JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 97, NO. C10, PAGES 15,573-15,577, OCTOBER
15, 1992
Observationsof InfragravityWaves
STEVE
ELGAR
1, T.H.C.HERBERS
2, MICHELE
OKIHIRO
2,
JOAN
OLTMAN-SHAY
3,andR. T. GUZA
2
Infragravity-wave(periodsof one-halfto a few minutes)energylevels observedfor about 1 year in 8-m
waterdepthin the Pacificand in 8- and 13-m depthsin the Atlanticare highly correlatedwith energyin the
swell-frequency
band (7- to 20-s periods),suggestingthe infragravitywaves were generatedlocally by the
swell.The amplificationof infragravity-waveenergybetween13- and8-m depth(separated
by 1 km in the cross
shore)is about2, indicatingthat the observed
infragravitymotionsaredominatedby free waves,not by groupforcedboundwaves,whichin theoryare amplifiedby an orderof magnitudein energybetweenthe two locations. However,boundwavesare moreimportantfor the relativelyfew caseswith very energeticswell, when
the observedamplificationbetween 13- and 8-m depth of infragravity-waveenergy was sometimes3 times
greaterthan expectedfor free waves. Bispectraare consistentwith increasedcouplingbetweeninfragravity
wavesandgroupsof swellandseafor high-energyincidentwaves.
1. INTRODUCTION
Motionsin the infragravity-frequency
band (frequencieslower
thanthe incidentseaandswell) are importantfor manynearshore
processes.Previous studieshave shown that infragravity- and
incident-waveenergylevels are correlated,and that waves in the
infragravitybandmay be either freely propagating(leaky waves
radiatingto or from deepwaterandedgewaves)or bound(forced
secondarywavesnonlinearlycoupledto groupsof incidentwaves
[Hasselmann,1962; Longuet-Higginsand Stewart, 1962]). Very
closeto shore,within the surf zone, low-modeedge wavesdominate the longshorevelocity field [Huntley et al., 1981], sometimes contributingwell over half the total infragravityenergy
[Oltman-Shayand Guza, 1987]. Althoughlow-modeedgewaves
are alsodetectablein the cross-shore
velocity and pressurefields
in the surf zone,othermotionscontributesubstantially[Suhayda,
1974; Huntley, 1976; Holman, 1981; Howd et al., 1991; and others]. Phasecouplingbetweeninfragravity and incident waves
suggestsomelocal forcingof infragravitywavesin the surf zone
[Guza et al., 1984; Huntley and Kim, 1984; Elgar and Guza,
1985;List, 1986]. Lesscomprehensive
observations
well seaward
of the surf zone show that the relative
contributions
to the total
energy by different types of infragravity motions vary with
offshore distance. In particular, low-mode edge waves may
becomelessimportantwith increasingoffshoredistancebecause
they are trappedcloseto shore.In 40-m water depth,a few hundred kilometersfrom shorein the North Sea, analysisof a few
hours of high-energysea-surfaceelevation data suggestedthat
boundwavescan dominatethe infragravityband [Sand, 1982].
Bound waves also have been shown to contribute as much as 50%
of theinfragravityenergyin pressuremeasurements
madecloseto
shore(within 1 km) in the PacificOceanin meandepthsof about
10 m [Okihiroet al., 1992].Bound-wavepredictionsin boththese
studieswere qualitativesince detailedmeasurementsof incident
wave directional propertieswere not available. Preliminary
resultsfrom measurements
madewith an arrayof pressuresensors
in 8-m depthsuggestthathigh-modeedgewavessometimesdom-
inate the infragravity-bandenergy [Elgar et al., 1989; OltmanShayet al., 1989]. Thus, somepreviousstudiesoutsidethe surf
zone have concludedthat high-modeedge waves contributethe
majority of the infragravityenergy, while others suggestthat
boundwavesare dominant. The causesof this apparentvariability in the relative contributionsof differenttypesof infragravity
wave motions are unknown.
