On the Energy Conversion during Geostrophic Adjustment

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  • 1 Lamont-Doherty Geological Observatory of Columbia University, Palisades, NY 10964
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Abstract

It is found that for a continuously stratified fluid which remains so during the geostrophic adjustment, the energy conversion ratio γ (≡ΔKEPE) is ½, in contrast to the value of ⅓ for a two-layer fluid. Since the two-layer fluid is an asymptotic limit of a continuously stratified fluid, it is deduced that γ decreases smoothly from ½ to ⅓ when density discontinuities are formed during the adjustment. Furthermore, the total energy released during the adjustment is found to be inversely proportional to the dimensionless horizontal scale (scaled by the baroclinic radius of deformation) characterizing the density variation in the initial state.

Abstract

It is found that for a continuously stratified fluid which remains so during the geostrophic adjustment, the energy conversion ratio γ (≡ΔKEPE) is ½, in contrast to the value of ⅓ for a two-layer fluid. Since the two-layer fluid is an asymptotic limit of a continuously stratified fluid, it is deduced that γ decreases smoothly from ½ to ⅓ when density discontinuities are formed during the adjustment. Furthermore, the total energy released during the adjustment is found to be inversely proportional to the dimensionless horizontal scale (scaled by the baroclinic radius of deformation) characterizing the density variation in the initial state.

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