JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106,NO. C6, PAGES 11,623-11,627,JUNE 15, 2001
Nearshore sandbar migration
SteveElgar
WoodsHole Oceanographic
Institution,WoodsHole, Massachusetts
Edith L. Gallagher
Departmentof Oceanography,
Naval Postgraduate
School,Monterey,California
R. T. Guza
Centerfor CoastalStudies,ScrippsInstitutionof Oceanography,
La Jolla,California
Abstract. Field observationssuggestthat onshoresandbarmigration, observedwhen
breaking-wave-driven
meanflowsareweak, may be relatedto the skewedfluid accelerations
associated
with the orbitalvelocitiesof nonlinearsurfazewaves.Large accelerations(both
increasesand decreases
in velocitymagnitudes),previouslysuggestedto increasesediment
suspension,occurunder the steepwave faces that immediatelyprecedethe maximum
onshore-directed
orbital velocities. Weaker accelerationsoccurunder the gently sloping
rear wave facesthat precedethe maximum offshore-directedvelocities. The timing of
strongaccelerationsrelative to onshoreflow is hypothesizedto produce net onshore
sedimenttransport.The observedaccelerationskewness,a measureof the differencein
the magnitudesof accelerationsunder the front and rear wave faces, is maximum near
the sandbarcrest. The corresponding
cross-shore
gradientsof an acceleration-related
onshoresedimenttransportwould causeerosionoffshoreand accretiononshoreof the bar
crest,consistentwith the observedonshoremigration of the bar crest. Furthermore,the
observations and numerical
simulations
of nonlinear
shallow water waves show that the
regionof stronglyskewedaccelerationsmovesshorewardwith the bar, suggestingthat
feedbackbetweenwavesandevolvingmorphologycanresultin continuingonshorebar
migration.
1. Introduction
celerations, as well as fluid velocities, determine sediment
transport. Here, field observations
are presentedthat link
Sandbars
areimportantmorphologicalfeaturesof beaches,
onshoresandbarmigrationwith the cross-shore
variationof
andchangesin theirpositionandheightarea primarysource
fluid accelerationskewness.Additionally,the observations
of beachprofile variability [Lippmannand Holman, 1990]. and numerical simulations of shallow water waves show that
Bars affect nearshore waves and circulation, both of which
the region of stronglyskewedaccelerationsmoves shorecausesedimenttransportand morphologicalevolution,inward with the bar, suggesting
that feedbackbetweenwaves
cludingbeacherosionandaccretion.Cross-shoremovement
and evolvingmorphologycan resultin continuingonshore
of sandbarsmay be importantfor artificial beachnourishbar migrationwhenmeanflowsare weak.
ment[Douglass,1994] andthe transportof sediment-bound
pollutants[Shortet al., 1996] and biota [Jumarsand Nowell, 1984]. During storms,intensewave breakingon the 2. Sandbar Migration
bar crestdrivesstrongoffshore-directed,
near-bottomflows
Offshore sandbarmigration during stormsresultsfrom
(undertow)that result in offshorebar migration [Thornton feedbackbetweenbreaking-wave-driven
undertowandbathyet al., 1996; Gallagheret al., 1998]. Beacheserodedby metricchange[Thorntonet al., 1996; Gallagher et al., 1998].
stormsarereplenishedat leastpartiallyby onshoretransport Observations on the North Carolina coast show that underandbar migrationduringlessenergeticconditions[Aubrey, tow is maximum just onshoreof the sandbarcrest [Gal1979]. However,the causesof shorewardbar migrationare lagher et al., 1998; Feddersenet al., 1998]. As the bar
not known. Laboratory[Madsen, 1974; Nielson, 1992] and crest moves offshore, so does the location of the maximum
field [Hanesand Huntley, 1986; Osborneand Greenwood, undertow. Assumingno gradientsin alongshoretransport,
1993;Jaffeeand Rubin, 1996] studiessuggestthat fluid ac- conservation
of sedimentyieldsdQ/d:c cr dh/dt, whereQ
Copyright2001 by the AmericanGeophysicalUnion.
is the time-averaged(over many wave periods)cross-shore
volumesedimenttransportperunitbeachwidthperunittime
Papernumber2000JC000389.
(unitsof length
2 time-i), a:is thecross-shore
coordinate,
h
0148•0227/0 !/2000JC000389509.00
is the elevation of the seafloor (relative to mean sea level),
11,623
11,624
300
200
ELGAR ET AL.: SANDBAR MIGRATION
largeraccelerations
underthe steepfrontfaceof the wave
(immediately
preceding
maximumonshore-directed
orbital
velocities)thanunderthe gentlyslopingrear face (preceding themaximumoffshore-directed
orbitalvelocities)
(Figure 1). Thus,if fluid accelerations
temporarilyincreasethe
Velocity (cm/s)
--Acceleration
amountof sedimentin motion [Madsen, 1974; Hailermeier,
o ,,.
