There is a growing need for surface wave information on the continental shelf and beach to estimate sea state, and to provide input for models of currents, sediment transport, radar backscatter and aerosol generation. While surface wave spectra in the open ocean evolve slowly over distances of O(100-1000 km), wave properties on the continental shelf and beach are highly variable (typical length scales of 0.1-10 km) owing to a variety of topographic effects (e.g., shoaling, refraction, scattering) and strongly enhanced nonlinear interactions and dissipation. The long-term goal of this research is to develop a better understanding of the physical processes that affect the generation, propagation and dissipation of surface waves in shallow coastal waters, and improve the accuracy of models that predict the transformation of wave properties across the shelf and beach.Award Numbers: N0001497WR30010 N0001497WR30011 N0001497WR30012 N0001497WR3007

Herbers, Thomas H.C.

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Calhoun, Institutional Archive of the Naval Postgraduate School

Calhoun: The NPS Institutional ArchiveDSpace RepositoryFaculty and Researchers Faculty and Researchers' Publications1997-09-30Surface Wave Processes on the ContinentalShelf and BeachHerbers, Thomas H.C.http://hdl.handle.net/10945/68943This publication is a work of the U.S. Government as defined in Title 17, UnitedStates Code, Section 101. Copyright protection is not available for this work in theUnited States.Downloaded from NPS Archive: CalhounSURFACE WAVE PROCESSES ON THE CONTINENTAL SHELF AND BEACHThomas H. C. HerbersDepartment of Oceanography, Code OC/HeNaval Postgraduate SchoolMonterey, California 93943-5122phone: (408) 656-2917; fax: (408) 656-2712; email: herbers@oc.nps.navy.milAward Numbers: N0001497WR30010 N0001497WR30011 N0001497WR30012N0001497WR30071LONG-TERM GOALThere is a growing need for surface wave information on the continental shelf and beach to esti-mate sea state, and to provide input for models of currents, sediment transport, radar backscatterand aerosol generation. While surface wave spectra in the open ocean evolve slowly over distancesof O(100-1000 km), wave properties on the continental shelf and beach are highly variable (typi-cal length scales of 0.1-10 km) owing to a variety of topographic eects (e.g., shoaling, refraction,scattering) and strongly enhanced nonlinear interactions and dissipation. The long-term goalof this research is to develop a better understanding of the physical processes that aect thegeneration, propagation and dissipation of surface waves in shallow coastal waters, and improvethe accuracy of models that predict the transformation of wave properties across the shelf andbeach.SCIENTIFIC OBJECTIVES- predict accurately the nonlinear shoaling transformation of waves over a gently sloping beach- determine the eects of wave breaking on the directional properties of waves in shallow water- predict accurately the nonlinear transfer of energy from wind waves to lower-frequency infra-gravity waves and the subsequent propagation and damping of these waves on the continentalshelf- determine the eects of refraction and bottom friction on the propagation of swell across awide, shallow continental shelf- determine the importance of resonant quartet interactions in the evolution of wind wave spectraon the continental shelfAPPROACHA combination of theory, analytical and numerical models, and eld experiments is used toinvestigate the physical processes that aect surface wave properties on the continental shelf andbeach. The transformation of wave spectra across the continental shelf is predicted with modelsbased on a spectral energy balance that include the eects of refraction and resonant quartetinteractions. On beaches near-resonant triad interactions cause strong evolution of wave spectraover distances of only a few wavelengths. A new stochastic shoaling model is under development,based on the Boussinesq equations for weakly nonlinear, weakly dispersive waves, that can beapplied to random, directionally spread wind waves propagating over a gently sloping beach withapproximately straight and parallel depth contours. While the wind waves and associated high-frequency harmonics are mostly dissipated in the surf zone, the nonlinearly excited infragravity1Report Documentation Page Form ApprovedOMB No. 0704-0188Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering andmaintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information,including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, ArlingtonVA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if itdoes not display a currently valid OMB control number. 