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Elliptic instability of a stratified fluid in a rotating cylinder

Published online by Cambridge University Press:  16 July 2010

D. GUIMBARD ,
S. LE DIZÈS ,
M. LE BARS ,
P. LE GAL  and
S. LEBLANC
D. GUIMBARD
Affiliation:
IRPHE, UMR 6594, CNRS, University of Aix-Marseille, 49 rue F. Joliot Curie, F-13013 Marseille, France LSEET, UMR 6017, CNRS, University of Toulon-Var, BP 20132, F-83957 La Garde Cedex, France
S. LE DIZÈS*
Affiliation:
IRPHE, UMR 6594, CNRS, University of Aix-Marseille, 49 rue F. Joliot Curie, F-13013 Marseille, France
M. LE BARS
Affiliation:
IRPHE, UMR 6594, CNRS, University of Aix-Marseille, 49 rue F. Joliot Curie, F-13013 Marseille, France
P. LE GAL
Affiliation:
IRPHE, UMR 6594, CNRS, University of Aix-Marseille, 49 rue F. Joliot Curie, F-13013 Marseille, France
S. LEBLANC
Affiliation:
LSEET, UMR 6017, CNRS, University of Toulon-Var, BP 20132, F-83957 La Garde Cedex, France
*
†Email address for correspondence: ledizes@irphe.univ-mrs.fr
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Abstract

In this paper, we analyse the characteristics of the elliptic instability in a finite cylinder in the presence of both background rotation and axial stratification. A general formula for the linear growth rate of the stationary sinuous modes is derived including viscous and detuning effects in the limit of small eccentricity. This formula is discussed and compared to experimental results which are obtained in a cylinder filled with salted water for two different eccentricities by varying the stratification, the background rotation and the cylinder rotation. A good agreement with the theory concerning the domain of instability of the sinuous modes is demonstrated. Other elliptic instability modes, oscillating at the cylinder angular frequency are also evidenced together with a new type of instability mode, which could be connected to a centrifugal instability occurring during the experimental phase of spin-up. The nonlinear regime of the elliptic instability is also documented. In contrast with the homogeneous case, no cycle involving growth, breakdown and re-laminarization is observed in the presence of strong stratification. The elliptic instability in a stratified fluid seems to yield either a persistent turbulent state or a weakly nonlinear regime.

JFM classification

Geophysical and Geological Flows: Stratified flows Vortex Flows: Vortex instability Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 660 , 10 October 2010 , pp. 240 - 257
Copyright
Copyright © Cambridge University Press 2010

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