Flow near the corner in buoyant convection in a rectangular cavity

Abstract

Corner flow, driven by differential heating at the vertical walls in a rectangular cavity, is studied. The flow is initiated from a stroma vertical stratification of a Boussinesq fluid. The system Rayleigh number is large and the Prandtl number is 0(l). Previous studies point to a considerable thickening of the boundary layer depth, which is referred to as the corner jet when the fluid moves vertically in and horizontally out near the corner. Some authors argue that the phenomenon is caused by an internal hydraulic jump. In some other investigations, the corner jet structure is shown to arise due to the temperature undershoots in the vertical boundary layer, which stem from the stable thermal stratification in the core. In this paper, the above controversy is resolved in part and a theoretical model for the corner flow,T is given. Furthermore, efforts are made to establish the condition for a smooth turning flow, without abrupt changes of the flow depth, near the corner.