

driving

forceortheundertow,but

it

was

chosen

because

it

includes

a

mechanism

for

breakingwavestoreforminthetroughshoreward

of

thelongshore

bar.

heinput

wave

parametersare

theroot-mean-squarewave

height

(J?J,

peak

wave

period,and

peak

wave

directionmeasuredatthelineararrayinadepthof8

m.

ne

hundredwaveheightswere

randomly

chosen

froma

Rayleigh

distribution

specifiedby

H^.

ach

of

the

one

hundred

wave

heightswasransformedacrosshebeachprofile,

assuming

the

same

periodand

incidentdirectionfor

each

wave,

accordingto

d Fcosd)

K

/?

.

1)

dx

where

F

0.125

pgffC

g

,energy

flux

pwaterdensity

g

gravitationalacceleration

H ndividualwaveheight

C

g

groupvelocity

6wavedirection,relativetoshorenormal

xcross-shore

coordinate,

positive

seaward

d

total

water

depth

(still-water

plus

setup)

F,

table

energy

fluxassociatedwiththe

stable

waveheight,H,

H

Vd,

with

r

=

0.4

(Dally,

Dean,

andDalrymple1985)

TheparameterK

is

zeroseawardof

wavebreaking,with

breakingspecifiedbya

heightto

depth

ratio

less

than

0.78.

t

incipient

wave

breaking,Ks

set

to0.15.

Wave

breaking

ceases

when

thebroken

height

is

less

than

H

and

K

is

reset

tozero.he

wave

directions

are

determined

by

Snell'slaw.

he

wave

parameters

were

calculated

at

a

1-m

cross-shore

spaced

gridusing

an

explicit

finite

difference

solution.

The

H ,

was

calculated

at

each

grid

point

fromthe

100

individualwaveheights.

The

wave

setup,

j,

s

calculated

fromthe

time-

anddepth-averaged

cross-shore

momentum

equation

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2830

OASTALENGINEERING

1992

PSfr

i)

P C WW

2)

f c

t c

where

h

=till-waterdepth

(including

th e

tide)

p

a

=

air

density

C

w

=

winddrag

coefficient

W

wind

speed

W

x

=ross-shore

component

ofthewindvelocity

S

=cross-shore

component

of

radiation

stress

Thetwo

driving

forces

ofth e

setupare

the

gradient

in

radiation

stress

and

th ecross-shore

wind

stress.

he

radiation

stressis

calculated

using

linearwave

theory

(Longuet-Higgins

and

tewart

964)

basedn

H^.

onsidering

heimplifying

ssumptionsused

o

representtherandomwavefield,

a

more

ophisticatedevaluationof

theradiationstress

(Svendsen

and

Putrevu

1992a)

s

not

justified.he

wind

drag

coefficient

givenby

the

WAMDIGroup(1988)isadoptedinth emodel

C

=0012875for

W

7.5

m/sec).he

bedshearstress

is

known

to

be

small

and

isneglectedin

Eq.

2 .ne

iteration

was

required

between

thecalculation

of

the

wave

height

transformationandth e

wave

setup.

TheCross-shoreCurrent

The

vertical

variation

of

th e

current

is

modeled

with

a

three-layer

approach

(Hansen

andSvendsen

1984;

Stiveandde

Vriend

1987;

Svendsen

and

Hansen1988).he

velocity

distribution

inthe

central

ayer

s

calculatedas

a

localolution

of

thedepth-dependent,

cross-shore

momentumequation

with

th e

surface

andlowerlayers

contributingboundary

conditions.he

central

layer

extends

from

the

bottom

boundary

layer

to

thetrough

level.

Thelowerlayer,

th ebottom

boundarylayer,

relatesth enearbottomcurrent

velocity

to

the

mean

bottom

stressSvendsen

and

Putrevu1990).

he

upper

layer

contributes

themass

flux

which

is

balancedbyth e

undertowin

the

centrallayer.n

th e

present

application,

it

is

assumed

thatno

net

cross-shoreflowexists,i.e.,th e

massfluxabove thetroughbalances

the

undertow.

orcing

fo r

th evertical

variation

includes

gradients

in

radiation

stress,

mean

current,

and

etup.

he

horizontal

gradient

terms

n

th e

model

are

calculated

rom

th e

depth-integrated,

one-dimensional

model

describedabove.

