Double-diffusive convection with sidewalls

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Abstract
The effect of rigid vertical boundaries on the onset of convective instability is calculated for the salt finger regime of double-diffusive convection. The unperturbed state is a quiescent fluid with constant vertical gradients of temperature and solute, which are stabilizing and destabilizing, respectively. The horizontal boundaries are taken to be stress-free and perfectly conducting. The lateral boundaries are perfectly insulating for solute. Changing from thermally insulating to thermally conducting sidewalls results in a strong destabilization of the flow for large thermal Rayleigh numbers even in the limit that the separation between the sidewalls approaches infinity. Further, for thermally conducting sidewalls, a decrease in the separation of the sidewalls may destabilize the system.

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