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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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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