The

vertical

currentstructure

iscalculated

from

a

double

integration

of

the

depth-

dependent,

cross-shore

momentumequation(PutrevuandSvendsen

1991)

U

h

a

Si

3

2v

z

pv

fz

where

f

=verticalcoordinate,measuredpositivefromthebottom

U

=cross-shore

velocityatelevation

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DELILAH

VERTICAL

STRUCTURE

83 1

r

ta

bottom

stress(Eq.

4)

U

b

=bottomvelocity

(Eq.5)

adrivingforce

for

th eundertow

(Eq.6)

v

a

ddy

viscosity

(Eq.

8)

In

deriving

Eq.

both

and

K

have

beenassumedconstant

over

depth.

The

bottom

boundaryconditionincludes

the

bottomstress

where

f

=bottomfrictionfactor

u

0

=

wave

orbital

velocity

at

th e

bottom

and

the

bottom

velocity.

hebottom velocity

is

determined

fromth e

depth

integrationof

Eq.3

with

Eq.

4

substituted

for

th e

bottomstress

u

ad

t

2

6v

*

du

0

U

b

L 5)

2ltv

*

where

4

=

depth

totroughlevel

U =

meanundertow

velocity

(Eq.

7)

Thedrivingforcein

Eqs.

3and5is

given

by

dn ndU

-

.

dx

x

w

x

p

d

t

g

*3.

uj

+

22 Il

6 )

where

u

w

isthe

depth-averaged

wave

velocityand

p

a

is

thedensity

of

air.

he

boundary

condition

from

theupper

layer

isthemasstransport

above

the

trough

elevation,which

balancestheundertow.hemasstransportisproportionalto

CEP/d,whereCisthewave

celerity,

andthe

constantofproportionality

was

foundto

be

approximately

-0.3

based

on

theundertow

measurements.

ThemeanundertowinEq.5is

given

by

U

-3

Vg(A

ri)g

2

cos6

7)

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2832

COASTALENGINEERING1992

In

the

numerical

computations

we

have

used

th esame

eddy

viscosityat

alldepths,

given

by

v

w

o.05

-

om^g H*i\)

k

h*i\),

(8)

where

the

subscriptb

indicatesincipient

breaking

conditions.nlaboratory

experiments

on

a

plane

beach,

K

has

been

foundto

vary

as

hVgh.

he

simplification

of

constantp

e

is

chosen

because

he

depth

over

he

egion

of

th eDELILAH

measurementsvaries

only

between

1.2

and

2.2m,

and

little

information

is

availableabout

the

variation

of

a

under

field

conditions.

MODELRESULTS

The

model

was

applied

to

th e

8

cases

of

DELILAH

sled

data.

heresults

from

3

cases

are

hownin

Figs.

4

hrough

9.

hese

cases

were

elected

becausethey

cover

a

variety

of

conditions

with

th e

largest

number

of

sledpositions.hese

casesare

typical

of

theconditionsandmeasurements

during

th e

final

week

of

DELILAH.

able

1

summarizes

th einput

conditions

forthecases

hown

in

Figs.

4

through

9.

he

wind

< j > nd

wave

directionsaremeasuredounter-clockwise

rom

horenormal.he

nputpeak

wave

direction,0,

andpeakspectral

period,T

,weremeasuredat

the

8-marray.hepeakwave

parameters

best

representthe

dominantwave

characteristics.

ig.2

hows

considerable

spreadn

hedirectionaldistribution

of

waveenergy,hichcould

trongly

nfluence

longshorecurrents,

buthas

less

effect

on

cross-shore

currents.

heinputwaveheight

was

taken

from

the

most

eaward

of

the

nine

nearshore

pressure

gages

4-m

depth),

and

the

height

wasnversely

efractedandhoaledto

he8-mdepth

ocorrespond

o

he

wave

direction

nd

eriodnputs.

he

height

measured

t

he

-m

rray

aused

5

overprediction

of

he

wave

height

at

he

most

eaward

pressure

gage,hich

may

be

attributableto

the

useoflinearrefraction

andshoaling

in

the

model.

he

tideand

wind

measurements

ere

ade

theRF

ie r

ndreveragedaluesverheled

deployment.or

thesecases,

he

ledwasdeployed

spanning

low

tide

to

minimizethe

effectofvaryingtideelevation.

Table

1 .odelinput

conditions

fo rsampleresults.