In this study,long-termobservations
of infragravitywavesin
8- and 13-m depths, offshore of Duck, North Carolina, are
presented. As in previous studies, the total infragravity and
incident-swellenergy are stronglycorrelated.The amplification
of infragravity-waveenergybetween13- and 8-m depth is comparedto the theoreticalamplificationfor free leaky surface-gravity
waves and group-forcedbound waves. The results show that
bound-wave contributionsto the infragravity band are small
except for the relatively few cases with very energeticswell.
Theseobservationsmay provide useful constraintson modelsof
infragravitywave generationnow underdevelopment.
2. OBSERVATIONS
Data were collectedwith bottom-mounted
pressuresensors24
hours/dayfor 3 monthsand 12 hours/dayfor 6 monthsin 8- and
13-m waterdepth(about1 and 2 km from shore,respectively)
betweenSeptember1990 andJune1991 at the U.S. Army Corps
of EngineersField ResearchFacility,Duck,North Carolina. The
field siteis locatedneara sandybeachalonga barrierislandwith
no nearby headlandsor inlets [Birkemeier et al., 1981]. Additionaldatawereobtainedfrom a bottom-mounted
pressure
sensor
in 8-m depthnear the mouth of a small harborcloseto Barber's
Point, Hawaii.
The Barber's Point data were collected for 9
hours/dayfor more than 1 year [Okihiro et al., 1992]. All three
data sets were subdivided into 85-min records, detrended to
removefides,tapered,andFouriertransformed
to producespectral
estimates,E (f), with a final frequencyresolutionof 0.0078 Hz
and80 degreesof freedom.The pressurespectrawere converted
to sea-surface
elevationspectrain the swell and sea frequency
range(0.04 < f < 0.30 Hz, wheref is the frequency)usinglinear
theory. The 0.04 Hz divisionbetweenswell and infragravity
1 ElectricalEngineering
& ComputerScience,Washington
State energyis intendedto insureinfragravitywave estimateswere not
University,Pullman.
contaminatedby long-periodswell (for further discussion,see
2 Scripps
Institution
ofOceanography,
LaJolla,California.
Okihiroet al. [1992]).
3 QUEST
Integrated
Inc.,Kent,Washington.
Mean frequencies,
corresponding
to the centroidof the power
Copyright1992by the AmericanGeophysical
Union.
spectrum,
0.3
Hz
0.3
Hz
I fE(f)dfl I E(f)df
Papernumber9ZIC01316.
0148-0227/92/9ZIC-01316505.00
O.04Hz
15,573
O.04Hz
15,574
ELOARET
AL.:OBSERVATIONS
OFINFRAORAVffY
WAVF3
andtotalenergies
of theincident
wavesat Duckranged
from0.08
to 0.24Hz, andfrom25 to 11,000cm2, respectively
(Figurela).
Thisis somewhat
largerthantherangeatBarber's
Point,Hawaii,
wherelow-frequency
swellwaspredominant
(Figurelb). The
frequency
waves
areprimarily
locallydriven
(asopposed
toarriv-
ingfromremote
locations
withdifferent
incident-wave
energy).
Asshown
in Table1, thecorrelation
of E•swithswellenergy
(E•,n, defined
astheenergy
in therange0.04< f < 0.14Hz,
gauges
werewell outsidethesurfzoneexceptfor a few occasions Figure2b) is significantly
higherthanthe correlation
with sea
atDuckwithveryenergetic
waves,
whenthegauge
in 8-mdepth energy
(E,,,,defined
astheenergy
in therange
0.14< f < 0.3Hz,
waswithinthesurfzone.Themaximum
significant
waveheight Figure2c) or withEtot(Figure2a). A stronger
infragravity
in 13-mdepthat Duckwas4.2 m. Theratioof waveheightto response
toswellthantoseaisconsistent
withbound-wave
theory
waterdepthindicatesthat wave breakingalsooccurredat the [Hasselmann,
1962;Longuet-Higgins
andStewart,
1962],andhas
13-mdepthgaugeduringthelargest
waveevents.
beenobserved
previously
[MMdleton
et al., 1987;Nelsonet al.,
Infragravity
energy(E•s
, defined
as theenergy
in therange 1988;Okihiroet al., 1992].
