Transient Growth of Ageostrophic Perturbations in a Baroclinic Shear Flow

Abstract

Ageostrophic instabilities of shear flows are important for the meso-scale dynamics of atmospheric fronts, especially for the generation of gravity waves and front destabilisation leading to secondary cyclogenesis. In this work a Generalized Stability Theory (GST) analysis of a constant baroclinic shear flow is performed for a wide range of values for the Richardson number Ri  ~ 0.1–100. GST is a linear stability theory that subsumes the modal stability theory of Rayleigh while also addresses explosive transient growth of perturbations. It is found that for large Richardson numbers, the results for the quasi-geostrophic (QG) regime are recovered, with growth of perturbations occurring due to the baroclinic conversion of mean available potential energy to perturbation energy via the eddy heat flux. However, the growth found for the primitive equations exceeds the corresponding growth of the QG dynamics by one percent. In the parameter regime away from QG (even for large Richardson numbers), an additional mechanism for perturbation growth is found: the direct conversion of mean kinetic energy to perturbation kinetic energy via the eddy momentum flux. In this case perturbation growth is found to greatly exceed QG growth by as much as 67 % for Ri = 100.