Nonseparable Baroclinic Instability. Part I: Quasi-geostroPhic Dynamics

G. W. Kent Moore Department of Physics. University of Toronto. Toronto, Ontario. Canada

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W. R. Peltier Department of Physics. University of Toronto. Toronto, Ontario. Canada

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Abstract

We address the problem of the stability of nonseparable baroclinic mean states against small-amplitude quasi-geostrophic perturbations. A general numerical methodology is developed that allows us to construct solutions to such problems without requiring any simplifying assumptions.

A previous investigation of frontal stability (Moore and Peltier) which was based upon the use of the primitive equations, demonstrated that frontal zones are unstable to a cyclone-scale mode of baroclinic instability. This mode had not been detected in any previous stability analysis. No evidence of this new mode is found in the results for the quasi-geostrophic problems reported here. In fact, it is shown that the dynamical constraints implied by the quasi-geostrophic approximation forbid the existence of such modes. We also show that recently reported quasi-geostrophic stability analyses that make simplifying assumptions regarding the meridional structure of the basic state have a markedly limited validity.

The present study, therefore, serves to reemphasize the fact that the stability characteristics of nonseparable mean states can be rather complex. The only way to truly understand them is to solve the stability problem without approximating either the field equations employed in the analysis or the structure of the mean state whose stability is under investigation.

Abstract

We address the problem of the stability of nonseparable baroclinic mean states against small-amplitude quasi-geostrophic perturbations. A general numerical methodology is developed that allows us to construct solutions to such problems without requiring any simplifying assumptions.

A previous investigation of frontal stability (Moore and Peltier) which was based upon the use of the primitive equations, demonstrated that frontal zones are unstable to a cyclone-scale mode of baroclinic instability. This mode had not been detected in any previous stability analysis. No evidence of this new mode is found in the results for the quasi-geostrophic problems reported here. In fact, it is shown that the dynamical constraints implied by the quasi-geostrophic approximation forbid the existence of such modes. We also show that recently reported quasi-geostrophic stability analyses that make simplifying assumptions regarding the meridional structure of the basic state have a markedly limited validity.

The present study, therefore, serves to reemphasize the fact that the stability characteristics of nonseparable mean states can be rather complex. The only way to truly understand them is to solve the stability problem without approximating either the field equations employed in the analysis or the structure of the mean state whose stability is under investigation.

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