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Instabilities and waves on a columnar vortex in a strongly stratified and rotating fluid

Junho Park 1, * Paul Billant 1 
Abstract : This paper investigates the effect of the background rotation on the radiative instability of a columnar Rankine vortex in a strongly stratified fluid. We show that a cyclonic background rotation strongly stabilizes the radiative instability. The modes become neutral when the Rossby number Ro is below a critical value which depends on the azimuthal wavenumber of the wave. In the limit of small Rossby number, there exist fast neutral waves that are not captured by the quasi-geostrophic theory. In the presence of anticyclonic background rotation, the centrifugal instability dominates the radiative instability only when -400 less than or similar to Ro < -1. The numerical stability analysis is completed by asymptotic analyses for large wavenumbers which explain the properties and mechanisms of the waves and the instabilities. The stability of a continuous smoothed Rankine vortex is also investigated. The most amplified azimuthal wavenumber is then finite instead of infinite for the Rankine vortex. (C) 2013 AIP Publishing LLC.
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Submitted on : Tuesday, May 27, 2014 - 3:32:06 PM
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Junho Park, Paul Billant. Instabilities and waves on a columnar vortex in a strongly stratified and rotating fluid. Physics of Fluids, 2013, 25 (8), pp.086601. ⟨10.1063/1.4816512⟩. ⟨hal-00996422⟩



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