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Double-diffusive convection with large variable gradients

Published online by Cambridge University Press:  20 April 2006

I. C. Walton
I. C. Walton
Affiliation:
Department of Mathematics, Imperial College, London SW7
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Abstract

The onset of double-diffusive convection is discussed for a layer of fluid in which the vertical salinity gradient varies with depth and for which the thermal and saline Rayleigh numbers R and Rs are large. These conditions are similar to those that exist in a solar pond prior to the onset of any instability. It is shown that when convection occurs it takes the form of an overstable mode and is essentially confined to a narrow region of vertical extent $\sim R_{\rm s}^{-\frac{1}{14}} \times $ depth of the fluid layer, centred at the critical depth where the salt gradient is smallest. The leading terms in asymptotic expansions of the ratio R/Rs, the frequency of oscillation p and the horizontal wavenumber a are determined for R, [Gt] 1. The results predicted by the theory are shown to be in good agreement with numerical results and with observations of solar ponds.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 125 , December 1982 , pp. 123 - 135
Copyright
© 1982 Cambridge University Press

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