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The stability of finite amplitude cellular convection and its relation to an extremum principle

Published online by Cambridge University Press:  28 March 2006

F. H. Busse
F. H. Busse
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, Los Angeles
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Abstract

The stability of cellular convection flow in a layer heated from below is discussed for Rayleigh number R close to the critical value Rc. It is shown that in this region the stable stationary solution is determined by a minimum of the integral \[ \int_0^{H_0}R(H)\,dH, \] where R(H) is a functional of arbitrary convective velocity fields which satisfy the boundary conditions. For the stationary solutions R(H) is equal to the Rayleigh number. H0 is a given value of the convective heat transport. In a second part of the paper explicit results are derived for the convection problem with deviations from the Boussinesq approximation owing to the temperature dependence of the material properties.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 30 , Issue 4 , 22 December 1967 , pp. 625 - 649
Copyright
© 1967 Cambridge University Press

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References

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