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.
Bibliographical note© 2015 American Physical Society
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Shishkina, O., Horn, S., Wagner, S., & Ching, E. S. C. (2015). Thermal boundary layer equation for turbulent Rayleigh-Bénard convection. Physical Review Letters, 114(11), . https://doi.org/10.1103/PhysRevLett.114.114302