Thermohaline instability with thermal diffusion and horizontal gradients

Abstract

The effect of thermal diffusion on an unbounded vertically stratified thermohaline fluid with compensating horizontal thermal and salinity gradients (i.e., with no horizontal density gradient) is investigated in this analysis. It is observed that the maximum growth rate of instability, the slope of the wave front and the wave number depend on the Soret parameter, S. For 1+S=τ ⁻¹, the system is stable for any value of the horizontal gradient where τ is the ratio of mass diffusivity to thermal diffusivity. For 1+S<0, there is convective instability when both vertical gradients are stable even in the absence of the horizontal gradient. When 1+S>τ ⁻¹, the slopes of the wave fronts tilt such that there is a diffusive set-up when stationary convection sets in and finger formation when there is oscillatory convection.