The stability of a periodically heated layer of fluid

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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.

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