Editorial Type:
Article
Article Type:
Research Article

The Wavy Ekman Layer: Langmuir Circulations, Breaking Waves, and Reynolds Stress

James C. McWilliams IGPP, University of California, Los Angeles, Los Angeles, California

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Edward Huckle IGPP, University of California, Los Angeles, Los Angeles, California

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Jun-Hong Liang IGPP, University of California, Los Angeles, Los Angeles, California

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Peter P. Sullivan MMM, NCAR, Boulder, Colorado

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Print Publication:
01 Nov 2012
DOI:
https://doi.org/10.1175/JPO-D-12-07.1
Page(s):
1793–1816
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Abstract

Large-eddy simulations are made for the canonical Ekman layer problem of a steady wind above a uniformly rotating, constant-density ocean. The focus is on the influence of surface gravity waves: namely, the wave-averaged Stokes-Coriolis and Stokes-vortex forces and parameterized wave breaking for momentum and energy injection. The wave effects are substantial: the boundary layer is deeper, the turbulence is stronger, and eddy momentum flux is dominated by breakers and Langmuir circulations with a vertical structure inconsistent with both the conventional logarithmic layer and eddy viscosity relations. The surface particle mean drift is dominated by Stokes velocity with Langmuir circulations playing a minor role. Implications are assessed for parameterization of the mean velocity profile in the Ekman layer with wave effects by exploring several parameterization ideas. The authors find that the K-profile parameterization (KPP) eddy viscosity is skillful for the interior of the Ekman layer with wave-enhanced magnitude and depth scales. Furthermore, this parameterization form is also apt in the breaker and Stokes layers near the surface when it is expressed as a Lagrangian eddy viscosity (i.e., turbulent Reynolds stress proportional to vertical shear of the Lagrangian mean flow, inclusive of Stokes drift) with a derived eddy-viscosity shape and with a diagnosed vertical profile of a misalignment angle between Reynolds stress and Lagrangian mean shear.

Corresponding author address: James C. McWilliams, IGPP, University of California, Los Angeles, Los Angeles, CA 90095-1567. E-mail: jcm@atmos.ucla.edu

Abstract

Large-eddy simulations are made for the canonical Ekman layer problem of a steady wind above a uniformly rotating, constant-density ocean. The focus is on the influence of surface gravity waves: namely, the wave-averaged Stokes-Coriolis and Stokes-vortex forces and parameterized wave breaking for momentum and energy injection. The wave effects are substantial: the boundary layer is deeper, the turbulence is stronger, and eddy momentum flux is dominated by breakers and Langmuir circulations with a vertical structure inconsistent with both the conventional logarithmic layer and eddy viscosity relations. The surface particle mean drift is dominated by Stokes velocity with Langmuir circulations playing a minor role. Implications are assessed for parameterization of the mean velocity profile in the Ekman layer with wave effects by exploring several parameterization ideas. The authors find that the K-profile parameterization (KPP) eddy viscosity is skillful for the interior of the Ekman layer with wave-enhanced magnitude and depth scales. Furthermore, this parameterization form is also apt in the breaker and Stokes layers near the surface when it is expressed as a Lagrangian eddy viscosity (i.e., turbulent Reynolds stress proportional to vertical shear of the Lagrangian mean flow, inclusive of Stokes drift) with a derived eddy-viscosity shape and with a diagnosed vertical profile of a misalignment angle between Reynolds stress and Lagrangian mean shear.

Corresponding author address: James C. McWilliams, IGPP, University of California, Los Angeles, Los Angeles, CA 90095-1567. E-mail: jcm@atmos.ucla.edu
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  • Ardhuin, F., L. Marie, N. Rascle, P. Forget, and A. Roland, 2009: Observation and estimation of Lagrangian, Stokes, and Eulerian currents induced by wind and waves at the sea surface. J. Phys. Oceanogr., 39, 2820–2838.

    • Search Google Scholar
    • Export Citation

  • Bye, J., 1966: The wave-drift current. J. Mar. Res., 25, 95–102.

  • Craig, P., and M. Banner, 1994: Modeling wave-enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr., 24, 2546–2559.

  • Grant, A., and S. Belcher, 2009: Characteristics of Langmuir turbulence in the ocean mixed layer. J. Phys. Oceanogr., 39, 1871–1887.

    • Search Google Scholar
    • Export Citation

  • Harcourt, R., and E. D’Asaro, 2008: Simulation of Langmuir turbulence in pure wind seas. J. Phys. Oceanogr., 38, 1542–1562.

    • Search Google Scholar
    • Export Citation

  • Huang, N., 1979: On surface drift currents in the ocean. J. Fluid Mech., 91, 191–208.

