Thermal boundary layer equation for turbulent Rayleigh-Bénard convection

Shishkina, Olga; Horn, Susanne; Wagner, Sebastian; Ching, E. S. C.

doi:10.1103/PhysRevLett.114.114302

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Thermal boundary layer equation for turbulent Rayleigh-Bénard convection

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Shishkina, Olga
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Horn, Susanne
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Wagner, Sebastian
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.114302
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Citation

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): 114302. doi:10.1103/PhysRevLett.114.114302.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-7B34-C

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.