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Logarithmic temperature profiles in turbulent Rayleigh-Bénard convection

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Ahlers,  G.
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Bodenschatz,  E.
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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He,  X.
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Ahlers, G., Bodenschatz, E., Funfschilling, D., Grossmann, S., He, X., Lohse, D., et al. (2012). Logarithmic temperature profiles in turbulent Rayleigh-Bénard convection. Physical Review Letters, 109(11): 114501. doi:10.1103/PhysRevLett.109.114501.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-291E-4
Abstract
We report results for the temperature profiles of turbulent Rayleigh-Bénard convection (RBC) in the interior of a cylindrical sample of aspect ratio Γ≡D/L=0.50 (D and L are the diameter and height, respectively). Both in the classical and in the ultimate state of RBC we find that the temperature varies as A×ln(z/L)+B, where z is the distance from the bottom or top plate. In the classical state, the coefficient A decreases in the radial direction as the distance from the side wall increases. For the ultimate state, the radial dependence of A has not yet been determined. These findings are based on experimental measurements over the Rayleigh-number range 4×1012≲Ra≲1015 for a Prandtl number Pr≃0.8 and on direct numerical simulation at Ra=2×1012, 2×1011, and 2×1010, all for Pr=0.7.