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Scaling of hard thermal turbulence in Rayleigh-Bénard convection

Published online by Cambridge University Press:  26 April 2006

Bernard Castaing ,
Gemunu Gunaratne ,
François Heslot ,
Leo Kadanoff ,
Albert Libchaber ,
Stefan Thomae ,
Xiao-Zhong Wu ,
Stéphane Zaleski  and
Gianluigi Zanetti
Bernard Castaing
Affiliation:
CNRS-CRTBT, 25 Avenue des Martyrs-P.B. 166X, 38042 Grenoble Cedex, France
Gemunu Gunaratne
Affiliation:
The Research Institutes, The University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637, USA
François Heslot
Affiliation:
Collège de France, Matiere Condensée, Place Marcellin Berthelot, 75005 Paris, France
Leo Kadanoff
Affiliation:
The Research Institutes, The University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637, USA
Albert Libchaber
Affiliation:
The Research Institutes, The University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637, USA
Stefan Thomae
Affiliation:
Institut für Festkörperforschung der KFA, Postfach 1913, D-5170 Jülich, W. Germany
Xiao-Zhong Wu
Affiliation:
The Research Institutes, The University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637, USA
Stéphane Zaleski
Affiliation:
Laboratoire de Physique Statistique, ENS, 24 rue Lhomond, 75231 Paris Cedex 05, France
Gianluigi Zanetti
Affiliation:
The Research Institutes, The University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637, USA
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Abstract

An experimental study of Rayleigh-Bénard convection in helium gas at roughly 5 K is performed in a cell with aspect ratio 1. Data are analysed in a ‘hard turbulence’ region (4 × 107 < Ra < 6 × 1012) in which the Prandtl number remains between 0.65 and 1.5. The main observation is a simple scaling behaviour over this entire range of Ra. However the results are not the same as in previous theories. For example, a classical result gives the dimensionless heat flux, Nu, proportional to $Ra^{\frac{1}{3}}$ while experiment gives an index much closer to $\frac{2}{7}$. A new scaling theory is described. This new approach suggests scaling indices very close to the observed ones. The new approach is based upon the assumption that the boundary layer remains in existence even though its Rayleigh number is considerably greater than unity and is, in fact, diverging. A stability analysis of the boundary layer is performed which indicates that the boundary layer may be stabilized by the interaction of buoyancy driven effects and a fluctuating wind.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 204 , July 1989 , pp. 1 - 30
Copyright
© 1989 Cambridge University Press

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