The Effect of Wave Breaking on Surf-Zone Turbulence and Alongshore Currents: A Modeling Study

Falk Feddersen Scripps Institution of Oceanography, La Jolla, California

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J. H. Trowbridge Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

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Abstract

The effect of breaking-wave-generated turbulence on the mean circulation, turbulence, and bottom stress in the surf zone is poorly understood. A one-dimensional vertical coupled turbulence (kε) and mean-flow model is developed that incorporates the effect of wave breaking with a time-dependent surface turbulence flux and uses existing (published) model closures. No model parameters are tuned to optimize model–data agreement. The model qualitatively reproduces the mean dissipation and production during the most energetic breaking-wave conditions in 4.5-m water depth off of a sandy beach and slightly underpredicts the mean alongshore current. By modeling a cross-shore transect case example from the Duck94 field experiment, the observed surf-zone dissipation depth scaling and the observed mean alongshore current (although slightly underpredicted) are generally reproduced. Wave breaking significantly reduces the modeled vertical shear, suggesting that surf-zone bottom stress cannot be estimated by fitting a logarithmic current profile to alongshore current observations. Model-inferred drag coefficients follow parameterizations (Manning–Strickler) that depend on the bed roughness and inversely on the water depth, although the inverse depth dependence is likely a proxy for some other effect such as wave breaking. Variations in the bed roughness and the percentage of breaking-wave energy entering the water column have a comparable effect on the mean alongshore current and drag coefficient. However, covarying the wave height, forcing, and dissipation and bed roughness separately results in an alongshore current (drag coefficient) only weakly (strongly) dependent on the bed roughness because of the competing effects of increased turbulence, wave forcing, and orbital wave velocities.

* Woods Hole Oceanographic Institution Contribution Number 11123

Corresponding author address: Falk Feddersen, Scripps Institution of Oceanography, 9500 Gilman Dr., 0209, La Jolla, CA 92093-0209. Email: falk@coast.ucsd.edu

Abstract

The effect of breaking-wave-generated turbulence on the mean circulation, turbulence, and bottom stress in the surf zone is poorly understood. A one-dimensional vertical coupled turbulence (kε) and mean-flow model is developed that incorporates the effect of wave breaking with a time-dependent surface turbulence flux and uses existing (published) model closures. No model parameters are tuned to optimize model–data agreement. The model qualitatively reproduces the mean dissipation and production during the most energetic breaking-wave conditions in 4.5-m water depth off of a sandy beach and slightly underpredicts the mean alongshore current. By modeling a cross-shore transect case example from the Duck94 field experiment, the observed surf-zone dissipation depth scaling and the observed mean alongshore current (although slightly underpredicted) are generally reproduced. Wave breaking significantly reduces the modeled vertical shear, suggesting that surf-zone bottom stress cannot be estimated by fitting a logarithmic current profile to alongshore current observations. Model-inferred drag coefficients follow parameterizations (Manning–Strickler) that depend on the bed roughness and inversely on the water depth, although the inverse depth dependence is likely a proxy for some other effect such as wave breaking. Variations in the bed roughness and the percentage of breaking-wave energy entering the water column have a comparable effect on the mean alongshore current and drag coefficient. However, covarying the wave height, forcing, and dissipation and bed roughness separately results in an alongshore current (drag coefficient) only weakly (strongly) dependent on the bed roughness because of the competing effects of increased turbulence, wave forcing, and orbital wave velocities.

* Woods Hole Oceanographic Institution Contribution Number 11123

Corresponding author address: Falk Feddersen, Scripps Institution of Oceanography, 9500 Gilman Dr., 0209, La Jolla, CA 92093-0209. Email: falk@coast.ucsd.edu

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  • Agrawal, Y. C., E. A. Terray, M. A. Donelan, P. A. Hwang, A. J. Williams, W. Drennan, K. Kahm, and S. Kitaigorodskii, 1992: Enhanced dissipation of kinetic energy beneath breaking waves. Nature, 359 , 219220.

    • Search Google Scholar
    • Export Citation
  • Anis, A., and J. N. Moum, 1995: Surface wave–turbulence interactions: Scaling ε(z) near the sea surface. J. Phys. Oceanogr., 25 , 20252045.

    • Search Google Scholar
    • Export Citation
  • Babanin, A. V., I. R. Young, and M. L. Banner, 2001: Breaking probabilities for dominant surface waves on water of finite constant depth. J. Geophys. Res., 106 , 1165911676.

    • Search Google Scholar
    • Export Citation
  • Bryan, K. R., K. P. Black, and R. M. Gorman, 2003: Spectral estimates of dissipation rate within and near the surf zone. J. Phys. Oceanogr., 33 , 979993.

    • Search Google Scholar
    • Export Citation
  • Burchard, H., 2001: Simulating the wave-enhanced layer under breaking surface waves with two-equation turbulence models. J. Phys. Oceanogr., 31 , 31333145.

