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Thermal boundary layer profiles in turbulent Rayleigh-Bénard convection in a cylindrical sample

Richard J. A. M. Stevens1, Quan Zhou2, Siegfried Grossmann3, Roberto Verzicco1,4, Ke-Qing Xia5, and Detlef Lohse1

  • 1Physics of Fluids Group, Department of Science and Technology and J. M. Burgers Center for Fluid Dynamics, University of Twente, P. O. Box 217, 7500 AE Enschede, The Netherlands
  • 2Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 3Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany
  • 4Dept. of Mech. Eng., Universitá di Roma “Tor Vergata,” Via del Politecnico 1, 00133 Roma, Italy
  • 5Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China

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Phys. Rev. E 85, 027301 – Published 7 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.027301

Abstract

We numerically investigate the structures of the near-plate temperature profiles close to the bottom and top plates of turbulent Rayleigh-Bénard flow in a cylindrical sample at Rayleigh numbers Ra=108 to Ra=2×1012 and Prandtl numbers Pr=6.4 and Pr=0.7 with the dynamical frame method [Zhou and Xia, Phys. Rev. Lett. 104, 104301 (2010)], thus extending previous results for quasi-two-dimensional systems to three-dimensional systems. The dynamical frame method shows that the measured temperature profiles in the spatially and temporally local frame are much closer to the temperature profile of a laminar, zero-pressure gradient boundary layer (BL) according to Pohlhausen than in the fixed reference frame. The deviation between the measured profiles in the dynamical reference frame and the laminar profiles increases with decreasing Pr, where the thermal BL is more exposed to the bulk fluctuations due to the thinner kinetic BL, and increasing Ra, where more plumes are passing the measurement location.

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Phys. Rev. E 85, 027301– Published 7 February, 2012
  • Received 31 October 2011

©2012 American Physical Society

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