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Elliptical instability in a rotating spheroid

Published online by Cambridge University Press:  21 April 2004

LAURENT LACAZE
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre, UMR 6594, CNRS & Universités d'Aix-Marseille I et II, 49 rue F. Joliot-Curie, BP146, Technopole de Château-Gombert, 13384 Marseille Cédex 13, France
PATRICE LE GAL
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre, UMR 6594, CNRS & Universités d'Aix-Marseille I et II, 49 rue F. Joliot-Curie, BP146, Technopole de Château-Gombert, 13384 Marseille Cédex 13, France
STÉPHANE LE DIZÈS
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre, UMR 6594, CNRS & Universités d'Aix-Marseille I et II, 49 rue F. Joliot-Curie, BP146, Technopole de Château-Gombert, 13384 Marseille Cédex 13, France

Abstract

This paper concerns the elliptical instability of a flow in a rotating deformed sphere. The aim of our work is to analyse the characteristics of this instability experimentally and to provide a theoretical model which accounts for the observations. For this purpose, an elastic and transparent hollow sphere has been moulded in a silicone gel block. The flow is visualized using Kalliroscope flakes illuminated with a laser sheet as the sphere is set into rotation and compressed by two rollers. The elliptical instability occurs by the appearance of the so-called ‘spin-over’ mode whose growth rate and saturation amplitude are measured by video image analysis at different Ekman numbers. Growth rates are predicted well by the linear stability analysis. A nonlinear model is developed and is shown to describe correctly the saturated regimes observed in the experiments. At low Ekman numbers, a secondary instability leading to an intermittent regime is also discovered.

Type
Papers
Copyright
© 2004 Cambridge University Press

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