0.004< f < 0.04Hz) andtotalincident-wave
energy
(E,ot,defined If theinfragravity
motions
wereboundwaves,nonlinearly
astheenergyin therange0.04< f < 0.30Hz) arestrongly
corre- driven
bygroups
of swell,thenE•so•E2,,•n
[Hasselmann,
1962;
latedat bothfield sites(Figure2a), suggesting
that the low- Longuet-Higgins
andStewart,
1962].The constant
of proportionality
depends
onthewaterdepthandthefrequency-directional
, ,i,11H I
0.30
i :1,,1111 i i•1•11,I
spectrum
of theincidentwaves,E(f, 0) (0 is thedirection
relative
• i ttlw
(o)
I
to the beachnormal),but bound-wave
energyis expected
to
increase
nonlinearly
withswellenergy.However,
fittingpower
lawsto theobserved
relationship
between
E•sandE,,,nyields
Ec•o•E•, n atBarber's
Point,whiletheexponents
are1.0and0.9
in 8- and13-mdepths,
respectively,
at Duck(Figure2b). The
N 025
ß
•
observed
large
deviations
froma quadratic
dependence
ofEison
0.20
E•,•n suggestthat motionsother than boundwaves contribute
significantly
toinfragravity-band
energy
atbothsites.
•
Asshown
inFigure
3,thetotal
infragravity
energy
in8-(E•s)
++
o.15
and13-m(Els,) depths
arehighlycorrelated.
A leastsquares
fit
between
logEis
s andlogEts, yieldsEis
s= 1.7Eis,, a nearly
.i
o
linear
dependence.
Thetheoretical
ratio,
R,between
E/sin8-and
ß
0.10
O. 05 ....... i .......
i
......
j ,
10110•10j'10
4105 101'10) 10• 1041"0
5
Energy (cm 2)
Energy (cm 2)
13-mdepthsfor boundwavesis markedlydifferentfrom the
observed
ratio. Neglecting
alongshore
depthvariations,
boundwaveenergyforcedby unidirectional,
normally-incident
long
wavesis proportional
to h-$ [Longuet-Higgins
andStewart,
1962],whichforthedepths
of 8 and13m yieldsR = 11(upper
dashed
linein Figure3). Ontheotherhand,fornormally
incident
free(leaky)surface-gravity
wavesthe amplification
in shallow
is[e.g.,Eckart,
1951]h-• = 1.3(lower
dashed
lineinFigFig.l. Centroidal
frequency
versus
totalsea-surface
elevation
energy
for water
the frequency
range0.04to 0.3 Hz. (a) Duck,NorthCarolina;
(b) ure3). Directional
andfinite-depth
effects
change
theselimiting
Barber's
Point,Hawaii.Thedepth
atbothlocations
wasapproximately
8 valuesof R onlyslightly,asdemonstrated
by calculations
based
m.
(a)
ooo.o
.•o 10.0
L•- 0.1
1.0
(b)
(c)
?"'
1000.0
E
•
100.0
10.0
.?
,.,
1.0
0.1
I
'
E100.0' '...%•.:::..:....,
&
•0.0•
..
•u- 011.0I
101
102
105 104
E,o,(cm2)
105 10
100
1000
E,wo,
(cm•)
100001
10
100 1000 10000
E,oo
(cm•)
Fig.2. Infragravity-band
energy,
Els(0.004< f < 0.04Hz)versus
(a)totalincident-wave
energy
Etot(0.04< f < 0.3Hz);(b)
incident-swell
energy
Eswdt
(0.04<f< 0.14Hz);and(c)incident-sea
energy,
Ese,(0.14<f< 0.3Hz).Thetoppanels
areBarber's
Point;
themiddle
panels
amDuck,8-mdepth;
andthelower
panels
areDuck,13-mdepth.
