The influence of a third diffusing component upon the onset of convection

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Abstract
The small amplitude stability analysis for the onset of double-diffusive convection when the density gradient is gravitationally stable is extended to include a third diffusing component. Special attention is given to systems with κ1 [Gt ] κ2, κ3 and Pr [Gt ] κ/κ1, where κi is the molecular diffusivity of the ith component and Pr is the Prandtl number based on the largest of the Ki. It is found that the boundary for the onset of overstability is approximated by two straight lines in a Rayleigh number plane. Small concentrations of a third property with a smaller diffusivity can have a significant effect upon the nature of diffusive instabilities, the magnitude of this effect being proportional to κ1/Ki. Oscillatory and direct ‘salt-finger’ modes are found to be simultaneously unstable under a wide range of conditions when the density gradients due to the components with the greatest and smallest diffusivities are of the same sign.

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