Baroclinic Instability in a Fluid with Three Layers

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  • 1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England
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Abstract

A three-layer model is used to study the effect of curvature in the vertical profile of the horizontal velocity on the linear baroclinic instability of a simple quasi-geostrophic flow. Potential vorticity is conserved and the β-effect is included. The results indicate that the range of unstable wavelengths increases as the curvature is increased from zero. For a given physical state, there may be more than one critical wavelength for which the waves are marginally stable. Growth rates for β = 0 and the structure of the fastest growing waves are given. A comparison is made between two-layer, three-layer and continuous systems.

Abstract

A three-layer model is used to study the effect of curvature in the vertical profile of the horizontal velocity on the linear baroclinic instability of a simple quasi-geostrophic flow. Potential vorticity is conserved and the β-effect is included. The results indicate that the range of unstable wavelengths increases as the curvature is increased from zero. For a given physical state, there may be more than one critical wavelength for which the waves are marginally stable. Growth rates for β = 0 and the structure of the fastest growing waves are given. A comparison is made between two-layer, three-layer and continuous systems.

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