Nonseparable Baroclinic Instability. Part II: Primitive-Equations Dynamics

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  • 1 Department of Physics, University of Toronto, Toronto, Ontario, Canada
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Abstract

The problem of the origin of midlatitude cyclonic disturbances having characteristic spatial scales of 1000 km or less has remained outstanding for most of this century. Although the theory of baroclinic instability of Charney and Eady has often been assumed to account for their appearance, Charney himself recognized that this was not so. In an attempt to develop a unique explanation for the observed scale of these systems we have been reinvestigating the classical problem of the baroclinic instability of synoptic-scale frontal zones. This work has shown that when the stability of such regions is analyzed using the hydrostatic primitive equations, a new mode of baroclinic instability is revealed, which has precisely the required scale. The new mode is completely filtered out in both the quasi-geostrophic and semigeostrophic systems.

In the present paper we return to the primitive equations system to further analyze this problem and to refine the numerical formulation so as to enable an accurate investigation of the sensitivity of the growth rate and spatial scale of the new mode to the detailed properties of the background frontal flow. This demonstrates that focusing of the region of low Richardson number near the surface is most conducive to the growth of the cyclone wave.

Abstract

The problem of the origin of midlatitude cyclonic disturbances having characteristic spatial scales of 1000 km or less has remained outstanding for most of this century. Although the theory of baroclinic instability of Charney and Eady has often been assumed to account for their appearance, Charney himself recognized that this was not so. In an attempt to develop a unique explanation for the observed scale of these systems we have been reinvestigating the classical problem of the baroclinic instability of synoptic-scale frontal zones. This work has shown that when the stability of such regions is analyzed using the hydrostatic primitive equations, a new mode of baroclinic instability is revealed, which has precisely the required scale. The new mode is completely filtered out in both the quasi-geostrophic and semigeostrophic systems.

In the present paper we return to the primitive equations system to further analyze this problem and to refine the numerical formulation so as to enable an accurate investigation of the sensitivity of the growth rate and spatial scale of the new mode to the detailed properties of the background frontal flow. This demonstrates that focusing of the region of low Richardson number near the surface is most conducive to the growth of the cyclone wave.

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