Thermal convection in a cavity: the core structure near the horizontal boundaries

Abstract

Cavity flows driven by an applied horizontal temperature gradient are encountered in a variety of industrial and environmental situations. Determination of the core structure, away from the flow boundaries, depends strongly on the corner behaviour of the vertical boundary layer equations. An analysis of these corner zones is given for flows in which both the Rayleigh number and the Prandtl number are large. It is shown that both corner flows have a double structure with the outer layers being convection dominated. The consequences of the analysis for the core mass flux, a much debated question in the literature, are discussed. Numerical integration, with spectral decomposition, is shown to lead to values of the core mass flux that are in good agreement with existing experimental data.