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