Date

Time

(m)

e

(deg)

(sec)

Tide

(m )

W

(m/s)

(deg)

10/17 1000

0.54

-15.0

9.7

-0.47

7.8

130.5

10/18 1100

0.57

-43.0 5.6 -0.62

11.9 79.7

|

10/19

1200 0.65 24.0 7.0 -0.48

9.1

-51.9

The

modelresultsare

comparedto

th efield

measurements

inFigs.

4,

6 ,

and8fo r

thecaseslistedin

Table

1.he

figures

howth e

measured

wave

heightfromthecross-

shorearray

(x),

alculated

aveeight

solid

line),

alculatedetupchain-dotline),

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e n

l

CM

X>

DELILAH

VERTICAL

STRUCTURE

_

0.5m/s

2833

da te

=901017

time

=

1000

~r

100 120 140

160

180

200

220

Distance

Offshore

m)

i

240 260

Figure4.Modelresultsversusmeasurements

(17

October

1990).

V

X

CM

O

0.5

m/s

date

=901017

time=1000

1

1 00 1 2 0 140 160 180 200

220

Distance

Offshorem)

~r

n

240 260

Figure5.odelresults

(17

October

1990).

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2834

COASTAL

ENGINEERING1992

.E*-

V

o

-o

0.5

rr/s

date=901018

t ime

=

1 00

120 140

160

1 80

200

2 2 0

Distance

Offshorem)

i

2 40

260

Figure

6.

odel

results

versus

measurements

(1 8

October

1990).

V

-t

K

T

0.5

m /s

date

=

901018

t ime

=

I

100 120

T

140

160

1 80

200

2 2 0

Distance

Offshore

m)

2 40

2 60

Figure

7.

odel

results

(1 8October

1990).

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E

1

C M

to

TJ

I

DELILAHVERTICALSTRUCTURE

_ 0.5

m/s

date=

901019

t ime

=

1200

100 120

140

160

1 80

200

2 2 0

DistanceOffshorem)

2835

T

Figure

8.Modelresults

versus

measurements19

October

1990).

2 40

2 60

E

i_

C M

D

0.5

m /s

date=901019

t ime

=

1200

l

~

100

120

140

160

1 80

2 00

2 2 0

Distance

Offshore

m)

i

2 40

2 60

Figure

9.

odel

results(1 9

October

1990).

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2836

OASTALENGINEERING1992

measured

cross-shore

current

from

th e

sled

(vectors),andth e

calculated

cross-shore

current

atthesledpositions.igs.5,

7,and9

howth ecalculatedcross-shorecurrentat10-m

intervalsto

show th e

cross-shorevariationof

th eundertowprofile.

ffshoreof

th e

breaker

zone,he

profiles

are

airlyuniformover

depth

with

a

mallncrease

n

he

offshore

velocity

near

th e

wave

trough

level.

n

the

region

of

rapid

wave

decay,

on

th e

bar

crest,

theprofiles

show

a

characteristic

parabolicshapewith

highest

velocitiesnear

the

bedand

smallervelocitiesatth e

wave

trough.horewardofth ebar,the

waves

havereformedand

thecurrent

profilesare

uniform

over

depth.

he

cross-shore

velocities

are

low

shoreward

of

the

bar.he

waves

break

againon

thesteep

oreshore,

and

th evelocity

profiles

are

similar

to

those

on

th e

bar.

For

all

cases,

the

bottom friction

factorwas

settoa

constant

value

of

0.01andthe

eddy

viscosityto

a

value

of

0 05 he

model

is

relatively

insensitive

to

value

of

the

bottom

friction

factor,

but

the

hape

of

the

undertow

profiless

ensitive

to

he

value

ofeddy

viscosity.

heoretically,

th e

value

of

the

eddy

viscosity

should

be

lower

in

regions

of

low

turbulence(nowave

breaking)andhigherin

regions

of

intense

turbulence

(breakerzone),

but

ince

he

elationship

between

eddy

viscosity

and

he

modelparameters

snot

well

known,

a

constantvaluewas

applied.lthoughth ewindspeedsweresignificantduring

the

measurements

8

to

2m/sec),he

wind

hadverylittle

influenceon

th e

results.

or

th e

three

cases

isted

nTable

1,

hemaximum

difference

nundertowvelocitybetween

with-andwithout-wind

imulations

was0.005m/secand

heoot-mean-square

RMS)

difference

was

0.0012

m/sec.