Thelinesthrough
thedataonpanels
b
amleastsquares
fitstothelogarithm
ofthedata.Thecorrelation
coefficients
foreachpanelamlistedin Table1.
Et.oAa•rr tin.: OaSm•VAT•ONS
Ol••oa•vrrY
TABLE
WAVES
15,575
1. Number of Data Runs and Corrdation Coefficients for the Three Data Sets
DataSet
Number
ofRuns
ElsVersus
Etot
ElsVersus
E•w•n
F-4s
Versus
E•
Barber's Point
3644
0.90
0.93
0.60
Duck, 8 m
Duck, 13 m
2154
2154
0.87
0.82
0.96
0.95
0.63
0.58
on moregeneralnonlinear[Hasselmann,
1962] and linear [e.g.,
Collins, 1972] theories(Figures4a and 4b, respectively).For
incident-wavedirectionalspreadstypical of thoseobservedat
Duck,thevaluesof R predicted
for boundwaves(5 < R < 10, Figure4a) aremuchlargerthanthevaluesof R for leakywaves(1.0
< R < 1.3, Figure4b). For edgewaveswith a turningpoint
decreasingswell energy,as shownin Figures5 and 6. Additionally, R (f) is largestin the 0.03 to 0.05-Hz range(Figures5 and
6). The averageratio of 1.8 heavily weightsboth the frequently
occurringlow-energy incident waves at Duck (Figures 2b, 2c),
and the generallymore-energeticinfragravitymotions with frequencies- 0.02 Hz (Figure 7, upperpanels). Higher valuesof R
offshore of both measurement locations, R - 1. However, sea- (- 34) observedat higher infragravityfrequencies(- 0.04 Hz)
wardof theirturningpoint,edge-waveamplitudesdecayexponen- during cases of energetic swell (Figures 5b, 6) suggestthat
tially [Eckart,1951]. Consequently,
if the edge-waveturning significantcontributionsof boundwaves sometimesoccur. How-
point occursbetween8- and 13-m depth,then the edge-wave
energywill be muchgreaterin 8- thanin 13-m depth,with a
correspondingly
largevalueof R. Thus,smallvaluesof R (R =
0(1)) suggest
thatboundwavesarenot important,whereaslarge
valuesof R (R = 0(10)) suggest
thateitherboundwavecontributions are importantor that a significantfraction of the
infragravity-wave
energy observedin 8-m depth is trapped
between
8- and13-mdepthanddoesnotcontribute
to Eigin 13-m
depth.
40
35
•
30
•
25
•
20
The overallaveragevalueof R, definedasthemeanvalueover
all datarunsof theobserved
ratiobetween
Eigin 8- and13-m
depthis approximately
1.8,suggesting
E• is notgenerally
dominatedby boundwaves. On the otherhand,for datasetswith
energetic
infragravity
waves,R is higher(Figure3). Moreover,
theenergyratiosfor individualfrequency
bands,R (of'),areoften
largerthan1.8.To investigate
thevariation
of R (0f'),thedatawere
15
<:l 10
subdividedinto five groupsaccordingto the swell energy. At all
frequencies
below 0.06 Hz, R (J') systematically
decreases
with
(a)
0
0.08
1000.0
I
i
''•"1
0.12
0.16
0.20
/
/
/
/
6O
/
h-?,'
/
5O
100.0
/
//
+:
/
,,,
/
/
/
/
/
/
/
/
•
40
•
$0
/
/
/
J
10.0
/
/
/
/
/
20
1.0
10
0.1
1.0
10.0
100.0
Eig13
(Cruz)
1000.0
(b)
i
0.04
f
0.08
(Hz)
Fig. 3. Infragravityenergyobservedin 8-m depthversusinfragravity
energyobserved
in 13-mdepthat Duck. The
solidline is a leastsquares Fig. 4. Contoursof the theoreticalratio of infragravityenergyin 8-m
11
fittothelogarithm
ofthedata,
Ei•s= 1.7E•it3,withcorrelation
coefficientdepthto that in 13-m depth. (a) Boundwaveswith frequency0.03 Hz
0.99. The dashedlines indicatethe theoretic-ill
shallowwater relationships forcedby thenonlineardifference-frequency
interaction
of two swellcombetweenthe energiesin 8- and 13-m depth for normally incidentfree ponentswith frequencies
f-Af/2
andf + All 2 (whereAf = 0.03 Hz)
waves
(energy
- h4s,EissTM
1.3Eis
t.•)andbound
waves
(energy- and propagationdirections-0/2 and +0/2 relative to normal incidence.
