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Prandtl–Blasius temperature and velocity boundary-layer profiles in turbulent Rayleigh–Bénard convection

Published online by Cambridge University Press:  08 September 2010

QUAN ZHOU ,
RICHARD J. A. M. STEVENS ,
KAZUYASU SUGIYAMA ,
SIEGFRIED GROSSMANN ,
DETLEF LOHSE  and
KE-QING XIA
QUAN ZHOU
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
RICHARD J. A. M. STEVENS
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J. M. Burgers Centre for Fluid Dynamics, and Impact-Institute, University of Twente, 7500 AE Enschede, The Netherlands
KAZUYASU SUGIYAMA
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J. M. Burgers Centre for Fluid Dynamics, and Impact-Institute, University of Twente, 7500 AE Enschede, The Netherlands Department of Mechanical Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bukyo-ku, Tokyo 113-8756, Japan
SIEGFRIED GROSSMANN
Affiliation:
Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany
DETLEF LOHSE
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J. M. Burgers Centre for Fluid Dynamics, and Impact-Institute, University of Twente, 7500 AE Enschede, The Netherlands
KE-QING XIA*
Affiliation:
Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China
*
†Email address for correspondence: kxia@phy.cuhk.edu.hk
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Abstract

The shapes of the velocity and temperature profiles near the horizontal conducting plates' centre regions in turbulent Rayleigh–Bénard convection are studied numerically and experimentally over the Rayleigh number range 108 ≲ Ra ≲ 3 × 1011 and the Prandtl number range 0.7 ≲ Pr ≲ 5.4. The results show that both the temperature and velocity profiles agree well with the classical Prandtl–Blasius (PB) laminar boundary-layer profiles, if they are re-sampled in the respective dynamical reference frames that fluctuate with the instantaneous thermal and velocity boundary-layer thicknesses. The study further shows that the PB boundary layer in turbulent thermal convection not only holds in a time-averaged sense, but is most of the time also valid in an instantaneous sense.

JFM classification

Boundary Layers: Boundary Layers Convection: Convection

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Type
Papers
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Journal of Fluid Mechanics , Volume 664 , 10 December 2010 , pp. 297 - 312
Copyright
Copyright © Cambridge University Press 2010

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References

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