• Alves, J. H. G. M., , and M. L. Banner, 2003: Performance of a saturation-based dissipation-rate source term in modeling the fetch-limited evolution of wind waves. J. Phys. Oceanogr., 33 , 12741298.

    • Search Google Scholar
    • Export Citation
  • Alves, J. H. G. M., , M. L. Banner, , and I. R. Young, 2003: Revisiting the Pierson–Moskowitz asymptotic limits for fully developed wind waves. J. Phys. Oceanogr., 33 , 13011323.

    • 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
  • 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
  • Ding, L., , and D. Farmer, 1994: Observations of breaking surface wave statistics. J. Phys. Oceanogr., 24 , 13681387.

  • Hasselmann, K., 1974: On the spectral dissipation of ocean waves due to white capping. Bound.-Layer Meteor., 6 , 107127.

  • Jansons, K. M., , and G. D. Lythe, 1998: Stochastic stokes drift. Phys. Rev. Lett., 81 , 31363139.

  • Klyatskin, V. I., , and W. A. Woyczynski, 1995: Fluctuations of passive scalar with nonzero mean concentration gradient in random velocity fields. J. Theor. Exp. Phys., 81 , 770773.

    • Search Google Scholar
    • Export Citation
  • Komen, G. J., , S. Hasselmann, , and K. Hasselmann, 1984: On the existence of a fully developed wind-sea spectrum. J. Phys. Oceanogr., 14 , 12711285.

    • Search Google Scholar
    • Export Citation
  • Komen, G. J., , L. Cavaleri, , M. Donelan, , K. Hasselmann, , and S. Hasselmann, 1994: Dynamics and Modelling of Ocean Waves. Cambridge University Press, 532 pp.

    • Search Google Scholar
    • Export Citation
  • Lane, E. M., , J. M. Restrepo, , and J. C. McWilliams, 2007: Wave–current interaction: A comparison of radiation-stress and vortex-force representations. J. Phys. Oceanogr., 37 , 11221141.

    • Search Google Scholar
    • Export Citation
  • 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
  • Melsom, A., 1996: Effects of wave breaking on the surface drift. J. Geophys. Res., 101 , 1207112078.

  • Melsom, A., , and O. Saetra, 2004: Effects of wave breaking on the near-surface profiles of velocity and turbulent kinetic energy. J. Phys. Oceanogr., 34 , 490504.

    • Search Google Scholar
    • Export Citation
  • Merton, R. C., 1976: Option pricing when underlying stock returns are discontinuous. J. Financ. Econ., 3 , 124144.

  • Olla, P., , and P. Paradisi, 2004: Relations between Lagrangian models and synthetic random velocity fields. Phys. Rev., E70 .046 305, doi:10.1103/PhysRevE.70.046305.

    • Search Google Scholar
    • Export Citation
  • Restrepo, J. M., 2007: A path integral method for data assimilation. Physica D, in press.

  • Restrepo, J. M., , and G. K. Leaf, 2002: Wave-generated transport induced by ideal waves. J. Phys. Oceanogr., 32 , 23342349.

  • Sullivan, P. P., , J. C. McWilliams, , and W. K. Melville, 2004: The oceanic boundary layer driven by wave breaking with stochastic variability. I: Direct numerical simulation of neutrally-stratified shear flow. J. Fluid Mech., 507 , 143174.

    • Search Google Scholar
    • Export Citation
  • Vanden-Broeck, C., 1999: Stokes’ drift: An exact result. Europhys. Lett., 46 , 15.

  • WAMDI Group, 1988: The WAM Model—A third generation ocean wave prediction model. J. Phys. Oceanogr., 18 , 17751810.

  • Warner, C. D., , and M. E. McIntyre, 1999: Toward an ultra-simple spectral gravity wave parameterization. Earth Planets Space, 51 , 475484.

    • Search Google Scholar
    • Export Citation
  • Wu, J., 1979: Distribution and steepness of ripples on carrier waves. J. Phys. Oceanogr., 9 , 10141021.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 26 26 2
PDF Downloads 12 12 2

Wave Breaking Dissipation in the Wave-Driven Ocean Circulation

View More View Less
  • 1 Department of Mathematics, and Department of Physics, The University of Arizona, Tucson, Arizona
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

If wave breaking modifies the Lagrangian fluid paths by inducing an uncertainty in the orbit itself and this uncertainty on wave motion time scales is observable as additive noise, it is shown that within the context of a wave–current interaction model for basin- and shelf-scale motions it persists on long time scales. The model of McWilliams et al. provides the general framework for the dynamics of wave–current interactions. In addition to the deterministic part, the vortex force, which couples the total flow vorticity to the residual flow due to the waves, will have a part that is associated with the dissipative mechanism. At the same time the wave field will experience dissipation, and tracer advection is affected by the appearance of a dissipative term in the Stokes drift velocity. Consistency leads to other dynamic consequences: the boundary conditions are modified to take into account the diffusive process and proper mass/momentum balances at the surface of the ocean. In addition to formulating how a wave–current interaction model is modified by the presence of short-time events that induce dissipation, this study proposes a stochastic parameterization of dissipation. Its relation to other alternative parameterizations is given. Two focal reasons make stochastic parameterizations attractive: one can draw from extensive practical modeling experience in other fields, and it ties in a very natural way to a wealth of observational data via statistics.

Corresponding author address: Juan M. Restrepo, Departments of Mathematics and Physics, The University of Arizona, Tucson, AZ 85721. Email: restrepo@physics.arizona.edu

Abstract

If wave breaking modifies the Lagrangian fluid paths by inducing an uncertainty in the orbit itself and this uncertainty on wave motion time scales is observable as additive noise, it is shown that within the context of a wave–current interaction model for basin- and shelf-scale motions it persists on long time scales. The model of McWilliams et al. provides the general framework for the dynamics of wave–current interactions. In addition to the deterministic part, the vortex force, which couples the total flow vorticity to the residual flow due to the waves, will have a part that is associated with the dissipative mechanism. At the same time the wave field will experience dissipation, and tracer advection is affected by the appearance of a dissipative term in the Stokes drift velocity. Consistency leads to other dynamic consequences: the boundary conditions are modified to take into account the diffusive process and proper mass/momentum balances at the surface of the ocean. In addition to formulating how a wave–current interaction model is modified by the presence of short-time events that induce dissipation, this study proposes a stochastic parameterization of dissipation. Its relation to other alternative parameterizations is given. Two focal reasons make stochastic parameterizations attractive: one can draw from extensive practical modeling experience in other fields, and it ties in a very natural way to a wealth of observational data via statistics.

Corresponding author address: Juan M. Restrepo, Departments of Mathematics and Physics, The University of Arizona, Tucson, AZ 85721. Email: restrepo@physics.arizona.edu

Save