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Instability of steady natural convection in a vertical fluid layer

Published online by Cambridge University Press:  12 April 2006

R. F. Bergholz
R. F. Bergholz
Affiliation:
Argonne National Laboratory, Argonne, Illinois 60439
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Abstract

The instability of steady natural convection of a stably stratified fluid between vertical surfaces maintained at different temperatures is analysed. The linear stability theory is employed to obtain the critical Grashof and Rayleigh numbers, for widely varying levels of the stable background stratification, for Prandtl numbers ranging from 0·73 to 1000 and for the limiting case of infinite Prandtl number. The energetics of the critical disturbance modes also are investigated. The numerical results show that, if the value of the Prandtl number is in the low to moderate range, there is a transition from stationary to travelling-wave instability if the stratification exceeds a certain magnitude. However, if the Prandtl number is large, the transition, with increasing stratification, is from travelling-wave to stationary instability. The theoretical predictions are in excellent agreement with the experimental observations of Elder (1965) and of Vest & Arpaci (1969), for stationary instability, and in fair to good agreement with the experimental results of Hart (1971), for travelling-wave instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 84 , Issue 4 , 27 February 1978 , pp. 743 - 768
Copyright
© 1978 Cambridge University Press

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