1. REPORT DATE 30 SEP 1997 2. REPORT TYPE 3. DATES COVERED   00-00-1997 to 00-00-1997  4. TITLE AND SUBTITLE Surface Wave Processes on the Continental Shelf and Beach 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Postgraduate School,Department of Oceanography,Monterey,CA,93943 8. PERFORMING ORGANIZATIONREPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT  15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Same asReport (SAR) 18. NUMBEROF PAGES 5 19a. NAME OFRESPONSIBLE PERSON a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 waves reect from the beach and radiate seaward across the shelf as free waves. A spectral WKBapproximation is used to describe the refraction and topographic trapping of infragravity wavesradiated from shore.Extensive eld data are used to verify predictions of topographic and nonlinear eects, and toestimate the energy losses owing to bottom friction and wave breaking. The data sets includecoherent arrays of pressure sensors and current meters deployed near Duck, NC, Cape Canaveral,FL, Norfolk, VA, and Point Conception, CA, and single point wave measurements (pressuresensors and directional buoys) from numerous eld sites. Analysis techniques applied to themeasurements include various inverse methods to extract directional and wavenumber propertiesfrom array cross-spectra, bispectral and trispectral analysis to detect nonlinear coupling, as wellas standard statistical methods to determine empirical relationships between observed variables.WORK COMPLETEDThe shelf-wide variability of swell (Herbers, Hendrickson, and O'Reilly, manuscript in prepara-tion) and infragravity waves (Herbers, Evangelidis, and Jessen, manuscript in preparation) wasinvestigated with measurements from a cross-shelf transect of ten pressure transducers, deployedon the seaoor of the North Carolina shelf during the DUCK94 experiment. The observationsgenerally show weak variations in swell energy across the shelf during benign conditions, in qual-itative agreement with predictions of an energy conserving spectral refraction model. However,strong attenuation of swell energy levels across the shelf (up to a factor 4) observed on a fewoccasions suggests that bottom friction is important in high-energy conditions. Larger cross-shelf variations in infragravity motions were observed, with energy levels near the shelf breaktypically 2 orders of magnitude smaller than the levels observed close to shore. The observedstrong attenuation of infragravity waves across the sloping inner shelf is primarily the result ofrefractive trapping of waves radiated from shore at oblique angles, and is well described by aWKB model. Across the relatively at (but irregular) outer shelf, the attenuation is weaker butincreases with increasing swell energy. These results indicate that the attenuation of infragravitywaves across the shelf is caused by a combination of trapping and damping eects.RESULTSA new stochastic Boussinesq model was developed that describes the shoaling evolution of ran-dom, directionally spread wind waves on a gently sloping beach (Herbers and Burton, 1997).Existing deterministic Boussinesq models (Freilich and Guza, 1984; and many others) describeaccurately the nonlinear wave shoaling process, but require large computing resources and adetailed specication of incident waves at the oshore boundary of the model domain, that isoften not available. The new stochastic formulation, based on a third-order closure for weaklynonGaussian statistics, yields a numerically ecient coupled set of evolution equations for thewave spectrum and bispectrum that smoothly matches (in the limit of weak nonlinearity) thewell known third-order stochastic solutions of dispersive nite depth theory (Hasselmann et al.,1963). Predictions of both the new stochastic Boussinesq model and Freilich and Guza's de-terministic Boussinesq model are in good agreement with eld observations of wave shoalingcollected by S. Elgar and R. T. Guza in the DUCK94 experiment (Figure 1, from Norheim etal., 1997).The eects of wave breaking (not incorporated in the energy-conserving wave shoaling models)on the directional properties of shoaling waves were investigated with measurements from across-shore array of bi-directional current meters deployed by R. T. Guza and S. Elgar in theDUCK94 experiment (Figure 2, from Herbers, Elgar and Guza, manuscript in preparation). Inbenign conditions when most of the instruments were