Logarithmic Temperature Profiles in Turbulent Rayleigh-Bénard Convection

Guenter Ahlers, Eberhard Bodenschatz, Denis Funfschilling, Siegfried Grossmann, Xiaozhou He, Detlef Lohse, Richard J. A. M. Stevens, and Roberto Verzicco
Phys. Rev. Lett. 109, 114501 – Published 14 September 2012

Abstract

We report results for the temperature profiles of turbulent Rayleigh-Bénard convection (RBC) in the interior of a cylindrical sample of aspect ratio ΓD/L=0.50 (D and L are the diameter and height, respectively). Both in the classical and in the ultimate state of RBC we find that the temperature varies as A×ln(z/L)+B, where z is the distance from the bottom or top plate. In the classical state, the coefficient A decreases in the radial direction as the distance from the side wall increases. For the ultimate state, the radial dependence of A has not yet been determined. These findings are based on experimental measurements over the Rayleigh-number range 4×1012Ra1015 for a Prandtl number Pr0.8 and on direct numerical simulation at Ra=2×1012, 2×1011, and 2×1010, all for Pr=0.7.

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  • Received 21 April 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.114501

© 2012 American Physical Society

Authors & Affiliations

Guenter Ahlers1,2, Eberhard Bodenschatz2,3,4, Denis Funfschilling5, Siegfried Grossmann6, Xiaozhou He2, Detlef Lohse7, Richard J. A. M. Stevens7,*, and Roberto Verzicco7,8

  • 1Department of Physics, University of California, Santa Barbara, California 93106, USA
  • 2Max Planck Institute for Dynamics and Self-Organization, D-37073 Göttingen, Germany
  • 3Institute for Nonlinear Dynamics, University of Göttingen, D-37073 Göttingen, Germany
  • 4Laboratory of Atomic and Solid-State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA
  • 5LSGC CNRS - GROUPE ENSIC, BP 451, 54001 Nancy Cedex, France
  • 6Fachbereich Physik der Philipps-Universität, Renthof 6, D-35032 Marburg, Germany
  • 7Department of Science and Technology and J. M. Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
  • 8Department of Mechanical Engineering, Universitá di Roma ’Tor Vergata’, Via del Politecnico 1, 00133 Roma, Italy

  • *Present address: Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA.

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Vol. 109, Iss. 11 — 14 September 2012

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