JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 97, NO. C10, PAGES 15,573-15,577, OCTOBER 15, 1992 Observationsof InfragravityWaves STEVEELGAR 1, T.H.C. HERBERS2, MICHELE OKIHIRO 2, JOANOLTMAN-SHAY 3, and R. T. GUZA2 Infragravity-wave(periods of one-halfto a few minutes)energy levels observedfor about 1 year in 8-m water depthin the Pacificand in 8- and 13-m depthsin the Atlanticare highly correlatedwith energyin the swell-frequencyband (7- to 20-s periods),suggesting the infragravitywaves were generatedlocally by the swell.The amplificationof infragravity-waveenergy between 13- and 8-m depth(separated by 1 km in the cross shore)is about2, indicatingthat the observedinfragravity motions are dominatedby free waves,not by group- forcedbound waves, which in theoryare amplifiedby an orderof magnitudein energybetween the two loca- tions. However,bound waves are more importantfor the relativelyfew caseswith very energeticswell, when the observedamplification between 13- and 8-m depth of infragravity-waveenergy was sometimes3 times greaterthan expectedfor free waves. Bispectraare consistentwith increasedcoupling between infragravity wavesand groups of swelland seafor high-energyincident waves. 1. INTRODUCTION inate the infragravity-bandenergy [Elgar et al., 1989; Oltman- Motions in the infragravity-frequencyband (frequencieslower Shayet al., 1989]. Thus, someprevious studies outside the surf thanthe incidentsea and swell) are importantfor many nearshore zone have concludedthat high-modeedge waves contributethe processes.Previous studieshave shown that infragravity- and majority of the infragravity energy, while others suggestthat incident-waveenergy levels are correlated,and that waves in the boundwaves are dominant. The causesof this apparentvariabil- infragravityband may be either freely propagating(leaky waves ity in the relative contributionsof different typesof infragravity radiatingto or from deepwater and edgewaves) or bound(forced wave motions are unknown. secondarywaves nonlinearly coupled to groupsof incidentwaves In this study,long-term observations of infragravitywaves in [Hasselmann,1962; Longuet-Higginsand Stewart, 1962]). Very 8- and 13-m depths, offshore of Duck, North Carolina, are closeto shore,within the surf zone, low-modeedge wavesdom- presented. As in previous studies, the total infragravity and inate the longshorevelocity field [Huntley et al., 1981], some- incident-swellenergy are stronglycorrelated. The amplification times contributingwell over half the total infragravityenergy of infragravity-waveenergy between 13- and 8-m depth is com- [Oltman-Shayand Guza, 1987]. Althoughlow-mode edge waves paredto the theoreticalamplification for free leaky surface-gravity are alsodetectable in the cross-shorevelocity and pressurefields waves and group-forcedbound waves. The results show that in the surf zone, other motionscontribute substantially [Suhayda, bound-wave contributionsto the infragravity band are small 1974; Huntley, 1976; Holman, 1981; Howd et al., 1991; and oth- except for the relatively few cases with very energetic swell. ers]. Phasecoupling between infragravity and incident waves These observationsmay provide useful constraintson modelsof suggestsome local forcingof infragravitywaves in the surf zone infragravitywave generationnow underdevelopment. [Guza et al., 1984; Huntley and Kim, 1984; Elgar and Guza, 1985;List, 1986]. Lesscomprehensive observations well seaward 2. OBSERVATIONS of the surf zone show that the relative contributions to the total Data were collectedwith bottom-mountedpressure sensors 24 energy by different types of infragravity motions vary with hours/dayfor 3 monthsand 12 hours/dayfor 6 monthsin 8- and offshore distance. In particular, low-mode edge waves may 13-m water depth(about 1 and 2 km from shore,respectively) becomeless important with increasingoffshore distance because betweenSeptember 1990 and June1991 at the U.S. Army Corps they are trappedclose to shore.In 40-m water depth,a few hun- of EngineersField ResearchFacility, Duck, North Carolina. The dred kilometersfrom shore in the North Sea, analysisof a few field site is locatednear a sandybeach along a barrierisland with hours of high-energysea-surface elevation data suggestedthat no nearby headlandsor inlets [Birkemeier et al., 1981]. Addi- boundwaves can dominatethe infragravityband [Sand, 1982]. tionaldata were obtained from a bottom-mountedpressure sensor Bound waves also have been shown to contribute as much as 50% in 8-m depthnear the mouth of a small harbor close to Barber's of the infragravityenergy in pressuremeasurements made close to Point, Hawaii. The Barber's Point data were collected for 9 shore(within 1 km) in the PacificOcean in meandepths of about hours/dayfor more than 1 year [Okihiro et al., 