Transient Growth in Exactly Counter-Rotating Couette–Taylor Flow |
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| Authors: | Hristina Hristova Sébastien Roch Peter J Schmid Laurette S Tuckerman |
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| Institution: | (1) Ecole Polytechnique de Montréal, C.P. 6079, succ. Centre-ville Montréal (Qc) H3C 3A7, Canada and Ecole Polytechnique, 91128 Palaiseau, France, CA;(2) Department of Applied Mathematics, University of Washington, Box 352420, Seattle, WA 98195, U.S.A. and Laboratoire pour l'Hydrodynamique à l'Ecole Polytechnique (LADHYX-CNRS), 91128 Palaiseau, France, US;(3) Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI-CNRS), B.P. 133, 91403 Orsay, France and Ecole Polytechnique, 91128 Palaiseau, France, FR |
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| Abstract: | Transient growth due to non-normality is investigated for the Couette-Taylor problem with counter-rotating cylinders as a function
of aspect ratio η and Reynolds number Re. For all Re≤500, transient growth is enhanced by curvature, i.e. is greater for η<1 than for η=1, the plane Couette limit. For fixed
Re>130, it is found that the greatest transient growth is achieved for η on the linear stability boundary. Transient growth
is approximately 20% higher near the Couette-Taylor linear stability boundary at Re=310, η=0.986 than at Re=310, η=1, near the threshold observed for transition in plane Couette flow. For 106<Re<130, the greatest transient growth occurs for a value of η between the linear stability boundary and one. For Re<106, the flow is linearly stable and the greatest transient growth occurs for a value of η less than one. The energy in the
optimal inputs is primarily meridional; that in the optimal outputs is primarily azimuthal. Pseudospectra are calculated for
two contrasting cases.
Received 5 November 2001 and accepted 29 March 2002 Published online: 2 October 2002
Communicated by H.J.S. Fernando |
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