%0 Journal Article
%T Thermal Boundary Layer Equation for Turbulent Rayleigh-Benard Convection
%A Olga Shishkina
%A Susanne Horn
%A Sebastian Wagner
%A Emily S. C. Ching
%J Physics
%D 2014
%I arXiv
%R 10.1103/PhysRevLett.114.114302
%X We report a new thermal boundary layer equation for turbulent Rayleigh-Benard convection for Prandtl number Pr>1 that takes into account the effect of turbulent fluctuations. These fluctuations are neglected in existing equations, which are based on steady-state and laminar assumptions. Using this new equation, we derive analytically the mean temperature profiles in two limits: (a) Pr>1, Pr~1 and (b) Pr>>1. These two theoretical predictions are in excellent agreement with the results of our direct numerical simulations for Pr=4.38 (water) and Pr=2547.9 (glycerol) respectively.
%U http://arxiv.org/abs/1411.5826v2