Three-dimensional instability of isolated vortices

Abstract : We study the three-dimensional stability of the family of vortices introduced by Carton and McWilliams [Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence, edited by Nikhoul and Jamart (Elsevier, New York, 1989)] describing isolated vortices. For these vortices, the circulation vanishes outside their core over a distance depending on a single parameter, the steepness a. We proceed to the direct numerical simulation of the linear impulse response to obtain both temporal and spatio-temporal instability results. In the temporal instability framework, growth rates are calculated as a function of the axial wavenumber k and the azimuthal wavenumber m. The stability analysis is performed at a Reynolds number of Re=667. It is shown that the most unstable mode is the axisymmetric mode m=0, regardless of the steepness parameter in the investigated range. When the steepness a is increased the band of unstable azimuthal modes widens, i.e., larger m are destabilized. The study of the spatio-temporal spreading of the wave packet shows that the m=2 mode is always the fastest traveling mode, for all studied values of the steepness parameter. © 2003 American Institute of Physics.
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Physics of Fluids, American Institute of Physics, 2003, 15 (8), pp.2113-2126. 〈10.1063/1.1580481〉
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François Gallaire, Jean-Marc Chomaz. Three-dimensional instability of isolated vortices. Physics of Fluids, American Institute of Physics, 2003, 15 (8), pp.2113-2126. 〈10.1063/1.1580481〉. 〈hal-01024926〉

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