(b) Leakywavesof frequency
f anddeep-water
direction0.
h-s,Eigs
= 11Eis•).
15,576
El.otto • AL.: OBSERVATIONS
OFINFRA•VffY
WAVES
(b)
(a)
MAY
04
MAY
lO5½
000
19
lOO
5.0
lO
lO2
2.5
3
2.0
1.5
0.00
0.05
0.10
0.15
0.20
Frequency (Hz)
0.00
0.05
0.10
0.15
0.20
Frequency(Hz)
0.08
1.0
0.00
•: 0.06
0.02
0.04
0.06
0 08
0.00
Frequency(Hz)
0.02
0.04
0.06
0.08
Frequency(Hz)
Fig. 5. The ratio (R (f)) of infragravity-wave
energyobservedin 8-m
depthto that observedin 13-m depthversusfrequency.(Left) Small
incidentwaves,240 observations
with swellenergyrangingfrom 25 to 50
crn
2,(Right)Energetic
incident
waves,
18observations
withswellenergy
ranging
from3200to 11,000crn
2. Thebarsindicate
+ 1 standard
deviation of the observed ratios.
•.• 0.04
0.02
0.08
0.06
•..•0.04
o.o2
0.06
0.12
0.18
0.06
fl (Hz)
0.12
0.18
fl (Hz)
Fig.7. (Fromtopto bottom)Energyspectra,
ratio(R(/')) of infragravity
energyin 8-m depthto that in 13-m depth,bicoherence
in 13-m depth,
bieoherenee
in 8-m depth.The solidanddottedlinesin thetoppanelsare
the 8- and 13-m depth spectra,respectively.The minimum value of
bicohemceplottedis 0.3 (99% significance
level),with contom every
0.1. Owingto symmetries
(i.e., redtmdancies)
of the bieoherence
[Hasselmannet al., 1963],onlyvaluesin theindicatedtriangleare shown.(Left)
Small
incident
waves
(total
energy
= 75cmz,May4, 1991).(Right)
Large
incident
waves
(totalenergy
= 4000crn
z, May19,1991).(b)Thevertical
(uppertwo pands)andhorizontal(lowertwo pands)dashedlinesat f =
0.03 andf = 0.08 Hz for May 19 delineatethe rangeof infragravityfrequencies
moststronglyphasecoupledto swellandsea.
(e.g.,Figure4a), but the dependence
of free-infragravity
energy
onE(f, 0) is unknown.
If thehighR valuesareindeedcausedby bound-wave
contribu[ions,and not by trappingof edge-waveenergybetween8- and
13-m depth,thennon-Gaussian
staffsties
are expectedowingto
Frequency
(Hz)
phasecouplingbetweenfreeswellandbound-infragravity
waves.
Nonlinearcouplingbetweenwavetriadswith frequencies
f•, f2
andfl + f2 canbe detectedwith the bicoherence
[Hasselmann
et
Fig. 6. Histogram
of theratio(R (f)) of infragravity
energyin 8-m depth al., 1963], definedas
to that in 13-m depthas a functionof frequencyand swellenergy.The
verticalaxis (ratio)is logarithmic,as is the spacingof the swell-energy
b2(f,f) =
bins. The frequencybins are 0.0078 Hz wide, and spacedlinearly. The
<
rangeof swell energy(andthe numberof datarimsfor eachbin) are 25 -
I<A
+
IA(f)A(f.)12><lA(f
>I
(1)
50cmz (240runs),
50- 200(1043),200- 800(691),800- 3200(163),and
whereA is the complexFouriercoefficientat frequencyf, the
asterisk
denotescomplexconjugate,
andanglebracketsdenotethe
expectedvalue. Phasecouplingbetweenboundlow-frequency
ever,thesehighervaluesof R (f) are still not aslarge aswouldbe waves(frequencyf2) and higher-frequency
incidentwaves(freexpectedif the infragravitymotionsconsistedentirelyof bound quenciesfl > f2 and fl +f2) results in nonzero b Oei, f2),
waves(Figure4a), implyingthatfree- (leaky or edge)infragravity whereasb = 0 for statisticallyindependent
free waves. Spectra,
wavesarerarelynegligiblein theseobservations.
