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The stability of a periodically heated layer of fluid

Published online by Cambridge University Press:  20 April 2006

John Dowden
John Dowden
Affiliation:
Department of Mathematics, University of Essex, Colchester C04 3SQ, U.K.
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Abstract

The stability of an infinite layer of fluid of uniform thickness at rest with two horizontal boundaries is investigated when the difference between the temperatures at the top and bottom boundaries has a component which is a fluctuating periodic function of time in addition to a constant part. When both boundaries are free small fluctuations have a stabilizing effect on the layer, while large fluctuations tend to make it less stable, consistently with the numerical results of Yih & Li (1972); the effect is attributable entirely to the variation of the temperature gradient with time. An approximate relation between the mean Rayleigh number and the amplitude of the fluctuations is found which separates stable situations from unstable ones. This is compared with the criteria deduced by Homsy (1974) using energy arguments for disturbances of any amplitude.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 110 , September 1981 , pp. 149 - 159
Copyright
© 1981 Cambridge University Press

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