The influence of side walls on finite-amplitude convection in a layer heated from below

Abstract

Finite-amplitude convection rolls of an infinite-Prandtl-number fluid in a long channel heated from below are investigated. Because of the side walls, the convection rolls depend on all three spatial co-ordinates, although only two velocity components are of importance for a wide range of Rayleigh numbers and aspect ratios. Accurately converged solutions are presented for a range of aspect ratios between 0 (Bénard convection) to 100 (Hele Shaw convection) and for Rayleigh numbers up to about 50 times the critical linear stability value. The influence of rigid versus slip boundaries as well as the wavelength of the convection rolls on the heat transport is investigated in detail. Comparisons with existing results for the analogous problem of convection in a porous medium indicates that the similarity tends to disappear at Rayleigh numbers less than a few times the critical value. Whenever possible, the theoretical findings are compared with experimental results. In all cases close agreement is found.