On the Steady Flow in a Cell Created by a Double-Diffusive Convection Instability

Abstract

The stability of a stationary fluid in which there are gradients of two concentrations c ₁ and c ₂ with different molecular diffusivities к ₁ and к ₂ (arranged so that к ₁ > к ₂) has been thoroughly studied (see for example Turner 1973). The fluid density, depends linearly on the concentrations as

$$ \rho = {\rho _1}\left( {1 + {\alpha _1}{c_1} + {\alpha _2}{c_2}} \right) \equiv {\rho _0} + {\rho _1} + {\rho _2} $$

where ρ ₀,α₁and α₂ are constants.