ratiosbetweeninfragravity-energy
spectraldensitiesin 8- and13There is considerablevariability in the ratiosshownin Figure m depth(R (,f)), andbieoherences
for two representative
example
5, as indicatedby the bars. This scatteris partiallyowing to sta- easesof low- andhigh-energyswell are shownin Figures7a and
tisticaluncertaintyof the spectralestimates,but may alsobe the 7b, respectively.When the swell energyis low (Figure7a), both
3200- 11,000(18).
result of different incident-wave E(f, 0) or beach morphology. R (f)- 1 andthebicoheren,
cesin 8- and13-mdeptharesmall,
The theoreticalbound-waveenergycertainlydependson E(f, 0) consistent
with infragravitymotionsdominated
by freewaves.On
F.,LOAR
ETAL.'. OBSERVATIONS
OF•VFRAORAVITY
WAVES
15,577
the otherhand,with energeticswdl (Figure7b), the bicoherence (significant
wave heightsbetween0.5 and 1.5 m), free waves
is nonzeroin 8- and 13-m depth,andR (f) is larger.In thiscase, dominate
infragravity
energyin 8- and13-mdepth.
thebicoherence
in 13-mdepthis maximtunfor thefrequencies
f2
Acknowledgments.
Supportwas providedby the Office of Naval
= 0.06, f• = 0.11, f• + f2 = 0.17 Hz, indicatingthat 0.06-Hz Research
(Coastal
Sciences
andGeology& Geophysics)
andtheNational
bound waves are forced by the differenceinteractionbetween Science
Foundation
(Physical
Oceanography).
W. Birkemeier,
C. Long,
andall thestaffof theFieldResearch
Facility(FRF),Coas0.11-Hz swelland0.17-Hz sea. Note that0.06 Hz is in a spectral K. Hathaway,
valley(Figure7b, 13-mdepth,upperpanel),andthebicoherence tal EngineeringResearchCenter, Duck, North Carolina, contributed
greatlyto this effort.
is smallat frequencies
f2 corresponding
to the 0.01- to 0.04-Hz
infragravity
peak. In 8-m depth,thebicoherence
is evenlargerfor
REFEP.•CES
the (0.17, 0.11 Hz) sea-swelldifferenceinteraction,and is statisti-
W., A. DeWaU,C. Gorbics,andH. Miller, A user'sguideto
callysignificantfor a widerfrequencyrange(0.01 < f2 < 0.07 Hz, Birkemeier,
Facility,Rep. CERCMR 81-7, U.S. Army
0.08 < f• < 0.14 Hz), corresponding
to difference-frequency CERC'sField Research
Corpsof Eng.,WES, Vicksburg,Miss., 1981.
interactions
of the entiresea-swellspectrum(0.08 - 0.21 Hz). In Collins,J.I., Predictionof shallowwaterspectra,
J. Geophys.
Res.,77,
both 8- and 13-m depth,the rangeof f2 with largebicoherence 2693-2707, 1972.
values(0.04 - 0.06 Hz) corresponds
to the frequencyrange of Eckart,C., Surfacewavesonwaterof variabledepth,WaveReport100, 99
pp., ScrippsInstitutionof Oceanography,
Univ. of California,La Jolla,
largestR (f). The biphases(approximately180ø, not shown)are
1951.
consistent
with second-order
theoryfor weaklynonlinearwavesin
Elgar,S., andR. T. Guza,Observations
of bispectra
of shoalingsurface
firtim-waterdepth[Hasselmannet al., 1963].
gravitywaves,J. Fluid Mech., 161,425-448, 1985.
