Double-diffusive convection with large variable gradients

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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 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.

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