0
10
20
30
40
50
60
1982; Hanesand Huntley, 1986; Nielson, 1992; Osborne
and Greenwood,1993;Jaffeeand Rubin, 1996], the timing
of strongaccelerations
relativeto onshoreorbitalvelocities
in asymmetrical
wavescouldresultin net shoreward
transport.
Time (s)
Figure 1. Near-bottom
cross-shore
velocity(solidcurve)
and acceleration(dashedcurve) versustime for asymmetric wavesobservedin 1.5-m water depthnear the seaward
3. Observations
Nearly continuous
observations
of waves,near-bottomvelocities, and bathymetryobtainedfor 45 days on a sandy,
edgeof the surfzone. Strongonshore(positive)accelerabarred beach near Duck, North Carolina, are used here to
tionsare associated
with the steepfront facesof the waves
(propagating
towardtheleft) wheretheflowchanges
rapidly investigatethe relationshipbetweenwave orbital velocity
from maximum offshore-directed(negative) to maximum and accelerationand sandbarlocationand migration. The
onshore-directed
(positive)velocities.Underthesteepfront observationswere made along a cross-shoretransect(Figfacetheoffshoreflow decelerates
rapidly,followedby strong ure 2) extendingfrom near the shoreline(mean sediment
acceleration of the onshore flow.
grain size • 0.30 mm) to approximately4-m water depth
(grain size ,•, 0.15 mm) [Elgar et al., 1997; Gallagher et
andt is time. Predictions
of bathymetric
change(dh/dt)
basedon modelsfor Q that include both mean and oscilla-
al., 1998; Feddersen et al., 1998]. The 11 bidirectional
electromagnetic
currentmeterswere adjustedverticallyas
the bathymetryevolvedto maintainabout50-cm elevation
tory flowssuggestthatthe offshorebar migrationobserved above the seafloor. Acceleration time series were comduring stormsis drivenprimarily by cross-shore
gradients
puted by differentiatingthe velocity in the frequencydoof undertow(and associatedgradientsof Q) that resultin
mainandinverseFouriertransforming.Skewhessandasymerosion onshore and accretion offshore of the sandbar crest
[Thorntonet al., 1996; Gallagher et al., 1998].
The onshoretransportandsandbarmigrationobservedbetween storms when mean currents on the bar crest are weak
metrywerecalculated
as the meancubeof the demeaned
time seriesandHilbert-transformed
time series,respectively,
normalizedby the variance[Elgar and Guza, 1985;Elgar,
1987]. Momentswere estimatedfrom 3-hour-longtime series (sampledat 2 Hz) by averagingmomentscalculated
from 512-s low-passed-filtered
(cutoff frequencyof 0.3 Hz)
have been hypothesized
to resultfrom the skewedorbital
velocities of nonlinear shallow water waves. With Q assumedto dependnonlinearlyon the instantaneous
orbital
subrecords.
velocity,moresedimentis transported
by the largeonshoredirectedvelocitiesunderthe sharplypeakedcrestsof skewed
waves than by the longer-duration,but smaller, offshoredirectedvelocitiesunder their broad, flat troughs[Bowen,
o.ok............
R
1980; Bailard, 1981]. Althoughskewedvelocitiesmay be •
importantin somecircumstances
[Trowbridgeand Young,
1989;Douglass,1994],velocityskewness-based
modelsfail
to predicttheonshorebarmigrationobserved
neartheshore'
line and in the surf zone [Roelvinkand Stive, 1989; Wright •(D
et al., 1991; Thornton et al., 1996; Rakha et al., 1997; Gal-
:: :.,•.•;p.......
....
26Sep
D
-4.5
lagheret al., 1998].
