SIEGFRIED GROSSMANN a1andDETLEF LOHSE a2 a1 Department of Physics, University of Marburg, Renthof 6, D-35032 Marburg, Germany a2 Department of Applied Physics and J. M. Burgers Centre for Fluid Dynamics University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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.
(Received January 3 2003) (Revised February 21 2003)