title: Thermal boundary layer equation for turbulent Rayleigh-Bénard convection.
abstract: We report a new thermal boundary layer equation for turbulent Rayleigh-Bénard 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 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.
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany.
authors.forename: Olga
authors.initials: O
authors.lastname: Shishkina
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany.
authors.forename: Susanne
authors.initials: S
authors.lastname: Horn
authors.affiliation: Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Wagner
authors.affiliation: Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong.
authors.forename: Emily S C
authors.initials: ES
authors.lastname: Ching