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

Junho Park (1) , Paul Billant (1)

1 LadHyX - Laboratoire d'hydrodynamique

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.

Domains: Physics [physics]; Mechanics [physics]; Fluid mechanics [physics.class-ph]; Engineering Sciences [physics]; Mechanics [physics.med-ph]; Fluids mechanics [physics.class-ph]

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⟩