150
200
250
300
350
400
As wavesshoal,their shapesand orbitalvelocitiesevolve
from skewedprofilesin intermediatewaterdepthsto asymCross-shore location (m)
metric shapeswith pitchedforward, steepfront facesand
locations
(symbols)anddepth(relative
more gentlyslopingrear facesjust prior to breakingand in Figure2. Instrument
to meansealevel)of the seafloor(curves)versuscross-shore
the surfzone(e.g., bores). Onshore-and offshore-directedlocation. Trianglesare colocatedcurrentmeters,pressure
velocities
areapproximately
equalinpurelyasymmetric
wavesgauges,
andsonaraltimeters
thatcontinuously
measure
the
(i.e., waves with zero velocity skewness),and thus over a seafloorlocationrelativeto a fixed frame [Gallagher et al.,
are colocatedcurrentmetersandpressure
wave period there is no net orbital velocity-driventrans- 1996]. SqUares
port. Althoughthe orbitalvelocityskewhess
is not zeroin
the nearshore,usuallyit is much smallerthan the orbital
velocityasymmetry.Asymmetricalwave orbitalvelocities
gauges.The depthprofileswereobtainedwith an amphibiousvehicleat the beginning(solidcurve)and end (dashed
curve)of an onshoresandbarmigrationeventin September
1994 near Duck, North Carolina. The shorelinefluctuated
result in skewedfluid accelerations(both increasesand de-
(owingto a 1-mtiderange)aboutcross-shore
locationequal
creasesin velocitymagnitudes)[Elgar et al., 1988], with
to 125 m.
ELGAR ET AL.: SANDBAR
MIGRATION
11,625
strongaccelerationsor decelerations.In addition, the veloc-
400
ity asymmetry(Figure3b) and acceleration
skewness(Fig-
E
3oo
ure 3c and Plate l c) maxima follow the bar crest, indicat-
ing that feedbackbetweenwaveevolutionand gradientsin
shorewardsedimenttransport(drivenby gradientsin skewed
accelerations)
may resultin onshoresandbarmigrationwhen
,- 200
o
o 400
mean flows (Plate 1b) are weak.
to
To test furtherthe relationshipbetweenwave orbital velocity and accelerationskewnessand bar location, waves
o
$00
o
200
30
40
50
60
70
Time (days since 1 Aug 1994)
Figure 3. Cross-shorelocation(circles) of maxima of near-
propagatingbetween3- and 1-m water depthsover barred
bathymetries
weresimulatednumerically.Observations
made
over a 3-hour period in 3-m water depth (significantwave
heightwas 75 cm) during an onshorebar migrationevent
(time equal to 54 days in Figure 3 and Plate 1, which is
September24, centeredin time betweenthe2 profilesshown
in Figure2) were usedto initializea nonlinearBoussinesq
wave model[Freilichand Guza, 1984]. Usingthe sameinitial conditions,the simulatedwave field was computedfor
eachof four fixed cross-shore
depthprofiles(Figure4c).
For thesewavesand profilesthe modeledorbital velocity
skewness
(Figure4a) wasnotaffectedgreatlyby thelocation
bottomorbital(a) velocityskewness,(b) velocityasymme- of the sandbar, but the cross-shorestructure of the modeled
try, and (c) accelerationskewnessversustime. The cross- accelerationskewness(Figure 4b) moved shorewardwith
shorelocationof the crestof the sandbaris indicatedby the the bar crest. Althoughthesesimulationsof nonbreaking
solidcurvein eachpanel.
wavesonly qualitativelyreproducethe cross-shore
structure
of the observedorbital velocity moments(which were affectedby breaking),they are consistentwith the observation
The cross-shore location of the crest of the sandbar was
(Figure 3c andPlate 1c) that the accelerationskewnessmaxestimatedfrom spatiallydensesurveysconductedwith an imum followsthe crestof the shorewardmigratingsandbar.
amphibious
vehicle[Lee and Birkemeier,1993] approximatelybiweeklyfor the first 30 daysand daily for the last
4. Conclusions
15 days,combinedwith 3-hourlyestimatesof seafloorelevationfrom sonaraltimetermeasurements
(Figure2) [GalField observationsand model simulations [Thornton et
lagheret al., 1998]. An exampleof approximately
25-m al., 1996; Gallagher et al., 1998] demonstratethat during
onshoresandbarmigrationovera 5-dayperiodis shownin stormsstrongundertowdominatesnet transportand bar miFigure2.
grationis offshore(e.g., time equalto 33-36 and 70-75 days
Forthewiderangeof waveconditions
duringthefieldob- in Plate 1). In contrast, when cross-shoremean currents
servations
presented
here[Gallagheret al., 1998;Feddersen (Plate lb) are relatively weak, but orbital velocities(proet al., 1998], the location of the maximum of near-bottom portionalto wave height, Plate 1a) are not small, net transcross-shore
orbitalvelocityskewness
usuallywasbetween port associatedwith gradientsin skewedfluid accelerations
the sandbarand the shoreline,and was not correlatedwith may dominatemorphologicalchange,resultingin onshore
thelocationof thebar crest(Figure3a). Althoughtrans- sandbarmigration(e.g., time equalto 50-60 daysin Plate 1).
port is not expectedif the velocityvarianceis small even When both waves and mean currents are small, there is little
for largevaluesof theskewness
(a normalized
quantity),
the transportand no morphologicalchange(e.g., time equal to
correlation between skewness and bar crest location was low
37-48 daysin Plate 1), eventhoughthe normalizedaccelerfor thewide rangeof wave(Plate 1a) andcurrentconditions ation skewnessmay be large.
observed.
