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Convection in a box: linear theory

Published online by Cambridge University Press:  28 March 2006

Stephen H. Davis
Stephen H. Davis
Affiliation:
The RAND Corporation, Santa Monica, California Present address: Department of Mathematics, Imperial College, London S.W. 7, England.
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Abstract

The linear stability of a quiescent, three-dimensional rectangular box of fluid heated from below is considered. It is found that finite rolls (cells with two non-zero velocity components dependent on all three spatial variables) with axes parallel to the shorter side are predicted. When the depth is the shortest dimension, the cross-sections of these finite rolls are near-square, but otherwise (in wafer-shaped boxes) narrower cells appear. The value of the critical Rayleigh number and preferred wave-number (number of finite rolls) for a given size box is determined for boxes with horizontal dimensions h, ¼ ≤ h/d ≤ 6, where d is the depth.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 30 , Issue 3 , 29 November 1967 , pp. 465 - 478
Copyright
© 1967 Cambridge University Press

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References

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