Stability of time-dependent double-diffusive convection in an inclined slot

Abstract

The two-dimensional motion of a stably stratified fluid containing two solutes with different molecular diffusivities in an inclined slot has recently been examined by Chen (1975, hereafter referred to as I). The two solutes have continuous opposing gradients with the slower-diffusing one more dense at the bottom. It is found that, in the steady state, there exists a slow upward flow along the slope driven by the slight buoyancy difference near the wall, not unlike the solution found by Wunsch (1970) and Phillips (1970) for a single solute. For the time-dependent flow resulting from switching on the diffusivities at t = 0, there may be a flow reversal near the wall depending on the relative magnitude of λ and τ (where λ is the ratio of the density gradient and τ−1 is the ratio of the diffusivity of the faster-diffusing solute T to that of the slower-diffusing one S). By examining the distributions of S and T across the slot, it becomes apparent that in cases with flow reversal double-diffusive instability is likely to occur.In this paper, we examine the stability of time-dependent double-diffusive convection in an inclined slot both analytically and experimentally. The time-dependent perturbation equations are numerically integrated starting with an initial distribution of small random disturbances in the vorticity. The growth or decay of the kinetic energy of the perturbations serves to indicate whether the flow is unstable or stable. The results show that the flow becomes more unstable (a) with increasing λ at a given angle of inclination with respect to the vertical and (b) with increasing angle of inclination at a given value of λ. Experiments were carried out in a 2[sdot ]54 cm wide slot using sugar and salt solutions at angles of inclination of 30°, 45° and 60°. Results obtained confirm the trends predicted by the analysis. Good agreement was obtained between the predicted and the experimental values of the critical wavelength for the case λ = 0[sdot ]7.