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The non-linear interaction of two disturbances in the thermal convection problem

Published online by Cambridge University Press:  28 March 2006

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

In the thermal convection problem with free boundaries, the interaction of two ‘roll’ disturbances is considered. The problem is reduced to a pair of non-linear ordinary differential equations, which should also provide a model for the interaction of two disturbances in more general situations than that for which these equations have been derived. The equations contain several parameters which necessitates a discussion of various possible types of solution. Some representative results are: (1) under certain circumstances, an equilibrium state may be composed of a mixture of a linearly stable disturbance and a linearly unstable disturbance; (2) for the thermal convection problem, when the Rayleigh number is slightly above the minimum critical value, the equilibrium state will contain only one of two linearly unstable disturbances. These and other results are compared with experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 14 , Issue 1 , September 1962 , pp. 97 - 114
Copyright
© 1962 Cambridge University Press

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