Baroclinic instability of ultra-long waves modelled by the planetary geostrophic equations

Abstract

Abstract The stability of a zonal flow with uniform vertical shear and planetary scale latitudinal variation to perturbations of ultra-long wavelength is examined analytically by means of the Planetary Geostrophic (PG) equations (Phillips' (1963) Quasi-Geostrophic equations of type 2). When applied to a two leve1 model these equations imply instability only for strong easterly shear. With continuous vertical resolution instability is found for both westerly and strong easterly shear. For moderate westerly shear the growth rates are larger than predicted by Quasi-Geostrophic theory (of type 1) in the case of wave-numbers one and two. nese modes have pronounced amplitude maxima in the upper atmosphere and may play an important role in the dynamics of the winter stratosphere especially in the southern hemisphere. In the case of uniform westerly wind the predicted motion is a vertically trapped mode whose westward phase-speed is largely independent of the magnitude of the background flow. For wavenumber one t...