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The structure of non-linear cellular solutions to the Boussinesq equations

Published online by Cambridge University Press:  28 March 2006

Lee A. Segel
Lee A. Segel
Affiliation:
Rensselaer Polytechnic Institute, Troy, New York
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Abstract

A model equation is constructed whose analysis reveals the same features, including stable hexagonal cells, as analysis of genuine approximate equations for the thermal convection problem. Taking advantage of the relative simplicity of the calculations an attempt is made to clarify certain procedures customarily used in non-linear stability theory; in particular, the basis for the usual formal expansions and the appropriateness of neglecting terms of fourth and higher order are discussed. It is demonstrated that a whole class of equations leads to hexagonal cells, thereby giving confidence that results on convection cells found elsewhere in idealized situations will remain valid when more realistic situations are studied.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 21 , Issue 2 , February 1965 , pp. 345 - 358
Copyright
© 1965 Cambridge University Press

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