Baroclinic Instability at Long Wavelengths on a β-Plane

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, ?-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.