An estimate of the fraction of energy at a particular Elgar,S., andG. Scheft,Statistics
of bicoherence
andbiphase,
J. Geophysical Res.,94, 10,993-10,998, 1989.
infragravity-frequency
band that is locally forced by nonlinear
and P. Howd, Observations
of infragravitydifference-frequency
interactionsof directionallynarrow surface Elgar,S., J. Oltman-Shay,
wavescanbe obtained
by summing
thebicoherence
values(b2)
frequencylong waves. I, Couplingto wind waves,Eos Trans.AGU,
alonglinesof constant
f2 in f•, f2 space(afteraccounting
for statisticalbias [Elgar and Sebert, 1989]). Thus, for example,the
fractionof energyat 0.03 Hz excitedby differenceinteractionsof
0.08- to 0.15-Hz swell and sea wavesis roughlydeterminedby
Guza,R. T., E. B. Thornton,andR. A. Holman,Swashon steepandshallow beaches,
Proc.Int. CoastalEng. Conf.,19,708-723, 1984.
Hasselmann,
K., On thenon-linearenergytransferin a gravity-wave
spectrum,Part 1, Generaltheory,J. Fluid Mech. 12, 481-500, 1962.
Hasselmann,
K., W. Munk, andG. MacDonald,Bispectra
of oceanwaves,
in TimeSeriesAnalysis,editedby M. Rosenblatt,
pp. 125-139,Wiley,
summing
thedebiased
b2Oel,
f2) forconstant
f2 = 0.03Hz andfor
0.08 _<fa _<0.12 Hz. For thelow-energyincidentwavesshownin
Figure 7a, the contributionof bound waves to the infragravity
wave spectrumis lessthan 10% in both8- and 13-m depthsat all
frequencies.On the other hand, for the high-energyincident
waves(Figure7b), boundwavesaccountfor approximately
30%
to 50% of the infragravityenergyin 13-m depth,while in 8-m
depth,this fractionis about70% to 100%. Thus, the bispectral
estimatessuggestthat with large incidentwaves the infragravity
energyin 13-m depthstill containsa significantamountof free
waves,whereasin 8-m depth,boundwavesare theprimarysource
of infragravityenergy. Thesebispectralresultsshowingnegligible bound-wavecontributionswith low-energy incident waves,
andsignificantbound-wavecontributions
with energeticswell are
qualitativelyconsistentwith the observedenergy ratios, R (f)
(Figures5-7). Detailed comparisons
of theoreticallypredicted
andobservedbound-waveenergies,andbispectralanalysisof this
entiredataset(andseveralothers)will be presentedelsewhere.
3. CONCLUSIONS
Wavedatafrom two approximately
1-yearlongdeployments
in
the Ariantic and Pacific oceansindicatethat infragravity-wave
energy(0.004 - 0.04 Hz) is well conelatedwith energylevelsof
swell, suggesting
the infragravitywaveswere locally generated.
The average(over all data sets) amplificationof infragravity
energybetween13- and 8-m depthis much lessthan would be
expectedif the infragravitywaves consistedentirely of bound
waves,nonlinearlyforcedby groupsof swell and sea. On the
otherhand,with energeticswellthe amplificationis sometimesa
factorof 3 greaterthanwouldoccurfor shoalingleaky wavesor
edgewavesnot near a turningpoint. The amplificationis usually
largest at the high-frequencyend of the infragravity band.
Bispectralanalysisshowsthat thisamplificationis associated
with
significant bound-wave contributions. Thus, for the data
presented
here,bound-wavecontributions
are significantfor energeticincidentwaves(significantwaveheightsgreaterthanabout2
m), but for more commonly observed moderate conditions
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(ReceivedJanuary6, 1992;
revisedJune 8, 1992;
acceptedJune8, 1992.)