Wavenumber-2 and wavenumber-m vortex Rossby wave instabilities in a generalized three-region model

Abstract

A recent study using a discrete three-region nondivergent approximation for the inner-core region of a mature hurricane-like vortex fails to catch wavenumber-2 azimuthal shear instabilities that are observed in experiments and predicted by similar continuous model representations. With hurricane applications in mind, a generalized version of a piecewise uniform three-region vortex model is presented. The necessary and sufficient criteria for wavenumber-2 and -m instabilities are derived and discussed. The peculiar dynamics of vortex Rossby waves on a discrete circular waveguide elucidate why wavenumber-2 instabilities have been difficult to find in previous analyses and also demonstrate some of the idiosyncrasies of the discrete model. The physical structure of the instabilities is also briefly examined.