  • Kim, S., B. Cornuelle, and E. Terrill, 2009: Anisotropic response of surface currents to the wind in a coastal regime. J. Phys. Oceanogr., 39, 1512–1532.

    • Search Google Scholar
    • Export Citation

  • Kukulka, T., A. Pluededdemann, J. Trowbridge, and P. Sullivan, 2010: Rapid mixed layer deepening by the combination of Langmuir and shear instabilities: A case study. J. Phys. Oceanogr., 40, 2381–2400.

    • Search Google Scholar
    • Export Citation

  • Large, W., J. McWilliams, and S. Doney, 1994: Oceanic vertical mixing: A review and a model with a non-local K-profile boundary layer parameterization. Rev. Geophys., 32, 363–403.

    • Search Google Scholar
    • Export Citation

  • Leibovich, S., 1983: The form and dynamics of Langmuir circulations. Annu. Rev. Fluid Mech., 36, 391–427.

  • McWilliams, J., and P. Sullivan, 2000: Vertical mixing by Langmuir circulations. Spill Sci. Technol., 6, 225–237.

  • McWilliams, J., and E. Huckle, 2006: Ekman layer rectification. J. Phys. Oceanogr., 36, 1646–1659.

  • McWilliams, J., P. Sullivan, and C. Moeng, 1997: Langmuir turbulence in the ocean. J. Fluid Mech., 334, 1–30.

  • Melville, W., F. Veron, and C. White, 2002: The velocity field under breaking waves: Coherent structures and turbulence. J. Fluid Mech., 454, 203–233.

    • Search Google Scholar
    • Export Citation

  • Moeng, C., 1984: A large eddy simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci., 41, 2052–2062.

    • Search Google Scholar
    • Export Citation

  • Polton, J., and S. Belcher, 2007: Langmuir turbulence and deeply penetrating jets in an unstratified mixed layer. J. Geophys. Res., 112, 1646–1659.

    • Search Google Scholar
    • Export Citation

  • Polton, J., D. Lewis, and S. Belcher, 2005: The role of wave-induced Coriolis-Stokes forcing on the wind-driven mixed layer. J. Phys. Oceanogr., 35, 444–457.

    • Search Google Scholar
    • Export Citation

  • Skyllingstad, E., and D. Denbo, 1995: An ocean large eddy simulation of Langmuir circulations and convection in the surface mixed layer. J. Geophys. Res., 100, 8501–8522.

    • Search Google Scholar
    • Export Citation

  • Smyth, W., E. Skyllingstad, G. Crawford, and H. Wijesekera, 2002: Nonlocal fluxes and Stokes drift effects in the K-profile parameterization. Ocean Dyn., 52, 104–115.

    • Search Google Scholar
    • Export Citation

  • Sullivan, P., and J. McWilliams, 2010: Dynamics of winds and currents coupled to surface waves. Annu. Rev. Fluid Mech., 42, 19–42.

    • Search Google Scholar
    • Export Citation

  • Sullivan, P., J. McWilliams, and W. Melville, 2007: Surface gravity wave effects in the oceanic boundary layer: Large eddy simulation with vortex force and stochastic breakers. J. Fluid Mech., 593, 405–452.

    • Search Google Scholar
    • Export Citation

  • Sullivan, P., J. McWilliams, and W. Melville, 2008: Catalyzing Craik-Leibovich instabilities by breaking waves. Proc. Fifth Int. Symp. on Environmental Hydraulics, Tempe, AZ, International Association of Hydraulic Engineering and Research, 171–184.

  • Sullivan, P., L. Romero, J. McWilliams, and W. Melville, 2012: Transient evolution of Langmuir turbulence in ocean boundary layers driven by hurricane winds and waves. J. Phys. Oceanogr., 42, 1959–1980.

    • Search Google Scholar
    • Export Citation

  • Terray, E., M. Donelan, Y. Agrawal, W. Drennan, K. Kahma, A. Williams, P. Hwang, and S. Kitaigorodskii, 1996: Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr., 26, 792–807.

    • Search Google Scholar
    • Export Citation

  • Weller, R., and J. Price, 1988: Langmuir circulations within the oceanic mixed layer. Deep-Sea Res., 35, 711–747.

  • Wu, J., 1983: Sea-surface drift currents induced by wind and waves. J. Phys. Oceanogr., 13, 1441–1451.

  • Zikanov, O., D. Slinn, and M. Dhanak, 2003: Large eddy simulations of the wind-induced turbulent Ekman layer. J. Fluid Mech., 495, 343–368.

    • Search Google Scholar
    • Export Citation
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