Transverse-roll global modes in a Rayleigh–Bénard–Poiseuille system with streamwise variable heating |
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Authors: | Philippe Carrire Peter A Monkewitz |
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Institution: | a Laboratoire de Mécanique des Fluides et d'Acoustique, UMR CNRS 5509, Ecole Centrale de Lyon-Université Claude Bernard Lyon I, BP163, 69131 Ecully cedex, France;b Laboratoire de Mécanique des Fluides, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland |
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Abstract: | The effect of a spatially inhomogeneous heating of the bottom wall in Rayleigh–Bénard–Poiseuille convection is studied for slow streamwise variations of the temperature profile. The problem is defined by the constant Reynolds number of the Poiseuille through flow, assumed to be low (typically 10), the constant Prandtl number, and the spatial evolution of the Rayleigh number
, assumed to be subcritical everywhere except in a limited region around its single maximum
. In this initial study, all spanwise inhomogeneities such as side walls or spanwise variable heating are neglected to obtain two-dimensional (transverse roll) global mode solutions by means of WKBJ asymptotics. The resulting frequency selection yields, at leading order, a global mode frequency equal to the local absolute frequency ωt at the streamwise location where the Rayleigh number is maximum, with higher-order corrections for non-parallelism. These allow the determination of critical values of
for global instability as a function of the profile of the local Rayleigh number
and of Prandtl and Reynolds numbers. |
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Keywords: | global modes mixed convection |
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