Laminar convection cells at high Rayleigh number

Abstract

The asymptotic behaviour for large Rayleigh number and Prandtl number of O(1) of two-dimensional convection cells in a fluid between horizontal plates heated from below has been discussed by Pillow (1952) and more recently by Robinson (1967). The flow models derived by Pillow and Robinson differ from each other. The purpose of the present paper is to point out the likelihood of an inconsistency in Robinson's flow model, and to discuss qualitatively a few hitherto unnoticed features of the flow.