Radiative instability of an anticyclonic vortex in a stratified rotating fluid

Journal of Fluid Mechanics

Journal of Fluid Mechanics / Volume 707 / September 2012, pp 381-392
Copyright © Cambridge University Press 2012
DOI: http://dx.doi.org/10.1017/jfm.2012.286 (About DOI), Published online: 27 July 2012

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Radiative instability of an anticyclonic vortex in a stratified rotating fluid

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park j [Google Scholar]
billant p [Google Scholar]

Junho Park^a1 ^c1 and Paul Billant^a1

^a1LadHyX, CNRS, École Polytechnique, F-91128 Palaiseau CEDEX, France

Abstract

In strongly stratified fluids, an axisymmetric vertical columnar vortex is unstable because of a spontaneous radiation of internal waves. The growth rate of this radiative instability is strongly reduced in the presence of a cyclonic background rotation $f/ 2$ and is smaller than the growth rate of the centrifugal instability for anticyclonic rotation, so it is generally expected to affect vortices in geophysical flows only if the Rossby number $Ro= 2\Omega / f$ is large (where $\Omega$ is the angular velocity of the vortex). However, we show here that an anticyclonic Rankine vortex with low Rossby number in the range $\ensuremath{-} 1\leq Ro\lt 0$ , which is centrifugally stable, is unstable to the radiative instability when the azimuthal wavenumber $\vert m\vert$ is larger than 2. Its growth rate for $Ro= \ensuremath{-} 1$ is comparable to the values reported in non-rotating stratified fluids. In the case of continuous vortex profiles, this new radiative instability is shown to occur if the potential vorticity of the base flow has a sufficiently steep radial profile. The most unstable azimuthal wavenumber is inversely proportional to the steepness of the vorticity jump. The properties and mechanism of the instability are explained by asymptotic analyses for large wavenumbers.