A NEW TYPE OF DOUBLE-DIFFUSIVE INSTABILITY

Abstract

Welander suggested the possibility of existence of a new (unstudied) type of convective instability in a two-component medium, in particular, in seawater stratified both in temperature and admixture (salt) concentration. According to this hypothesis, a medium stably stratified by density can, nevertheless, lose its stability not due to the difference in the transport coefficients of heat and admixture (a known mechanism) but owing to the difference in boundary conditions at the horizontal boundary for two substances. The possibility of such an instability would be of significant interest owing to the following reason: unlike the known mechanism (double or differential diffusion), it could also be realized by turbulent exchange, when effective transport coefficients for heat and salt are practically equal. This process corresponds to a greater degree to the real conditions in the upper oceanic layer. However, to our knowledge, the hypothesis mentioned above was neither proved theoretically nor confirmed experimentally. The author considered a simplified theoretical scheme (inviscid fluid, strongly idealized and strictly fixed boundary conditions, and so on). In the present paper, we perform a sufficiently strict analysis of linear stability with respect to monotonous perturbations in a semibounded problem. We demonstrate the real possibility of appearance of instability, although significantly different from that suggested by Welander. In particular, we found monotonous (rather than the previously supposed oscillatory) instability, which appears during heating from above rather than from below.