Consequently,
thecorresponding
cross-shore
graAlthough the constitutiverelationshipbetween fluid ve-
dientsin velocityskewness
do not supportthe hypothesis locity, fluid acceleration,and sedimentmotion is not known,
thatvelocityskewness-driven
sediment
transport
causes
the the field observationspresentedhere are consistentwith the
observedbar migration.
hypothesisthat net onshoresedimenttransportand sand-
In contrast,
velocityasymmetry
(Figure3b)andtheclosely bar migrationare relatedto cross-shoregradientsin skewed
relatedaccelerationskewness[Elgar and Guza, 1985; El- fluid accelerationsassociatedwith pitchedforward nonlingar, 1987] (Figure 3c) are maximumnearthe sandbarcrest. ear waves. Consequently,incorporatingthe effects of fluid
Largevaluesof velocityasymmetry
indicatepitchedforward accelerationson sedimenttransport(e.g., by including both
waveswith steepfrontfaces,gentlyslopingrearfaces,and velocity and accelerationstatisticsin wave-averagedtransskewedaccelerations
(Figure1). The spatialvariation(Plate port modelsor by includingboth velocity and acceleration
l c) and corresponding
cross-shore
gradients(Plate l d) of time historiesin instantaneous
transportmodels)may result
acceleration skewness are consistent with erosion offshore
in improvedmodelsfor nearshorebathymetricchangethat
andaccretiononshoreof the bar crestif Q is increased
by canpredictboththe undertow-drivenoffshorebar migration
11,626
ELGAR ET AL.: SANDBAR MIGRATION
500
ß,• -•0
E
400
o
r: -40
300
c -20
'"" 200
E
c
500
o
o
400
o
0.5
500
o
o.o
"200
I
-
--0.5
500
o
0.05
to 400
o.oo
300
o
2OO
30
40
Time
50
60
-0.05
70
(days since 1 Aug 1994)
Plate 1. Observedwaveandnear-bottomcross-shore
velocityandacceleration
statistics.(a) Significant
waveheight(4 timesthe standarddeviationof 3-hourlong recordsof sea-surface
elevationfluctuations
in the frequencybandbetween0.01 and0.3 Hz) observedin 5-m waterdepthversustime. Contoursof
(b) mean current(negativevaluesare offshore-directed),(c) accelerationskewness,and (d) cross-shore
gradientof the accelerationskewnessas a function of cross-shorelocationand time. The cross-shore
locationof the sandbarcrestis indicatedby the solidcurveon eachcontourplot.
ELGAR ET AL.: SANDBAR MIGRATION
Feddersen,F., R.T. Guza, S. Elgar, andT.H.C. Herbers,Alongshore
momentumbalancesin the nearshore,J. Geophys. Res., 103,
Boussinesq model simulations
.
"0.8
(o)
15,667-15,676, 1998.
ß 0.7
•
0.6
>
0.5
11,627
Freilich, M.H., and R.T. Guza, Nonlineareffectson shoalingsurface gravitywaves,Philos. Trans.R. Soc. London,Ser.,A 311,
1-41, 1984.
ß
...
.
Gallagher,E.L., B. Boyd, S. Elgar, R.T. Guza, andB.T. Woodward,
0.1
Performance of a sonar altimeter in the nearshore, Mar. Geol.,
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.
ß
ß
0.0
Gallagher,
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andR.T.Guza,
Observations
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.
ß
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-0.1
1998.
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S. Elgar, WoodsHole OceanographicInstitution,MS11, 266
WoodsHole Road,WoodsHole, MA 02543. ([email protected])
E. L. Gallagher,Departmentof Oceanography,
833 Dyer Road,
Naval PostgraduateSchool, Monterey, CA 93943-5122. ([email protected].
mil)
R. T. Guza, Centerfor CoastalStudies0209, ScrippsInstitution
of Oceanography,
La Jolla,CA 92093-0209. ([email protected].
edu)
(ReceivedApril 24, 2000; revisedJanuary23, 2001;
acceptedFebruary16, 2001.)