On Moist Quasi-Geostrophic Barotropic Instability

Abstract

The instability of quasi-geostrophic internal modes in a moist model atmosphere with the presence of a purely barotropic basic flow is investigated. The author's formulation for a self-induced condensational heating (Mak) is adopted in a prototype model that has a hyperbolic-tangent barotropic basic flow. It is shown that a cooperative interaction can occur between the quasi-geostrophic internal modes and the implicitly embedded convection. Such an internal mode, instead of the external mode, becomes the dominant unstable mode even when the heating is only moderately strong. While the generalized Rayleigh condition of shear instability (Kuo) is a necessary condition for having an unstable external mode, it is not so for having an unstable internal mode under the influence of condensational heating. Depending upon the heating intensity, the required shear for such instability can be greatly, reduced. As the heating is increased, the short-wave cutoff is significantly reduced, but the length scale of the most unstable mode is only asymptotically shortened toward an intermediate scale. The phase speed remains essentially controlled by the steering influence of the basic flow. When a heating profile with larger values in the lower troposphere than in the upper troposphere is used, there would be a larger maximum growth rate and a shorter preferred wavelength. The results concerning the structural and energetic properties of the most unstable wave are also presented. An application of this model is made with a basic flow of an easterly jet that has a Gaussian distribution. The results suggest that the moist dynamical mechanism under consideration would provide a more general explanation of the formation of the African easterly waves.