Eliassen–Palm Fluxes and the Momentum Equation in Non-Eddy-Resolving Ocean Circulation Models

Peter R. Gent National Center for Atmospheric Research, Boulder, Colorado

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James C. McWilliams National Center for Atmospheric Research, Boulder, Colorado and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Los Angeles, California

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Abstract

The concepts of residual-mean circulation, transformed Eulerian-mean equations, and Eliassen–Palm fluxes are generalized when the averaging is a low-pass operator in time and space rather than a zonal average. Thus, the eddy motions being considered are ocean eddies on short time and small space scales rather than either purely transient eddies or steady, zonally averaged, standing eddies as commonly considered for the atmosphere.

The generalized Eliassen–Palm fluxes are then parameterized as downgradient momentum diffusion plus the appropriate Coriolis term. This gives a momentum equation for use in non-eddy-resolving ocean circulation models. The resulting potential vorticity equation is then analyzed and the quasigeostrophic limit taken. When the adiabatic tracer parameterization of Gent and McWilliams is also used, this equation is close to showing that quasigeostrophic potential vorticity is advected by the geostrophic velocity and diffused by a Laplacian operator.

A discussion of the Antarctic Circumpolar Current and the meridional-plane circulation, the Deacon cell, in the Southern Hemisphere ocean follows. In an eddy-resolving model with nearly adiabatic interior dynamics, the Deacon cell essentially does not appear when the zonal averaging of the meridional velocity is taken along a constant density surface. This result has a counterpart in non-eddy-resolving ocean model simulations in that the Deacon cell is partially cancelled by the parameterized eddy-induced mass transport.

Abstract

The concepts of residual-mean circulation, transformed Eulerian-mean equations, and Eliassen–Palm fluxes are generalized when the averaging is a low-pass operator in time and space rather than a zonal average. Thus, the eddy motions being considered are ocean eddies on short time and small space scales rather than either purely transient eddies or steady, zonally averaged, standing eddies as commonly considered for the atmosphere.

The generalized Eliassen–Palm fluxes are then parameterized as downgradient momentum diffusion plus the appropriate Coriolis term. This gives a momentum equation for use in non-eddy-resolving ocean circulation models. The resulting potential vorticity equation is then analyzed and the quasigeostrophic limit taken. When the adiabatic tracer parameterization of Gent and McWilliams is also used, this equation is close to showing that quasigeostrophic potential vorticity is advected by the geostrophic velocity and diffused by a Laplacian operator.

A discussion of the Antarctic Circumpolar Current and the meridional-plane circulation, the Deacon cell, in the Southern Hemisphere ocean follows. In an eddy-resolving model with nearly adiabatic interior dynamics, the Deacon cell essentially does not appear when the zonal averaging of the meridional velocity is taken along a constant density surface. This result has a counterpart in non-eddy-resolving ocean model simulations in that the Deacon cell is partially cancelled by the parameterized eddy-induced mass transport.

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