On Mean Flow Instabilities within the Planetary Geostrophic Equations

Alain Colin de Verdière IFREMER, Centre de Brest, B.P. 337, 29273 Brest Cédex, France

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Abstract

This note draws attention to the natural instabilities of a mean zonal flow that arise with the planetary geostrophic equations increasingly used in theories of large-scale oceanic circulation. Baroclinic instability is not excised by the absence of the relative acceleration terms in the momentum equations. The growth rate is shown to increase linearly with wavenumber, yielding an ill-posed mathematical problem. A small amount of lateral friction cures the problem, however, as shown in a three-layer model, which possesses the minimal vertical structure to exhibit the instability.

Abstract

This note draws attention to the natural instabilities of a mean zonal flow that arise with the planetary geostrophic equations increasingly used in theories of large-scale oceanic circulation. Baroclinic instability is not excised by the absence of the relative acceleration terms in the momentum equations. The growth rate is shown to increase linearly with wavenumber, yielding an ill-posed mathematical problem. A small amount of lateral friction cures the problem, however, as shown in a three-layer model, which possesses the minimal vertical structure to exhibit the instability.

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