Convection in a stratified binary mixture near a thermally inhomogeneous vertical surface

Abstract

The stationary convection in a stratified two-component medium, for example, saline sea water, near a thermally inhomogeneous vertical surface is investigated analytically. Physically different cases of thermal inhomogeneities extended in the vertical or horizontal direction are considered. The solutions obtained can be applied to problems of convection in semibounded horizontal or vertical layers in the presence of thermal inhomogeneities at the “ends” of the layer. The solutions show that in two-component media convection is very specific. In particular, the spatial pattern of the thermal response to inhomogeneous heatingmay significantly differ from the case of an ordinary single-component medium: additional perturbation modes that penetrate deeply into the stably stratified medium appear. For an arbitrarily strong hydrostatic stability of the medium there exists an unexplored mechanism of convective instability related with the difference in the boundary conditions for the two substances. Weak variations of the background stratification of the admixture concentration (salinity) may significantly affect the heat exchange between a vertical surface and the medium. Even a very weak presence of the second component (a small contribution of the admixture stratification to the background density stratification) may lead not only to a significant quantitative change in the thermal response but also to a change in its sign, for example, to a significant decrease in the temperature of the medium in response to a heat influx from the vertical boundary.