Waves and instabilities on vortices in stratified and rotating fluids

Abstract : In stratified rotating fluids, waves sustained by a vertical columnar vortex can be unstable due to an outward radiation of waves, a phenomenon known as the radiative instability. In the first part of this thesis, we investigate numerically and analytically the effect of a planetary rotation on this instability. When the planetary rotation is cyclonic, the wave radiation is reduced so that the maximum growth rate of the radiative instability decreases exponentially as the rotation increases. It becomes negligibly small when the Rossby number is smaller than unity. When the planetary rotation is anticyclonic with Rossby number higher than -1, the centrifugal instability is stable but it is shown that the radiative instability also occurs when the azimuthal wavenumber is larger than 2 and the vorticity profile sufficiently steep. The maximum growth rate in this strong anticyclonic regime is comparable to the one in the cyclonic regime. The main conclusion is therefore that a columnar vortex in a stratified rotating fluid can be unstable for any Rossby number. The mechanism and properties of the radiative instability are explained by means of WKBJ analyses for large wavenumbers. In the second part of the thesis, the stability of the stratified Taylor-Couette flow is studied when the angular velocity increases radially, a regime never explored before. We show that such flow is unstable to a strato-rotational instability. Such instability is closely related to the radiative instability of a vortex in the anticyclonic regime. These results reveal that the stratified Taylor-Couette flow is always unstable except for pure solid-body rotation.
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Junho Park. Waves and instabilities on vortices in stratified and rotating fluids. Mechanics of the fluids [physics.class-ph]. Ecole Polytechnique X, 2012. English. ⟨pastel-00786642⟩

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