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The elephant mode between two rotating disks

Published online by Cambridge University Press:  25 February 2008

BERTRAND VIAUD ,
ERIC SERRE  and
JEAN-MARC CHOMAZ
BERTRAND VIAUD
Affiliation:
Centre de Recherche de l'Armée de l'Air, CReA BA701 13661 Salon de Provence, France
ERIC SERRE
Affiliation:
Laboratoire MSNM-GP, CNRS Universités Aix Marseille, IMT Chateau-Gombert 13451 Marseille, France
JEAN-MARC CHOMAZ
Affiliation:
Laboratoire d'Hydrodynamique-LadHyX, CNRS-Ecole Polytechnique, F-91128 Palaiseau, France
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Abstract

Spectral direct numerical simulations (DNS) are carried out for a source–sink flow in an annular cavity between two co-rotating disks. When the Reynolds number based on the forced inflow is increased, a self-sustained crossflow instability of finite amplitude is observed. We show that this nonlinear global mode is made up of a front located at the upstream boundary of the absolutely unstable domain, followed by a saturated spiral mode, and that its properties are in good agreement with results of the local stability theory. This structure is characteristic of the so-called elephant mode of Pier & Huerre (J. Fluid Mech. vol. 435, 2001, p. 145). The global bifurcation is subcritical since only large-amplitude initial perturbations are found to trigger the elephant mode. Small-amplitude perturbations induce a long-lasting transient growth but lead eventually to a damped linear global mode, showing that non-parallel effects counteract the absolute instability and restabilize the flow. A similar linear global stabilization due to non-parallel effects has been found in the case of the flow above a single rotating disk. For the single-disk geometry, the existence of an elephant mode would imply, together with results of Davies & Carpenter (2003) a subcritical global instability, which has not yet been demonstrated. Although the present geometry differs from the single-disk case, the existence of a subcritical global bifurcation is now established, allowing a precise analysis of the transition scenarios.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 598 , 10 March 2008 , pp. 451 - 464
Copyright
Copyright © Cambridge University Press 2008

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