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Thermal and viscous boundary layers in turbulent Rayleigh–Bénard convection

Published online by Cambridge University Press:  31 August 2012

J. D. Scheel ,
E. Kim  and
K. R. White
J. D. Scheel*
Affiliation:
Department of Physics, Occidental College, 1600 Campus Road, M21, Los Angeles, CA 90041, USA
E. Kim
Affiliation:
Department of Physics, Occidental College, 1600 Campus Road, M21, Los Angeles, CA 90041, USA
K. R. White
Affiliation:
Department of Applied Mathematics and Statistics, University of California Santa Cruz, Mail Stop SOE GRADS, 1156 High Street, Santa Cruz, CA 95064, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present the results from numerical simulations of turbulent Rayleigh–Bénard convection for an aspect ratio (diameter/height) of 1.0, Prandtl numbers of 0.4 and 0.7, and Rayleigh numbers from to . Detailed measurements of the thermal and viscous boundary layer profiles are made and compared to experimental and theoretical (Prandtl–Blasius) results. We find that the thermal boundary layer profiles disagree by more than 10 % when scaled with the similarity variable (boundary layer thickness) and likewise disagree with the Prandtl–Blasius results. In contrast, the viscous boundary profiles collapse well and do agree (within 10 %) with the Prandtl–Blasius profile, but with worsening agreement as the Rayleigh number increases. We have also investigated the scaling of the boundary layer thicknesses with Rayleigh number, and again compare to experiments and theory. We find that the scaling laws are very robust with respect to method of analysis and they mostly agree with the Grossmann–Lohse predictions coupled with laminar boundary layer theory within our numerical uncertainty.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 711 , 25 November 2012 , pp. 281 - 305
Copyright
Copyright © Cambridge University Press 2012

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