Abstract
The steady laminar natural-convection flow of air and water in a square heated cavity is calculated for increasingly large Rayleigh number. The flow is calculated by solving both the Navier-Stokes equations and the boundary-layer equations. The results are used to determine the proper scalings of the flow in the different asymptotic flow regions: vertical boundary layers, core region, corner region and horizontal boundary layers. In particular the scalings according to the Navier-Stokes equations agree with the asymptotic model for the core and vertical boundary layers as proposed by Gill [ J. Fluid Mech. 26, 515–536 (1966)].
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