Baroclinically Unstable Modes of a Two-Layer Model on the Sphere

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  • 1 Atmospheric Environment Service, Montreal, Quebec, Canada
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Abstract

A model consisting of two layers of inviscid, constant-density fluid in stable stratification on a rotating gravitating sphere is linearized about a basic state consisting of a steady zonal flow with arbitrary latitudinal variation in the upper layer, balanced geostrophically by mean free surface and interfacial slopes. Normal modes solutions are assumed and a Galerkin procedure employed to obtain approximate solutions to the resulting eigenproblem for various basic state wind profiles. Baroclinically unstable modes for the basic states of constant angular rotation in the upper layer and of jet-type wind profiles are compared with the results of mid-latitude β-plane studies. In general, it is found that the spherical model produces modes with growth rates in reasonable agreement to those predicted by β-plane theory, but for the parameter ranges consistent with the model their growth rates are somewhat smaller than those suitable for typical mid-latitude storms.

Abstract

A model consisting of two layers of inviscid, constant-density fluid in stable stratification on a rotating gravitating sphere is linearized about a basic state consisting of a steady zonal flow with arbitrary latitudinal variation in the upper layer, balanced geostrophically by mean free surface and interfacial slopes. Normal modes solutions are assumed and a Galerkin procedure employed to obtain approximate solutions to the resulting eigenproblem for various basic state wind profiles. Baroclinically unstable modes for the basic states of constant angular rotation in the upper layer and of jet-type wind profiles are compared with the results of mid-latitude β-plane studies. In general, it is found that the spherical model produces modes with growth rates in reasonable agreement to those predicted by β-plane theory, but for the parameter ranges consistent with the model their growth rates are somewhat smaller than those suitable for typical mid-latitude storms.

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