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Distant side-walls cause slow amplitude modulation of cellular convection

Published online by Cambridge University Press:  29 March 2006

Lee A. Segel
Lee A. Segel
Affiliation:
Rensselaer Polytechnic Institute, Troy, N.Y.
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Abstract

The effect of vertical boundaries on convection in a shallow layer of fluid heated from below is considered. By means of a multiple-scale perturbation analysis, results for horizontally unbounded layers are modified so that they ‘fit in’ to a rectangular region. The critical Rayleigh number and critical wave-number are determined. Motion is predicted to have the form of finite ‘rolls’ whose axes are parallel to the shorter sides of the dish. Aspects of the non-linear development and stability of this motion are studied. The general question of convective pattern selection in a bounded layer is discussed in the light of available theoretical and experimental results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 1 , 14 August 1969 , pp. 203 - 224
Copyright
© 1969 Cambridge University Press

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