Convection induced by insulated boundaries in a square

Abstract

Convection induced by insulated boundaries in a tilted square cavity is analyzed for large external Rayleigh number A. Two opposite walls of the cavity are insulated, and the other opposite walls are maintained at temperatures linear in ξ, the vertical coordinate. Two orientations of the cavity are analyzed in detail for φ<A−1/2 and φ=π/2, φ being the angle between the heated walls and the horizontal. For φ<A−1/2, the flow consists of boundary layers of thickness O(A−1/4) near the insulated wall and O(A−1/6) near the heated walls. For φ=π/2, the flow consists of double boundary layers O(A−1/6) and O(A−1/8) near the insulated walls, but no boundary layer exists near the heated walls, except at the end points of the double boundary layers. The flows for π/4 are qualitatively described. The analogy between the flows considered here and those in a rotating container is also discussed.