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Wavenumber selection in ramped Rayleigh–Bénard convection

Published online by Cambridge University Press:  21 April 2006

Jeffrey C. Buell  and
Ivan Catton
Jeffrey C. Buell
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, University of California, Los Angeles, CA 90024, USA
Ivan Catton
Affiliation:
Department of Mechanical, Aerospace and Nuclear Engineering, University of California, Los Angeles, CA 90024, USA
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Abstract

We consider wavenumber selection for the periodic two-dimensional Rayleigh–Bénard problem on a horizontally infinite domain. The temperature difference (and hence the Rayleigh number) is assumed to be a slowly varying function of the horizontal coordinate perpendicular to the convection rolls. Under this condition Kramer et al. have shown that a unique wavenumber of convection is selected by a certain solvability condition if the domain contains a subcritical region. They performed analytic calculations for a model problem and for small-amplitude convection of an infinite-Prandtl-number fluid between stress-free boundaries. Their results are extended here to the realistic case of large-amplitude convection of a finite-Prandtl-number fluid between rigid boundaries. The temperature difference may be ‘ramped’ by changing either the temperature at the lower boundary or at the upper boundary, or both. It is shown that the choice has a significant effect on the ‘mean flow’, but no effect on the selected wavenumber.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 171 , October 1986 , pp. 477 - 494
Copyright
© 1986 Cambridge University Press

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