Thermal boundary layer equation for turbulent Rayleigh-Bénard convection

O. Shishkina, S. Horn, S. Wagner, E.S.C. Ching

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Abstract

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.
Original languageEnglish
Article number114302
Number of pages5
JournalPhysical Review Letters
Volume114
Issue number11
DOIs
Publication statusPublished - 20 Mar 2015
Externally publishedYes

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