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Instability of unsteady flows or configurations. Part 2. Convective instability

Published online by Cambridge University Press:  29 March 2006

Chia-Shun Yih  and
Chin-Hsiu Li
Chia-Shun Yih
Affiliation:
Department of Engineering Mechanics, The University of Michigan
Chin-Hsiu Li
Affiliation:
Division of Fluid, Thermal and Aerospace Sciences, Case Western Reserve University, Cleveland
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Abstract

The formation of convective cells in a fluid between two horizontal rigid boundaries with time-periodic temperature distribution is studied by the use of the Floquet theory. Numerical results for the critical Rayleigh number are given for a Prandtl number of 0·73 (air) and for various values of the frequency and magnitude of the primary temperature oscillation. Some numerical results for a Prandtl number of 7·0 (water) are also given. The most striking feature of the results is that the disturbances (or convection cells) oscillate either synchronously or with half frequency.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 54 , Issue 1 , 11 July 1972 , pp. 143 - 152
Copyright
© 1972 Cambridge University Press

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