Thermal Boundary Layer Equation for Turbulent Rayleigh-Benard Convection

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.

4 pages, 3 figures

References in corpus (2)

• Boundary layer structure in turbulent Rayleigh-Benard convection
• Logarithmic temperature profiles of turbulent Rayleigh-Bénard convection in the classical and ultimate state for a Prandtl number of 0.8

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• Non-Boussinesq convection at low Prandtl numbers relevant to the Sun
• Oscillatory large-scale circulation in liquid-metal thermal convection and its structural unit
• Flow organization in laterally unconfined Rayleigh-Bénard turbulence