Boundary layers and wind in cylindrical Rayleigh-Bénard cells

Abstract

We analyse the wind and boundary layer properties of turbulent Rayleigh–Bénard convection in a cylindrical container with aspect ratio one for Prandtl number Pr = 0.786 and Rayleigh numbers (Ra) up to 10^9 by means of highly resolved direct numerical simulations. We identify time periods in which the orientation of the large scale circulation (LSC) is nearly constant to be able to perform a statistical analysis of the LSC. The analysis is then reduced to two dimensions by considering only the plane of the LSC. Within this plane the large scale circulation is treated as a wind with thermal and viscous boundary layers developing close to the horizontal plates. Special focus is set on the spatial development of the wind magnitude and the boundary layer thicknesses along the bottom plate. A method for the local analysis of the instantaneous boundary layer thicknesses is introduced which shows a dramatically changing wind magnitude along the wind path. Furthermore a linear increase of the viscous and thermal boundary layer thickness along the wind is observed for all considered Ra while their ratio is spatially constant but depends weakly on Ra. A possible explanation is a strong spatial variation of the wind magnitude and fluctuations in the boundary layer region.