Local fluctuations and fluxes in turbulent Rayleigh-B\'{e}nard convection

ORAL

Abstract

We numerically investigate the local velocity and temperature fluctuations and the local heat flux in a cylindrical Rayleigh-Benard cell for Rayleigh numbers from Ra = 2 $\times $10$^{6 }$ to 2$\times $10$^{9}$ at a fixed Prandtl number Pr = 5.2. The numerical measurements at different points in the cell reveal that the heat flux at the plume dominated edge is larger and that it always has a power law relationship with \textit{Ra}, i.e. $j \quad \sim $ \textit{A Ra}$^{\gamma }$ . The scaling exponent linearly depends on the radial distance from the center, with = 0.44 at the center to = 0.27 at the edge, similarly has found by Shang, Tong and Xia, PRL 2008 and predicted by Grossmann and Lohse, Phys. Fluids 2004. These values imply a transition to bulk dominated heat flux beyond Ra = 10$^{15}$. The velocity and temperature fluctuations also have a power law dependence on \textit{Ra} and the corresponding scaling exponents again dependent on the radial position.

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Authors

  • Rajaram Lakkaraju

    • Physics of Fluids Group, Faculty of Science and Technology, University of Twente, The Netherlands

  • Richard J.A.M. Stevens

    • Physics of Fluids Group, Faculty of Science and Technology, University of Twente, The Netherlands

  • Roberto Verzicco

    • Department of Mechanical Engineering, University of Rome ``Tor Vergata,'' Italy

  • Siegfried Grossmann

    • Department of Physics, University of Marburg, Germany

  • Chao Sun

    • Physics of Fluids Group, Faculty of Science and Technology, University of Twente, The Netherlands

  • Detlef Lohse

    • Physics of Fluids Group, Faculty of Science and Technology, University of Twente, The Netherlands