Journal of Fluid Mechanics


Boundary layers and wind in cylindrical Rayleigh–Bénard cells

Sebastian Wagnera1 c1, Olga Shishkinaa1 and Claus Wagnera1

a1 German Aerospace Center (DLR), Institute of Aerodynamics and Flow Technology, Bunsenstrasse 10, 37073 Göttingen, Germany


We analyse the wind and boundary layer properties of turbulent Rayleigh–Bénard convection in a cylindrical container with aspect ratio one for Prandtl number $\mathit{Pr}= 0. 786$ and Rayleigh numbers ($\mathit{Ra}$) up to $1{0}^{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 in order 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 LSC is treated as a wind with thermal and viscous boundary layers developing close to the horizontal plates. Special focus is 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 direction is observed for all $\mathit{Ra}$ considered while their ratio is spatially constant but depends weakly on $\mathit{Ra}$. A possible explanation is a strong spatial variation of the wind magnitude and fluctuations in the boundary layer region.

(Received November 04 2011)

(Reviewed January 30 2012)

(Accepted February 01 2012)

(Online publication March 06 2012)

Key Words:

  • boundary layer structure;
  • Bénard convection;
  • turbulent convection


c1 Email address for correspondence: