On sideways diffusive instability

Abstract

We consider the stability of the motion generated in a differentially heated vertical slot filled with a linearly stratified salt solution. The theoretical mean motion field between infinite plates is a function of the Rayleigh number R_s, = gβ(∂S₀/∂z) D⁴/k₈ν. If R_s is zero the salinity does not enter the problem and one finds instability in the form of stationary rolls which obtain most of their energy from the basic velocity field. Even at very small R_s of order -1000 these shear instabilities are replaced by diffusively destabilized convective rolls which appear at a thermal Rayleigh number R_a = gαΔTD³/k_Tν which is two orders of magnitude less than that required for the shear generated modes. The present calculations, which take proper account of both the mean fields and the boundary conditions, give results which compare somewhat more favourably with the experimental results of Thorpe, Hutt & Soulsby (1969) than the theory put forward by these authors. It is shown why their theory, which deals with different boundary conditions from those in the experiment, gives adequate results as R_s tends to negative infinity.