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Thermal boundary layer equation for turbulent Rayleigh-Bénard convection

MPG-Autoren
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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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Zitation

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.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0029-7B34-C
Zusammenfassung
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.