Baroclinic Instability at Long Wavelengths on a β-Plane

John E. Geisler Rosenstiel School of Marine and Atmospheric Science, University of Miami, Coral Gables, Fla. 33124

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Rolando R. Garcia National Center for Atmospheric Research, Boulder, Colo. 80307

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Abstract

The problem of the baroclinic instability of an atmospheric zonal flow which is a continuous function of altitude above a horizontal boundary on a, β-plane exhibits two classes of unstable normal mode solutions. One of these consists of the rapidly growing modes discovered by Charney (1947). A second class consisting of the more slowly growing modes at longer wavelengths first found by Green (1960) has received comparatively little attention. This paper presents results of a numerical study of this class of modes that show how their growth rate and vertical structure depend on basic state model parameters. In the absence of dissipation the e-folding times of these modes at planetary wave scales is about one week. The vertical structure at these scales is that of a trapped internal normal mode with associated wind and temperature fields typically an order of magnitude larger in the middle and upper stratosphere than at the ground.

Abstract

The problem of the baroclinic instability of an atmospheric zonal flow which is a continuous function of altitude above a horizontal boundary on a, β-plane exhibits two classes of unstable normal mode solutions. One of these consists of the rapidly growing modes discovered by Charney (1947). A second class consisting of the more slowly growing modes at longer wavelengths first found by Green (1960) has received comparatively little attention. This paper presents results of a numerical study of this class of modes that show how their growth rate and vertical structure depend on basic state model parameters. In the absence of dissipation the e-folding times of these modes at planetary wave scales is about one week. The vertical structure at these scales is that of a trapped internal normal mode with associated wind and temperature fields typically an order of magnitude larger in the middle and upper stratosphere than at the ground.

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