TheRMSerror

nth e

cross-shore

current

resultsfor

th e

3casesshownwas

5.9

cm/sec.he

errors

were

mallest

offshore

of

the

crest

of

thebar.

n

the

bathymetry

trough,th emeasured

velocities

weregenerally0to5

cm/sec,

andtheRMS

errorwasof

the

same

order.

hisis

not

surprising

since

th e

low

velocities

are

near

the

accuracyofth e

instruments

andare

usceptible

to

contamination

fromth e

ongshorecurrents

which

are

strongn

th e

rough.

he

argest

RMSerrors

occurred

on

he

top

ofth e

bar

3

o

15

cm/sec),

wherethe

model

tended

to

underpredict

th emeasurements,

although

the

model

predictedtheshapeof

th eundertow

profile

well.

he

model

esultsFigs.

5,7,and9)

show

he

maximumundertow

velocitiesjust

eaward

of

the

crest

of

the

bar,while

the

measurements

howheaximum

velocities

t

he

rest

f

he

bar.

rrors

n

he

calculation

of

th ewave

heightmay

contribute

to

the

underprediction

of

the

undertow

at

the

bar

crest

errorsn

wave

height

are

magnified

by

quaringth ewave

height

tocalculate

radiation

stress).

lso,

previous

laboratory

experiments

have

shown

a

shoreward

shift

in

the

initiation

of

setup

(the

driving

forcein

th e

model)

in

thetransition

region

ofbreaking

waves

Svendsen

1984;Roelvink

andStive

1989).

his

sameeffectmay

account

fo r

the

underprediction

of

the

undertowat

th ebarcrest.

nfortunately,

th emeasurements

arenot

dense

enough

inth e

region

of

thebarcrest

to

resolvethis

issue.

CONCLUSIONS

Comprehensive

measurements

ofthe

vertical

current

structureandth ewaveand

wind

forcing

were

made

duringth e

DELILAH

field

project

in

October

of

1990

on

a

barred

beach

bathymetry.

he

measurements

how

strong

offshore

velocities

over

th e

bar

0.5

m/sec),andvertical

tructure

ofth ecurrent

was

generallyparabolic.

n

the

bathymetry

trough,

the

offshore

currentwas

weak

(0

to

0.05

m/sec)

and

th e

structurewas

uniform

over

depth.ffshoreofthe

bar,

th e

current

wasfairly

uniform

over

depth(0.10

to

0.15

m/sec)

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DELILAH

VERTICALSTRUCTURE

83 7

to0.15m/sec)with

a

smallincreasein

velocity

near

the

wave

trough.

Thenumerical

modeldeveloped

to

calculate

th e

cross-shore

(1-D)

andomwave

transformation

and

verticalcurrent

structurecompared

well

with

the

measurements.he

RMS

error

in

prediction

of

th e

current

was

5.9

cm/sec.

he

model

represented

th e

shape

of

th e

vertical

currentstructurewell,

but

tended

tounderpredict

th ecurrentmagnitudeat

th e

bar

crest.

ACKNOWLEDGMENTS

The

authors

would

like

toacknowledge

th e

team

that

designed

andconstructed

th e

instrument

ledor

DELILAH:

essrs.

Kent

Hathaway,William

Grogg,

and

Eugene

Bichner(CERC)andDr.EdwardThorntonandMr.RobertWyland(NavalPostgraduate

School).

r.

Robert

Guza

(Scripps

Institution

of

Oceanography)

provided

useful

nsight

on

he

ield

calibration

of

current

meters

which

was

greatly

appreciated.

he

research

presented

in

this

paper

wasconducted

under

th e

Nearshore

WavesandCurrentswork

unit,

Coastal

Flooding

andStormProtection

Program,

by

he

US

Army

Engineer

Waterways

Experiment

Station,

Coastal

Engineering

Research

Center.

Permission

to

publish

this

paper

wasgrantedbyth eOffice,

Chief

of

Engineers.

REFERENCES

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Mason,

C.1984). The

CRAB: auniquenearshoreresearch

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Surveying

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Dally,

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Dean,R.G.,

and

Dalrymple,

R.

A.1985).

Wave

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beaches

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Hansen,

J.

.,nd

Svendsen,

..1984). A

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Larson,M.,

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Kraus,

N.C.

1991).

umerical

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eepSea Res.,1(4),529-562 .

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A.

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de

Vriend,

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1984).

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1990).earshore

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