Logarithmic Temperature Profiles in Turbulent Rayleigh-Benard Convection

Günter Ahlers, Eberhard Bodenschatz, Denis Funfschilling, Siegfried Grossmann, Xiaozhou He, Detlef Lohse, Richard J.A.M. Stevens, Roberto Verzicco

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We report results for the temperature profiles of turbulent Rayleigh-Bénard convection (RBC) in the interior of a cylindrical sample of aspect ratio Γ≡D/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 4×1012≲Ra≲1015 for a Prandtl number Pr≃0.8 and on direct numerical simulation at Ra=2×1012, 2×1011, and 2×1010, all for Pr=0.7.
Original languageEnglish
Article number1145001
Number of pages5
JournalPhysical review letters
Issue number11
Publication statusPublished - 2012


  • IR-81789
  • METIS-288412


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