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Equilibrium Statistical Mechanics of Barotropic Flow over Finite Topography

William J. MerryfieldInstitute of Ocean Sciences, Sidney, British Columbia, Canada

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Patrick F. CumminsInstitute of Ocean Sciences, Sidney, British Columbia, Canada

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Greg HollowayInstitute of Ocean Sciences, Sidney, British Columbia, Canada

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Abstract

Inviscid equilibria of barotropic flows over finite-amplitude topography are determined by means of statistical mechanics, extending previous quasigeostrophic theory. Imposing constraints of energy and enstrophy conservation leads to a linear relation between equilibrium mean potential vorticity and mean transport streamfunction. This relation is tested numerically and is found to hold over a wide range of topographic amplitudes. Implications for improving parameterizations of entropy generation by eddies are discussed.

Corresponding author address: William J. Merryfield, Institute of Ocean Sciences, P.O. Box 6000, 9860 West Saanich Road, Sidney, BC V8L 4B2, Canada.Email: merryfieldw@pac.dfo-mpo.gc.ca

Abstract

Inviscid equilibria of barotropic flows over finite-amplitude topography are determined by means of statistical mechanics, extending previous quasigeostrophic theory. Imposing constraints of energy and enstrophy conservation leads to a linear relation between equilibrium mean potential vorticity and mean transport streamfunction. This relation is tested numerically and is found to hold over a wide range of topographic amplitudes. Implications for improving parameterizations of entropy generation by eddies are discussed.

Corresponding author address: William J. Merryfield, Institute of Ocean Sciences, P.O. Box 6000, 9860 West Saanich Road, Sidney, BC V8L 4B2, Canada.Email: merryfieldw@pac.dfo-mpo.gc.ca

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