Session CN: Vortex Dynamics and Vortex Flows II
1:00 PM–3:10 PM, Sunday, November 21, 2010
Long Beach Convention Center Room: 202C
Chair: Bartosz Protas, McMaster University
Abstract ID: BAPS.2010.DFD.CN.5
Abstract: CN.00005 : A unified criterion for the centrifugal instability of vortices and swirling jets
1:52 PM–2:05 PM
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Abstract 
Authors:
Paul Billant
(LadHyX, CNRS-Ecole Polytechnique, F-91128 Palaiseau, France)
Francois Gallaire
(LFMI, EPFL, 1015 Lausanne, Switzerland)
It is well known that swirling jets can become centrifugally unstable like pure vortices but with a different azimuthal wavenumber selection. The Leibovich and Stewartson (1983) criterion is a generalization of the Rayleigh criterion to swirling jets: it is a sufficient condition for instability with respect to perturbations with both large axial and azimuthal wavenumbers. We have relaxed the large azimuthal wavenumber assumption in this criterion and obtained a new criterion that is valid whatever the azimuthal wavenumber and whatever the magnitude of the axial flow: from zero (pure vortex) to finite values (swirling jets). The new criterion recovers the Leibovich-Stewartson criterion when the azimuthal wavenumber is large and the Rayleigh criterion when the azimuthal wavenumber is small. The criterion is confirmed by comparisons with numerical stability analyses of various classes of swirling jet profiles. In the case of the Batchelor vortex, it provides more accurate results for perturbations with finite azimuthal wavenumbers than the Leibovich-Stewartson criterion. The criterion shows also that a whole range of azimuthal wavenumbers are destabilized as soon as a non-zero axial velocity component is present in a centrifugally unstable vortex.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2010.DFD.CN.5