LONG-TERM GOAL: 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: N0001499WR30012N0001499WR30117N0001499WR30011N0001499WR30008N0001499WR30009N0001499WR20063N0001499WR2015

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' Publications1999Surface Wave Processes on the Shelf and BeachHerbers, Thomas H.C.http://hdl.handle.net/10945/69531This 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 Shelf And BeachThomas H. C. HerbersDepartment of Oceanography, Code OC/HeNaval Postgraduate SchoolMonterey, California 93943-5122phone: (831) 656-2917   fax: (831) 656-2712   email: herbers@oc.nps.navy.milAward Numbers: N0001499WR30012; N0001499WR30117; N0001499WR30011; N0001499WR30008; N0001499WR30009; N0001499WR20063; N0001499WR20157http://cdip.ucsd.edu/showexLONG-TERM GOALThere is a growing need for surface wave information on the continental shelf and beach to estimatesea state, and to provide input for models of currents, sediment transport, radar backscatter and aerosolgeneration.  While surface wave spectra in the open ocean evolve slowly over distances of O(100-1000km), wave properties on the continental shelf and beach are highly variable (typical length scales of0.1-10 km) owing to a variety of topographic effects (e.g., shoaling, refraction, scattering) and stronglyenhanced nonlinear interactions and dissipation.  The long-term goal of this research is to develop abetter understanding of the physical processes that affect the generation, propagation and dissipation ofsurface waves in shallow coastal waters, and improve the accuracy of models that predict thetransformation of wave properties across the shelf and beach.OBJECTIVES• predict accurately the nonlinear transformation of waves in shallow water• predict accurately the nonlinear transfer of energy from wind waves to lower-frequency   infragravity waves• determine the effects of refraction and bottom friction on the propagation of swell across a wide   continental shelf• determine the importance of resonant quartet interactions in the evolution of wind wave spectra   on the continental shelf• improve the representation of nonlinear wave-wave interactions in operational wave prediction   models• determine the effects of wave nonlinearity and directional spreading on sea surface statisticsAPPROACHA combination of theory, analytical and numerical models, and field experiments is used to investigatethe physical processes that affect surface wave properties on the continental shelf and beach.  Thetransformation of wave spectra across the continental shelf is predicted with models based on aReport 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 1999 2. REPORT TYPE 3. DATES COVERED   00-00-1999 to 00-00-1999  4. TITLE AND SUBTITLE Surface Wave Processes On The 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,Code OC/He,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 spectral energy balance that include the effects of refraction and resonant quartet interactions.  Onbeaches near-resonant triad interactions cause strong evolution of wave spectra over distances of only afew wavelengths.  A new stochastic shoaling model is under development, based on the Boussinesqequations for weakly nonlinear, weakly dispersive waves, that can be applied to random, directionallyspread wind waves propagating over a gently sloping beach with approximately straight and paralleldepth contours.  While the wind waves and associated high-frequency harmonics are mostly dissipatedin the surf zone, the nonlinearly excited infragravity waves reflect from the beach and radiate seawardacross the shelf as free waves.  A spectral WKB approximation is used to describe the refraction andtopographic trapping of infragravity waves radiated from shore.Extensive field data are used to verify predictions of topographic and nonlinear effects, and to estimatethe energy losses owing to bottom friction and wave breaking.  The data sets include coherent arrays ofpressure sensors and current meters deployed near Duck, NC, Cape Canaveral, FL, Norfolk, VA, andPoint Conception, CA, and single point wave measurements (pressure sensors and directional buoys)from numerous field sites.  Analysis techniques applied to the measurements include various inversemethods to extract directional and wavenumber properties from array cross-spectra, bispectral andtrispectral analysis to detect nonlinear coupling, as well as standard statistical methods to determineempirical relationships between observed variables.WORK COMPLETEDA new stochastic wave shoaling model was developed based on a third-order statistical closure ofBoussinesq equations (Herbers and Burton, 1997).  A one-dimensional version of the model forunidirectional waves was validated through comparisons with field data (Norheim et al., 1998).  Atwo-dimensional implementation for directionally spread waves was completed and is currentlyevaluated with extensive directional wave measurements collected in the SandyDuck Experiment.Direct estimates of the contribution of nonlinear wave-wave interactions to the spectral energy balanceof breaking waves on a barred beach were obtained from measured wave spectra and bispectra basedon a stochastic formulation of Boussinesq equations. The main result of this analysis is a surprisinglyclose balance between energy losses in the energetic part of the spectrum and nonlinear energytransfers to higher frequencies. These observations show that the spectral evolution in the surf zone isstrongly controlled by nonlinear triad interactions while dissipation appears to be confined to the high-frequency tail of the spectrum.The effects of wave breaking on the directional properties of shoaling waves were investigated withmeasurements from a cross-shore array of bi-directional current meters deployed by R. T. Guza and S.Elgar in the DUCK94 experiment.  