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Transition to time-dependent convection

Published online by Cambridge University Press:  29 March 2006

R. M. Clever  and
F. H. Busse
R. M. Clever
Affiliation:
Science Applications, Inc., El Segundo, California 90245
F. H. Busse
Affiliation:
Department of Planetary and Space Sciences, University of California, Los Angeles
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Abstract

Steady solutions in the form of two-dimensional rolls are obtained for convection in a horizontal layer of fluid heated from below as a function of the Rayleigh and Prandtl numbers. Rigid boundaries of infinite heat conductivity are assumed. The stability of the two-dimensional rolls with respect to three-dimensional disturbances is analysed. It is found that convection rolls are unstable for Prandtl numbers less than about 5 with respect to an oscillatory instability investigated earlier by Busse (1972) for the case of free boundaries. Since the instability is caused by the momentum advection terms in the equations of motion the Rayleigh number for the onset of instability increases strongly with Prandtl number. Good agreement with various experimental observations is found.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 65 , Issue 4 , 2 October 1974 , pp. 625 - 645
Copyright
© 1974 Cambridge University Press

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