Logarithmic Temperature Profiles in Turbulent Rayleigh-Bénard Convection

Ahlers, Guenter; Bodenschatz, Eberhard; Funfschilling, Denis; Grossmann, Siegfried; He, Xiaozhou; Lohse, Detlef; Stevens, Richard J. A. M.; Verzicco, Roberto

doi:10.1103/PhysRevLett.109.114501

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Logarithmic Temperature Profiles in Turbulent Rayleigh-Bénard Convection

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

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

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

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引用

Ahlers, G., Bodenschatz, E., Funfschilling, D., Grossmann, S., He, X., Lohse, D., Stevens, R. J. A. M., & Verzicco, R. (2012). Logarithmic Temperature Profiles in Turbulent Rayleigh-Bénard Convection. Physical Review Letters, 109, 114501-1-114501-5. doi:10.1103/PhysRevLett.109.114501.

引用: https://hdl.handle.net/11858/00-001M-0000-0029-1087-C

要旨

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 4×10(12)≲Ra≲10(15) for a Prandtl number Pr≃0.8 and on direct numerical simulation at Ra=2×10(12), 2×10(11), and 2×10(10), all for Pr=0.7.