In benign conditions when most of the instruments were outside thesurfzone, the observations show a decrease in directional spreading of wave energy toward the shorethat is consistent with refraction toward normal incidence and nonlinear energy transfers to wavecomponents that propagate in approximately the same direction as the incident waves. In energeticconditions with wave breaking on a shallow sandbar, the observed directional spreading of waveenergy increases sharply in the surf zone.  The dramatic directional broadeningmay have important implications for wave-driven longshore currents and sediment transport.The evolution of swell across a wide continental shelf was investigated with measurements from atransect of ten bottom pressure transducers, deployed on the North Carolina shelf during the DUCK94Experiment. The results of this study generally show weak variations in swell energy across the shelfduring benign conditions, in qualitative agreement with predictions of an energy conserving spectralrefraction model. However, large energy losses across the shelf (up to about 70 %) were observedwhen incident swell energy levels were higher, but not high enough to cause steepness-limited wavebreaking. This strong attenuation is likely the result of energy losses in the bottom boundary layer. Theobserved damping rates suggest significantly larger bottom friction factors than are commonly used inwave prediction models.In collaboration with W. C. O’Reilly a cross-shelf transect of 6 Datawell Directional Waverider buoysand a coherent array of 5 pressure transducers were deployed on the North Carolina shelf, as part of theongoing ONR Shoaling Waves Experiment (SHOWEX).  Additional geological data were collected incollaboration with T. Drake and J. McNinch, including measurements of small scale bathymetry,wave-induced ripples, and sediment samples. The combined data sets (including several majorhurricanes) will be used to examine the effects of wave-bottom interaction processeson the attenuation and directional spreading of waves propagating across the continental shelf.RESULTSThe nonlinear dispersion of random surface gravity waves in shallow water was investigated withBoussinesq theory and extensive field data.  A theoretical dispersion relation for a root-mean-squareaverage wavenumber as a function of frequency, the local water depth, and local wave statistics wasderived for directionally spread waves propagating over a gently sloping beach.  Wavenumbers wereestimated using four arrays of pressure sensors deployed by S. Elgar and R. T. Guza in 3-5 m depthduring the SandyDuck experiment (Figure 1a). Observed wavenumbers deviate by as much as 20-30%from the linear dispersion relation and are in excellent agreement with the nonlinear Boussinesq theorypredictions (e.g., Figure 1c-e). In high-energy conditions with breaking or nearly breaking waves thetheoretical frequency and amplitude dispersion effects tend to cancel, yielding a nearly nondispersivewave field in which all components travel with approximately the shallow water wave speed,consistent with the observations (Figure 1).IMPACT/APPLICATIONSResults of this project have provided unique new insights in the statistical properties of ocean surfacewaves in shallow water and a numerically efficient approximation for nearshore surf predictionmodels.TRANSITIONSThe results of the SHOWEX experiment will be used in the ONR Advanced Wave Prediction Programto improve the parameterizations of shallow water effects in operational regional wave predictionmodels.FIGURE 1.  Wavenumbers of surface gravity waves observed in shallow water near Duck, NC, arecompared with the linear dispersion relation and nonlinear Boussinesq theory predictions. (a)Bathymetry (depth contours in m) and locations of pressure sensor arrays. (b) Wave spectra atarrays 7, 6, and 5. (c-e) Observed and predicted dispersion relations at arrays 7, 6, and 5.RELATED PROJECTSNearshore and inner shelf currents are investigated in collaborative efforts led by R. T. Guza and S. J.Lentz.  The effects of nonlinearity and directional spreading on sea surface statistics are investigated incollaboration with S. Elgar.  The stochastic Boussinesq model for shoaling waves developed in thisproject will be integrated in a comprehensive nearshore community model under sponsorship of theNational Ocean Partnership Program (PI: J. Kirby).REFERENCESHerbers, T. H. C., and M. C. Burton, Nonlinear shoaling of directionally spread waves on a beach, J.Geophys. Res., 102(C9), 21101-21114, 1997.Norheim, C. A., T. H. C. Herbers, and S. Elgar, Nonlinear evolution of surface wave spectra on abeach, J. Phys. Oceanogr., 28(7), 1534-1551, 1998.PUBLICATIONSLippmann, T. C., T. H. C. Herbers, and E. B. Thornton, Gravity and shear wave contributions tonearshore infragravity motions, J. Phys. Oceanogr., 29(2), 231-239, 1999.Herbers, T. H. C., S. Elgar, and R. T. Guza, Directional spreading of waves in the nearshore, J.Geophys. Res., 104(C4), 7683-7693, 1999.Lentz, S., R. T. Guza, S. Elgar, F. Feddersen, and T. H. C. Herbers, Momentum balances on the NorthCarolina inner shelf, J. Geophys. Res., 104(C8), 18,205-18,226, 1999.Herbers, T. H. C., N. R. Russnogle, and S. Elgar,  Spectral energy balance of breaking waves withinthe surf zone, accepted for publication in J. Phys. Oceanogr.Feddersen, F., R. T. Guza, S. Elgar, and T. H. C. Herbers, Velocity moments in alongshore bottomstress parameterizations, accepted for publication in J. Geophys. Res.Herbers, T. H. C., E. J. Hendrickson, and W. C. O'Reilly, Propagation of swell across a widecontinental shelf, submitted to J. Geophys. Res.Lentz, S., M. Carr, and T. H. C. Herbers, Barotropic tides on the North Carolina shelf, submitted to J.Phys. Oceanogr.Elgar, S., R. T. Guza, W. C. O'Reilly, B. Raubenheimer, and T. H. C. Herbers,  Wave energy anddirection observed near a pier, submitted to J. Waterway, Port, Coastal, and Ocean Eng.Herbers, T. H. C., S. Elgar, N. A. Sarap, and R. T. Guza, Nonlinear dispersion of surface gravity wavesin shallow water, submitted to J. Fluid Mech.

Surface Wave Processes on the Shelf and Beach

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Surface Wave Processes on the Shelf and Beach

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