    • Search Google Scholar
    • Export Citation
  • Canuto, V. M., A. Howard, Y. Cheng, and M. S. Dubovikov, 2001: Ocean turbulence. Part I: One-point closure model—Momentum and heat vertical diffusivities. J. Phys. Oceanogr., 31 , 14131426.

    • Search Google Scholar
    • Export Citation
  • Church, J. C., and E. B. Thornton, 1993: Effects of breaking wave induced turbulence within a longshore current model. Coastal Eng., 20 , 128.

    • Search Google Scholar
    • Export Citation
  • Chen, Q., J. T. Kirby, R. A. Dalrymple, F. Shi, and E. B. Thornton, 2003: Boussinesq modeling of longshore currents. J. Geophys. Res., 108 .3362, doi:10.1029/2002JC001308.

    • Search Google Scholar
    • Export Citation
  • Cox, D. T., and N. Kobayashi, 2000: Identification of intense, intermittent coherent motions under shoaling and breaking waves. J. Geophys. Res., 105 , 1422314236.

    • Search Google Scholar
    • Export Citation
  • Craig, P. D., 1996: Velocity profiles and surface roughness under breaking waves. J. Geophys. Res., 101 , 12651277.

  • Craig, P. D., and M. L. Banner, 1994: Modeling wave-enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr., 24 , 25462559.

    • Search Google Scholar
    • Export Citation
  • Craik, A. D. D., and S. Leibovich, 1976: A rational model for Langmuir circulations. J. Fluid Mech., 73 , 401426.

  • Deigaard, R., 1993: A note on the three-dimensional shear stress distribution in a surfzone. Coastal Eng., 20 , 156171.

  • Drennan, W. M., M. A. Donelan, E. A. Terray, and K. B. Katsaros, 1996: Oceanic turbulence dissipation measurements in SWADE. J. Phys. Oceanogr., 26 , 808815.

    • Search Google Scholar
    • Export Citation
  • Duncan, J. H., 1981: An experimental investigation of breaking waves produced by a towed hydrofoil. Proc. Roy. Soc. London,, 377A , 331348.

    • Search Google Scholar
    • Export Citation
  • Elgar, S., R. T. Guza, B. Raubenheimer, T. H. C. Herbers, and E. Gallagher, 1997: Spectral evolution of shoaling and breaking waves on a barred beach. J. Geophys. Res., 102 , 1579715805.

    • Search Google Scholar
    • Export Citation
  • Feddersen, F., R. T. Guza, S. Elgar, and T. H. C. Herbers, 1998: Alongshore momentum balances in the nearshore. J. Geophys. Res., 103 , 1566715676.

    • Search Google Scholar
    • Export Citation
  • Feddersen, F., E. L. Gallagher, S. Elgar, and R. T. Guza, 2003: The drag coefficient, bottom roughness, and wave-breaking in the nearshore. Coastal Eng., 48 , 189195.

    • Search Google Scholar
    • Export Citation
  • Feddersen, F., R. T. Guza, and S. Elgar, 2004: Inverse modeling of one-dimensional setup and alongshore current in the nearshore. J. Phys. Oceanogr., 34 , 920933.

    • Search Google Scholar
    • Export Citation
  • Fredsoe, J., and R. Deigaard, 1992: Mechanics of Coastal Sediment Transport. World Science, 369 pp.

  • Fredsoe, J., B. M. Sumer, A. Kozakiewicz, L. H. C. Chua, and R. Deigaard, 2003: Effect of externally generated turbulence on wave boundary layer. Coastal Eng., 49 , 155183.

    • Search Google Scholar
    • Export Citation
  • Gallagher, E. L., S. Elgar, and E. B. Thornton, 1998: Megaripple migration in a natural surf zone. Nature, 394 , 165168.

  • Gallagher, E. L., E. B. Thornton, and T. P. Stanton, 2003: Sand bed roughness in the nearshore. J. Geophys. Res., 108 .3039, doi:10.1029/2001JC001081.

    • Search Google Scholar
    • Export Citation
  • Garcez-Faria, A. F., E. B. Thornton, T. P. Stanton, C. M. Soares, and T. C. Lippmann, 1998: Vertical profiles of longshore currents and related bed shear stress and bottom roughness. J. Geophys. Res., 103 , 32173232.

    • Search Google Scholar
    • Export Citation
  • Gemmrich, J. R., and D. M. Farmer, 1999: Near-surface turbulence and thermal structure in a wind-driven sea. J. Phys. Oceanogr., 29 , 480499.

    • Search Google Scholar
    • Export Citation
  • George, R., R. E. Flick, and R. T. Guza, 1994: Observations of turbulence in the surf zone. J. Geophys. Res., 99 , 801810.

  • Grant, W. D., and O. S. Madsen, 1979: Combined wave and current interaction with a rough bottom. J. Geophys. Res., 84 , 17971808.

  • Kitaigorodskii, S. A., M. A. Donelan, J. L. Lumley, and E. A. Terray, 1983: Wave turbulence interactions in the upper ocean. Part II: Statistical characteristics of wave and turbulent components of the random velocity field in the marine surface layer. J. Phys. Oceanogr., 13 , 19881999.

