On geometry effects in Rayleigh–Bénard convection

Abstract

Various recent experiments hint at a geometry dependence of scaling relations in Rayleigh–Bénard convection. Aspect ratio and shape dependences have been found. In this paper a mechanism is suggested which can account for such dependences, based on Prandtl's theory for laminar boundary layers and on the conservation of volume flux of the large-scale wind. The mechanism implies the possibility of different thicknesses of the kinetic boundary layers at the sidewalls and at the top/bottom plates, as found experimentally, and also different Ra-scaling of the wind over the plates and at the sidewalls. A scaling argument for the velocity and temperature fluctuations in the bulk is also developed.