Dresden 2017 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 16: Focus: Fundamental aspects of turbulent convection

DY 16.9: Talk

Tuesday, March 21, 2017, 12:15–12:30, ZEU 118

Prediction of the temperature profiles in Rayleigh-Bénard convection. — •Mohammad Emran and Olga Shishkina — Max-Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.

Experiments and numerical simulations of Rayleigh-Bénard convection (RBC) show that the temperature profiles in RBC systematically deviate from those obtained as solutions of the classical Prandtl-Blasius or Falkner-Skan boundary layer equations. The deviations persist even after rescaling of the profiles in a fixed or dynamical frame. Some improvements have been made by adapting the pressure gradients and buoyancy effects in the classical boundary layer equations. Those improvements mostly influence the prediction of the viscous boundary layer structure, but not the structure of the thermal boundary layer, in particular at large Prandtl number. Here we report a recipe to predict the mean vertical temperature profiles in turbulent Rayleigh-Bénard convection for Prandtl numbers larger than one. It is based on the thermal boundary layer equation from Shishkina et al., Phys. Rev. Lett. 114, 114302 (2015), which incorporates the effect of turbulent fluctuations, and new Direct Numerical Simulations (DNS) of RBC in a cylindrical cell of the aspect ratio 1, for the Prandtl number variation of several orders of magnitude. Our modeled temperature profiles are found to agree with the DNS much better than those obtained with the classical Prandtl--Blasius or Falkner--Skan approaches.