    • Search Google Scholar
    • Export Citation
  • Lamarre, E., and W. K. Melville, 1991: Air entrainment and dissipation in breaking waves. Nature, 351 , 469472.

  • McWilliams, J. C., and J. M. Restrepo, 1999: The wave-driven ocean circulation. J. Phys. Oceanogr., 29 , 25232540.

  • McWilliams, J. C., J. M. Restrepo, and E. M. Lane, 2004: An asymptotic theory for the interaction of waves and currents in coastal waters. J. Fluid Mech., 511 , 135178.

    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., 2003: The three-dimensional current and surface wave equations. J. Phys. Oceanogr., 33 , 19781989.

  • Mellor, G. L., and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys., 20 , 851875.

    • Search Google Scholar
    • Export Citation
  • Melville, W. K., F. Veron, and C. J. White, 2002: The velocity field under breaking waves: Coherent structures and turbulence. J. Fluid Mech., 454 , 203233.

    • Search Google Scholar
    • Export Citation
  • Mohamed, M. S., and J. C. Larue, 1990: The decay power law in grid-generated turbulence. J. Fluid Mech., 219 , 195214.

  • Nikuradse, J., 1933: Stromungsgestze in glatten und rauhen rohren. Work Rep., VD1 , 361.

  • Rapp, R. J., and W. K. Melville, 1990: Laboratory measurements of deep-water breaking waves. Philos. Trans Roy. Soc. London, 331A , 735800.

    • Search Google Scholar
    • Export Citation
  • Raubenheimer, B., R. T. Guza, and S. Elgar, 1996: Wave transformation across the inner surf zone. J. Geophys. Res., 101 , 2558925597.

  • Reniers, A. J. H. M., E. B. Thornton, T. P. Stanton, and J. A. Roelvink, 2004: Vertical flow structure during SandyDuck: Observations and modeling. Coastal Eng., 51 , 237260.

    • Search Google Scholar
    • Export Citation
  • Reynolds, W. C., 1976: Computation of turbulent flow. Annu. Rev. Fluid. Mech., 8 , 183207.

  • Rodi, W., 1987: Examples of calculation methods for flow and mixing in stratified fluid. J. Geophys. Res., 92 , 53055328.

  • Ruessink, B. G., J. R. Miles, F. Feddersen, R. T. Guza, and S. Elgar, 2001: Modeling the alongshore current on barred beaches. J. Geophys. Res., 106 , 2245122463.

    • Search Google Scholar
    • Export Citation
  • Sleath, J. F. A., 1984: Sea Bed Mechanics. John Wiley and Sons, 335 pp.

  • Svendsen, I. A., 1984: Wave heights and set-up in a surf zone. Coastal Eng., 8 , 303329.

  • Tennekes, H., 1989: Two- and three dimensional turbulence. Lecture Notes in Turbulence, J. R. Herring and J. C. McWilliams, Eds., World Scientific, 371 pp.

    • Search Google Scholar
    • Export Citation
  • Terray, E. A., M. A. Donelan, Y. C. Agrawal, W. M. Drennan, K. K. Kahma, A. J. Williams, and P. Hwang, 1996: Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr., 26 , 792807.

    • Search Google Scholar
    • Export Citation
  • Terray, E. A., W. M. Drennan, and M. A. Donelan, 1999: The vertical structure of shear and dissipation in the ocean surface layer. Proc. Symp. on the Wind-Driven Air-Sea Interface-Electromagnetic and Acoustic Sensing, Wave Dynamics and Turbulent Fluxes, Sydney, Australia, University of New South Wales, 239–245.

  • Thornton, E. B., and R. T. Guza, 1983: Transformations of wave height distribution. J. Geophys. Res., 88 , 59255938.

  • Thornton, E. B., and R. T. Guza, 1986: Surf zone longshore currents and random waves: Field data and models. J. Phys. Oceanogr., 16 , 11651178.

    • Search Google Scholar
    • Export Citation
  • Thornton, E. B., J. L. Swayne, and J. R. Dingler, 1998: Small-scale morphology across the surf zone. Mar. Geol., 145 , 173196.

  • Trowbridge, J. H., and S. Elgar, 2001: Turbulence measurements in the surf zone. J. Phys. Oceanogr., 31 , 24032417.

  • Trowbridge, J. H., W. R. Geyer, M. M. Bowen, and A. J. Williams, 1999: Near-bottom turbulence measurements in a partially mixed estuary: Turbulent energy balance, velocity structure, and along-channel momentum balance. J. Phys. Oceanogr., 29 , 30563072.

    • Search Google Scholar
    • Export Citation
  • Umlauf, L., and H. Burchard, 2003: A generic length-scale equation for geophysical turbulence models. J. Mar. Res., 61 , 235265.

  • Voulgaris, G., and M. B. Collins, 2000: Sediment resuspension on beaches: Response to breaking waves. Mar. Geol., 167 , 167197.

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