Steady subcritical thermohaline convection

TLDR: In this article, it was shown that, for any value of the salt Rayleigh number R S, finite-amplitude convection can occur at values of the Ray-leigh number T much less than that necessary for infinitesimal oscillations, provided only that T is sufficiently small.

Abstract: Steady convective motions in a Boussinesq fluid with an unstable thermal and stable salinity stratification are investigated in the case that the ratio of diffusivities τ = κ S /κ T [Lt ] 1. Using perturbation theory, it is shown that, for any value of the salt Rayleigh number R S , finite-amplitude convection can occur at values of the Ray-leigh number R T much less than that necessary for infinitesimal oscillations, provided only that T is sufficiently small. A simple qualitative argument is used to show how R min , the minimum value of R T for steady convection, varies with R S , and it is shown that the analytical results of the present paper form a natural complement to the numerical ones of Huppert & Moore (1976). Results are presented both for stress-free and for rigid boundaries, and applicability of the method to other related problems is suggested.