Baroclinic Instability of a Slowly Varying Zonal Flow

Abstract

Eady's model of baroclinic instability is extended by allowing the basic velocity profile to vary slowly in the meridional direction. The eigenfunctions are found by simple use of the WKB technique, and the meridional scale of the growing baroclinic waves is found to be influenced by the width of the jet in the basic velocity profile and by the radius of deformation. Calculation of the eigenvalues reveals that the waves with the longest meridional wavelength are the most unstable. The same method is then applied to the two-layer model, and the same qualitative results are found as for the continuous model. These results are compared with some recent numerical work by Simmons. The present method extends the work of Stone who used a similar technique and included the ?-effect in his two-layer model. He assumed that the scale of the most unstable waves was always the Rossby radius of deformation, so that the meridional wave-number was proportional to the width of the channel considered. For disturbances between the pole and equator, he found that the meridional wavenumber of the most unstable waves was usually either 3 or 4.