Radiative Instability of a Barotropic Jet Flow in a Rotating Stratified Atmosphere

Abstract

This paper investigates the stability of a jet flow with a piecewise linear velocity profile in a rotating stratified atmosphere. The linearized set of perturbation equations is reduced to one longitudinal-velocity amplitude equation with turning points. An asymptotic solution of the equation, valid at small Rossby numbers, is derived in terms of the Airy functions. A flow that is stable in a quasi-geostrophic approximation is shown to become unstable due to the emission of inertia–gravity waves. An analytic expression for the growth increment of the perturbations is derived.