Vertical Solutal Gradients Research Articles

Double-diffusive instability in an inclined fluid layer Part 2. Stability analysis

Linear stability analysis is applied to the problem of a density-stratified fluid contained in an inclined slot being subjected to a lateral temperature gradient. Stability equations are solved using the Galerkin technique with 12 terms in the truncated expansion series. Within the range of θ considered, |θ| < 75°, critical instability was found to be of the stationary type. Results of critical thermal Rayleigh numbers and wavenumbers at all inclination angles are in good agreement with the experimental results obtained earlier (Paliwal & Chen 1980). Contrary to intuition, these results show that the system is more stable when the lower wall is heated. This is shown to be the result of the increased vertical solute gradient in the steady state prior to the onset of instabilities when the heating is from below.

Double-diffusive instability in an inclined fluid layer. Part 1. Experimental investigation

The stability boundary of a density-stratified fluid contained in an inclined slot subjected to a lateral temperature gradient was determined experimentally. The initial stratification due to salt was stable and linear in the vertical direction. Experiments were conducted in a 1·0 × 11.1 × 25·7 cm slot with the inclination angle θ from the vertical varying from −75° to + 75°. A positive angle denotes heating from the lower wall while a negative angle denotes heating from the upper wall. The temperature difference across the slot was increased slowly until the onset of instability was observed by means of a shadowgraph. The critical thermal Rayleigh number was found to be non-symmetrical with respect to θ = 0°, with heating of the upper wall less stable than heating of the lower wall. This is because there is a larger vertical solute gradient in the steady-state regime prior to the onset of instabilities when the lower wall is heated. The secondary flow consisting of horizontal convecting layers was very stable θ < 0° cases because of the stabilizing temperature effect. The motion of the layers when θ > 0° was quite vigorous. At θ = +75°, the secondary flow became unstable in a rather dramatic manner not observed heretofore.