On the relative contribution of inertia-gravity wave radiation to asymmetric instabilities in tropical cyclone-like vortices

Intense geophysical vortices may experience various asymmetric instabilities during their life cycles. This study presents a convenient method for evaluating the relative importance of different mechanisms that can simultaneously influence the growth of an asymmetric perturbation. The method is illustrated in the context of vortices whose basic states are barotropic and have nonmonotonic radial distributions of potential vorticity. A diagnostic formula for the growth rate of the perturbation is derived from an equation expressing conservation of angular pseudomomentum. In this formula, the growth rate is decomposed into several components relevant to the most unstable modes. One component accounts for the destabilizing interaction of phase-locked counter-propagating vortex Rossby (VR) waves. Other components account for inertia-gravity (IG) wave radiation and potential vorticity stirring in one or more critical layers.

The dominant instabilities are examined for Rossby numbers between 10 and 100, and transitional Froude numbers centered about unity. This parameter regime is applicable to tropical cyclone (TC) perturbations with vertical lenghtscales comparable to the depth of the vortex. As the Froude number increases from its lower bound, the main cause of instability typically transitions from VR-VR wave interaction to IG wave radiation. The transition begins abruptly at a critical point where the two most unstable modes switch their order of dominance. In some cases, growth of the newly prevailing mode is almost completely driven by radiation. In other cases, the Froude number must continue to increase before radiation thoroughly controls the growth mechanism. Radiation driven instabilities at Froude numbers of order unity are shown to be quite fast and potentially relevant to real-world TCs. Critical layer stirring generally modifies the growth rate to an extent that cannot be ignored. The direction and magnitude of the modification are sensitive to subtle aspects of the potential vorticity distribution.This work is supported by NSERC and NSF.