Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia–buoyancy wave emission

Abstract

This paper further examines the rate at which potential vorticity in the core of a monotonic cyclone becomes vertically aligned and horizontally axisymmetric. We consider the case in which symmetrization occurs by the damping of a discrete vortex Rossby (VR) wave. The damping of the VR wave is caused by its stirring of potential vorticity at a critical radius r*, outside the core of the cyclone. The decay rate generally increases with the radial gradient of potential vorticity at r*. Previous theories for the decay rate were based on “balance models” of the vortex dynamics. Such models filter out inertia–buoyancy (IB) oscillations, i.e., gravity waves. However, if the Rossby number is greater than unity, the core VR wave can excite a frequency-matched outward propagating IB wave, which has positive feedback. To accurately account for this radiation, we here develop a theory for the decay rate that is based on the hydrostatic primitive equations. Starting from conservation of wave activity (angular pseudomomentum), an expression for the decay rate is derived. This expression explicitly demonstrates a competition between the destabilizing influence of IB wave emission, and the stabilizing influence of potential vorticity stirring at r*. Moreover, it shows that if the radial gradient of potential vorticity at r* exceeds a small threshold, the VR wave will decay, and the vortex will symmetrize, even at large Rossby numbers.