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Spatiotemporal instability of a variable-density Batchelor vortex

Published online by Cambridge University Press:  12 June 2012

Bastien Di Pierro  and
Malek Abid
Bastien Di Pierro
Affiliation:
IRPHE – UMR 6594, Technopôle de Château-Gombert, 49 rue Joliot Curie – B.P. 146, 13384 Marseille CEDEX 13, France
Malek Abid*
Affiliation:
IRPHE – UMR 6594, Technopôle de Château-Gombert, 49 rue Joliot Curie – B.P. 146, 13384 Marseille CEDEX 13, France
*
†Email address for correspondence: [email protected]
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Abstract

Linear and nonlinear impulse responses are computed, using three-dimensional numerical simulations, for an incompressible and variable density (inhomogeneous) Batchelor vortex at a moderately high Reynolds number, . In the linear framework, the computed wavepacket is decomposed into azimuthal modes whose growth rates are determined along each spatiotemporal ray, in the laboratory frame. It is found that the Batchelor vortex undergoes a convective/absolute transition when the density ratio (inner/ambient), , is varied solely (there is no need for an external counter flow to trigger this transition like that needed in the constant density case). More precisely, it is shown that the transition occurs for heavy vortices when the density ratio reaches a critical value, . For light vortices () no transition was found. It is also shown that the first azimuthal mode that transits have an azimuthal wavenumber and the transition occurs for a swirl number (a measure of the azimuthal to axial velocity ratio), . It is followed by , then by . When nonlinearities are allowed, it is found that they saturate the amplitude within the linear-response wavepacket, leaving the wavepacket fronts unaffected. The conclusions should thus be the same as those obtained in the linear case: the linear convective/absolute transition should coincide with the nonlinear one for the variable-density Batchelor vortex.

JFM classification

Instability: Absolute/convective instability Instability: Nonlinear instability Vortex Flows: Vortex instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 703 , 25 July 2012 , pp. 49 - 59
Copyright
Copyright © Cambridge University Press 2012

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