1992]. All three 10 m [Okihiroet al., 1992]. Bound-wavepredictions in both these data sets were subdivided into 85-min records, detrended to studieswere qualitativesince detailedmeasurements of incident removefides, tapered, and Fourier transformed to producespectral wave directional properties were not available. Preliminary estimates,E (f), with a final frequencyresolution of 0.0078 Hz resultsfrom measurementsmade with an arrayof pressuresensors and 80 degreesof freedom.The pressurespectra were converted in 8-m depthsuggest that high-modeedge waves sometimes dom- to sea-surfaceelevation spectra in the swell and sea frequency range(0.04 < f < 0.30 Hz, wheref is the frequency)using linear theory. The 0.04 Hz divisionbetween swell and infragravity 1 ElectricalEngineering & ComputerScience, Washington State energyis intendedto insureinfragravity wave estimateswere not University,Pullman. 2 ScrippsInstitution of Oceanography,LaJolla, California. contaminatedby long-period swell (for further discussion,see 3 QUESTIntegrated Inc., Kent, Washington. Okihiroet al. [1992]). Mean frequencies,corresponding to the centroidof the power Copyright1992 by the AmericanGeophysical Union. spectrum, 0.3Hz 0.3Hz Papernumber 9ZIC01316. I fE(f)dfl I E(f)df 0148-0227/92/9ZIC-01316505.00 O.04Hz O.04Hz 15,573 15,574 ELOARETAL.: OBSERVATIONSOFINFRAORAVffY WAVF3 andtotal energies of theincident waves at Duckranged from 0.08 frequencywaves are primarily locally driven (as opposed toarriv- to 0.24Hz, andfrom 25 to 11,000cm 2, respectively(Figure la). ingfrom remote locations with different incident-wave energy). Thisis somewhatlarger than the range at Barber'sPoint, Hawaii, Asshown in Table1, thecorrelation of E•s with swell energy wherelow-frequency swell was predominant (Figure lb). The (E•,n, definedas the energy in therange 0.04 < f < 0.14Hz, gaugeswere well outsidethe surf zone except for a few occasions Figure2b) is significantlyhigher than the correlationwith sea at Duckwith very energetic waves, when the gauge in 8-mdepth energy(E,,,, definedas the energy in therange 0.14 < f < 0.3Hz, waswithin the surf zone. The maximum significant wave height Figure2c) or withEtot (Figure 2a). A strongerinfragravity in 13-mdepth at Duckwas 4.2 m. Theratio of waveheight to responsetoswell than to sea is consistent with bound-wave theory waterdepth indicates that wave breakingalso occurred at the [Hasselmann,1962; Longuet-Higgins and Stewart, 1962], and has 13-mdepth gauge during the largest wave events. beenobserved previously [MMdleton et al., 1987;Nelson et al., Infragravityenergy (E•s , definedas theenergy in therange 1988;Okihiro et al., 1992]. 0.004< f < 0.04Hz) andtotal incident-wave energy (E, ot, defined If the infragravitymotions were bound waves, nonlinearly asthe energy in therange 0.04 < f < 0.30Hz) arestrongly corre- drivenby groupsof swell,then E•s o• E2,,•n [Hasselmann, 1962; latedat bothfield sites(Figure 2a), suggestingthat the low- Longuet-HigginsandStewart, 1962]. The constantof propor- tionalitydepends on the water depth and the frequency-directional 0.30 , ,i,11H I i :1,,1111 i i•1•11,I • i ttlw spectrumof theincident waves, E(f, 0) (0 is thedirection relative (o) to the beachnormal), but bound-waveenergy is expectedto increasenonlinearly with swell energy. However, fitting power N 025 lawsto theobserved relationship between E•s and E,,,n yields I ß Ec•o• E•, n atBarber's Point, while the exponents are 1.0 and 0.9 in 8- and13-m depths, respectively, at Duck (Figure 2b). The observedlarge deviations from a quadraticdependence ofEis on • 0.20 E•,•n suggestthat motionsother than boundwaves contribute significantlytoinfragravity-band energy at both sites. ++ Asshown inFigure 3,the total infragravity energy in8- (E•s) • o.15 and13-m (Els,) depthsare highly correlated. A least squares fit .i o betweenlog Eis s andlog Ets, yieldsEis s= 1.7Eis,, a nearly lineardependence. Thetheoretical ratio, R, between E/s in 8- and ß 0.10 13-mdepths for boundwaves is markedlydifferent from the observedratio. Neglectingalongshore depth variations, bound- waveenergy forced by unidirectional,normally-incident long O. 05 ....... i .......i ......j , wavesis proportionalto h-$ [Longuet-Higginsand Stewart, 1962],which for the depths of 8 and13 m yieldsR = 11 (upper 10110 •10j'10 410 5 101' 10 ) 10• 104 1"05 dashedline in Figure3). Onthe other hand, for normally incident Energy (cm 2) Energy (cm 2) free (leaky)surface-gravity waves the amplificationin shallow Fig.l. Centroidalfrequency versus total sea-surface elevation energy for wateris [e.g.,Eckart, 1951] h -• = 1.3(lower dashed line in Fig- the frequencyrange 0.04 to 0.3 Hz. (a) Duck,North Carolina; (b) ure3). Directionaland finite-depth effects change these limiting Barber'sPoint, Hawaii. The depth at bothlocations