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Envelope equations for the Rayleigh–Bénard–Poiseuille system. Part 2. Linear global modes in the case of two-dimensional non-uniform heating

Published online by Cambridge University Press:  01 March 2004

DENIS MARTINAND ,
PHILIPPE CARRIÈRE  and
PETER A. MONKEWITZ
DENIS MARTINAND
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, UMR CNRS 5509, Ecole Centrale de Lyon-Université Claude Bernard Lyon I-INSA Lyon BP163, 69131 Ecully cedex, France Laboratoire de Mécanique des Fluides, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland Present address: Turbulence and Mixing Group, Department of Aeronautics, Imperial College London, London SW7 2BY, UK.
PHILIPPE CARRIÈRE
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, UMR CNRS 5509, Ecole Centrale de Lyon-Université Claude Bernard Lyon I-INSA Lyon BP163, 69131 Ecully cedex, France
PETER A. MONKEWITZ
Affiliation:
Laboratoire de Mécanique des Fluides, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland
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Abstract

Linear global modes in the Rayleigh–Bénard–Poiseuille system, for the case of two-dimensional non-uniform heating in the form of a single hot spot, are analysed in the framework of the envelope equation formalism. Global mode solutions are sought by means of WKBJ asymptotics. As for the one-dimensional case, an analytical selection criterion for the frequency may be derived from the breakdown of the WKBJ expansion at a two-dimensional double turning point located at the maximum of the local Rayleigh number. The analytical results, including the behaviour of the mode in the vicinity of the turning point, are compared with results obtained from numerical simulations of the envelope equation. Finally, the issue of the selection of the wavevector branches in the WKBJ expansion is discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 502 , 10 March 2004 , pp. 175 - 197
Copyright
© 2004 Cambridge University Press

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