outside the surfzone, the observations show2a decrease in directional spreading of wave energy toward the shore (squares) that is consistentwith refraction toward normal incidence and nonlinear energy transfers to wave components thatpropagate in approximately the same direction as the incident waves. In energetic conditions withwave breaking on a shallow sandbar, the observed directional spreading of wave energy increasessharply in the surfzone (asterisks). This dramatic directional broadening, possibly a scatteringeect associated with irregular wave breaking patterns, may have important implications forwave-driven longshore currents and sediment transport.Extensive arrays of pressure sensors are currently deployed on the beach and inner continentalshelf near Duck, NC (collaborative experiments with S. Elgar, R. T. Guza, B. Raubenheimer,and W. C. O'Reilly), to investigate in more detail the eects of nonlinear interactions and wavebreaking on shoaling waves.IMPACT/APPLICATIONSThe new nonlinear wave shoaling model developed in this project will be used extensively innumerical simulations of the transformation of ocean waves on beaches.TRANSITIONSThe results of this research will be used in the new ONR Advanced Wave Prediction Program toimprove the parameterizations of shallow water eects in operational regional wave predictionmodels.RELATED PROJECTSWave-driven nearshore currents are investigated in a collaborative eort led by R. T. Guza (SIO).Observations of shear waves and infragravity waves in the surf zone are analyzed in collaborationwith T. C. Lippmann (SIO) and E. B. Thornton (Naval Postgraduate School).REFERENCESFreilich, M. H., and R. T. Guza, 1984: Nonlinear eects on shoaling surface gravity waves. Phil.Trans. R. Soc. Lond., A311, 1-41.Hasselmann, K., W. Munk, and G. MacDonald, 1963: Bispectra of ocean waves. in Times SeriesAnalysis, edited by M. Rosenblatt, pp. 125-139, John Wiley, New York.Herbers, T. H. C., and M. C. Burton, 1997: Nonlinear shoaling of directionally spread waves ona beach, J. Geophys. Res., 102, 21101-21114.Norheim, C. A., T. H. C. Herbers, and S. Elgar, 1997: Nonlinear evolution of surface wavespectra on a beach, J. Phys. Oceanogr., in press.30.1 0.2 0.3 0.4101102103104(a)h = 4.2 mx = 320 m0.1 0.2 0.3 0.4101102103104(b)2.8 m264 m0.1 0.2 0.3 0.4101102103104(c)2.4 m220 mSpectral Density (cm2 /Hz)0.1 0.2 0.3 0.4101102103104(d)2.4 m205 m0.1 0.2 0.3 0.4101102103104(e)2.5 m169 mFrequency (Hz)0.1 0.2 0.3 0.4101102103104(f)1.6 m145 mFrequency (Hz)Figure 1: Comparison of observed (solid curves) with predicted (asterisks = stochastic model,circles = deterministic model) wave spectra at 6 instrument locations on a natural ocean beachnear Duck, NC. The distance x from shore, water depth h, and the initial spectrum at x =480 m (dashed curve) are indicated in each panel. Both models predict accurately the observedstrong nonlinear evolution of nonbreaking waves propagating over a shallow sandbar at x = 240m (Figure 2).4,. \ /\ \ '' \; Figure 2: Observed directional spread (the width of the directional distribution of wave energy)versus cross-shore position x. The estimates, obtained from a transect of bi-directional currentmeters, are normalized by the incident wave directional spread estimated from an oshore arrayof pressure sensors in 8 m depth. Asterisks represent estimates from 304 data records collected inhigh-energy wave conditions with intense breaking on the sandbar. Squares represent estimatesfrom 551 data records collected in low-energy wave conditions with small energy losses on thesandbar. Symbols and bars indicate the mean value and standard deviation of the estimates. Arepresentative beach prole with the instrument locations is shown in the lower panel. Whereasdirectional spreads decrease toward the shoreline in non-breaking conditions, consistent withrefraction of shoaling waves, directional spreads increase dramatically in breaking conditionswith a maximum slightly inshore of the crest of the sandbar.5• nonb re a kin g cond it ions 1 .4 -* bre ak in g con d itions -0 a Q) L 0.... 1/) 1.2 -0 C 0 :..;::: u • ~ -E-"°" -E-Q) 1 .0 ,._ -a -0 Q) • i::::! 0 .8 E L.. 0 C .6 ':j~ H · ,. ft - , #HH f* f t -I I I I I I 100 200 300 4 00 500 0 ,,......__ 1 E .___,, 2 ..c: 3 ..c: Q.. 4 <I) "D 5 6 100 200 300 40 0 500 d ista nce X from shore (m) 

Surface Wave Processes on the Continental Shelf and Beach

Thomas H. Herbers

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Surface Wave Processes on the Continental Shelf and Beach

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