Logarithmic temperature profiles in DNS of turbulent convection

ORAL

Abstract

We report numerical results for vertical profiles of mean and rms temperature fluctuations for confined turbulent thermal convection in a cylindrical sample of aspect ratio $\Gamma = 0.5$ and $1$ (diameter over height ratio) over a Rayleigh number range $2\times 10^{10} \leq Ra \leq 2\times 10^{12}$ and for a Prandtl number $Pr=0.7$. We found that both quantities vary linearly in $\ln (z)$ with $z$ the distance from the horizontal plates. This behaviour had been predicted for the ultimate regime but it was not expected for the classical state ($Ra \leq 10^{13}$). Similar findings have recently been obtained also experimentally\footnote{Ahlers G. et al. ``Logarithmic temperature profiles in turbulent Rayleigh-B\'enard convection'' To appear in Phys. Rev. Lett. 2012.} and an excellent agreement with the numerical results has been observed for the mean temperature profiles. The rms fluctuations, in contrast, present relevant differences with respect to the experiments and several explanations are possible.

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Authors

  • Roberto Verzicco

    Universit\`a di Roma ``Tor Vergata''

  • Richard Stevens

    Dept. Mech. Eng. Johns Hopkins University, Johns Hopkins University

  • Detlef Lohse

    University of Twente, Physics of Fluids, University of Twente, Enschede, Physics of Fluids, University of Twente, Physics of Fluids group, University of Twente, Netherlands, Universiteit Twente, University of Twente, Physics of Fluids Group, University of Twente, Enschede, The Netherlands, Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, and IMPACT Institute, University of Twente, NL, Physics of Fluids Group, University of Twente, The Netherlands

  • Sigfried Grossmann

    Dept. of Phys. University of Marburg