On Transversely Isotropic Eddy Viscosity

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  • 1 Institute of Geophysics and Planetary Physics, University of California, San Diego, La Jolla, California
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Abstract

The conventional parameterization of diffusion in geophysical fluid dynamics, which replaces v2u in the Navier-Stokes equations by [AHx2 + δy2) + AVδz2]u, where AH and AV are eddy viscosities, rests on the hypothesis that the Reynolds-stress tensor τij is a symmetric, transversely isotropic function of the mean velocity-gradient tensor. This implies that τij depends on both the mean rate of strain and the mean vorticity and that the kinetic energy of the turbulent fluctuations may be negative. The most general transversely isotropic relation that can be derived from the Boussinesq closure hypothesis, which separates the isotropic and deviatoric parts of. τij and excludes the vorticity, comprises three parameters. It is impossible to obtain the conventional parameterization through any choice of these parameters, but it is possible to obtain an equivalent parameterization if the hydrostatic and quasigeostrophic approximations are invoked.

Abstract

The conventional parameterization of diffusion in geophysical fluid dynamics, which replaces v2u in the Navier-Stokes equations by [AHx2 + δy2) + AVδz2]u, where AH and AV are eddy viscosities, rests on the hypothesis that the Reynolds-stress tensor τij is a symmetric, transversely isotropic function of the mean velocity-gradient tensor. This implies that τij depends on both the mean rate of strain and the mean vorticity and that the kinetic energy of the turbulent fluctuations may be negative. The most general transversely isotropic relation that can be derived from the Boussinesq closure hypothesis, which separates the isotropic and deviatoric parts of. τij and excludes the vorticity, comprises three parameters. It is impossible to obtain the conventional parameterization through any choice of these parameters, but it is possible to obtain an equivalent parameterization if the hydrostatic and quasigeostrophic approximations are invoked.

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