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Coriolis effects on the elliptical instability in cylindrical and spherical rotating containers

Published online by Cambridge University Press:  07 August 2007

M. LE BARS ,
S. LE DIZÈS  and
P. LE GAL
M. LE BARS
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre – CNRS, Aix-Marseille Université, UMR 6594, 49, rue F. Joliot Curie, B.P. 146, F-13384 Marseille Cedex 13, France
S. LE DIZÈS
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre – CNRS, Aix-Marseille Université, UMR 6594, 49, rue F. Joliot Curie, B.P. 146, F-13384 Marseille Cedex 13, France
P. LE GAL
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre – CNRS, Aix-Marseille Université, UMR 6594, 49, rue F. Joliot Curie, B.P. 146, F-13384 Marseille Cedex 13, France
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Abstract

The effects of the Coriolis force on the elliptical instability are studied experimentally in cylindrical and spherical rotating containers placed on a table rotating at a fixed rate . For a given set-up, changing the ratio ΩG of global rotation to flow rotation leads to the selection of various unstable modes due to the presence of resonance bands, in close agreement with the normal-mode theory. No instability occurs when ΩG varies between −3/2 and −1/2 typically. On decreasing ΩG toward −1/2, resonance bands are first discretized for ΩG<0 and progressively overlap for −1/2 ≪ ΩG < 0. Simultaneously, the growth rates and wavenumbers of the prevalent stationary unstable mode significantly increase, in quantitative agreement with the viscous short-wavelength analysis. New complex resonances have been observed for the first time for the sphere, in addition to the standard spin-over. We argue that these results have significant implications in geo- and astrophysical contexts.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 585 , 25 August 2007 , pp. 323 - 342
Copyright
Copyright © Cambridge University Press 2007

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