Wavenumber-2 and Wavenumber-m Vortex Rossby Wave Instabilities in a Generalized Three-Region Model

Wesley D. Terwey Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado

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Michael T. Montgomery Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado

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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.

Corresponding author address: Mr. Wesley D. Terwey, Dept. of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371. Email: terwey@atmos.colostate.edu

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.

Corresponding author address: Mr. Wesley D. Terwey, Dept. of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371. Email: terwey@atmos.colostate.edu

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