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Finite amplitude convection between stress-free boundaries; Ginzburg–Landau equations and modulation theory

Published online by Cambridge University Press:  26 September 2008

Andrew J. Bernoff
Andrew J. Bernoff
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
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Abstract

The stability theory for rolls in stress-free convection at finite Prandtl number is affected by coupling with low wavenumber two-dimensional mean-flow modes. In this work, a set of modified Ginzburg–Landau equations describing the onset of convection is derived which accounts for these additional modes. These equations can be used to extend the modulation equations of Zippelius & Siggia describing the breakup of rolls, bringing their stability theory into agreement with the results of Busse & Bolton.

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Type
Research Article
Information
European Journal of Applied Mathematics , Volume 5 , Issue 3 , September 1994 , pp. 267 - 282
Copyright
Copyright © Cambridge University Press 1994

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