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

Abstract

We report on experimental determinations of the temperature field in the interior (bulk) of turbulent Rayleigh-Benard convection for a cylindrical sample with aspect ratio (diameter over height) of 0.50, both in the classical and in the ultimate state. The Prandtl number was close to 0.8. We find a "logarithmic layer" in which the temperature varies as A*ln(z/L) + B with the distance z from the bottom plate of the sample. The amplitude A varies with radial position r. In the classical state these results are in good agreement with direct numerical simulations (DNS); in the ultimate state there are as yet no DNS. A close analogy between the temperature field in the classical state and the "Law of the Wall" for the time-averaged down-stream velocity in shear flow is discussed.

arXiv comment27 pages, 15 figures

References in corpus (17)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• Scaling in thermal convection: A unifying theory
• Thermal convection for large Prandtl numbers
• Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution
• The unifying theory of scaling in thermal convection: The updated prefactors
• Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection
• Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection
• On the triggering of the Ultimate Regime of convection
• Logarithmic temperature profiles in turbulent Rayleigh-Bénard convection
• Measured Instantaneous Viscous Boundary Layer in Turbulent Rayleigh-Bénard Convection
• Prandtl-Blasius temperature and velocity boundary layer profiles in turbulent Rayleigh-Bénard convection
• Heat transport by turbulent Rayleigh-Bénard convection for $\Pra\ \simeq 0.8$ and $4\times 10^{11} \alt \Ra\ \alt 2\times10^{14}$: Ultimate-state transition for aspect ratio $\Gamma =1.00$
• Heat transport by turbulent Rayleigh-Bénard convection for $\Pra\ \simeq 0.8$ and $3\times 10^{12} \alt \Ra\ \alt 10^{15}$: Aspect ratio $\Gamma =0.50$
• Non-Oberbeck-Boussinesq effects in turbulent thermal convection in ethane close to the critical point
• Thermal boundary layer profiles in turbulent Rayleigh-Bénard convection in a cylindrical sample
• Logarithmic temperature profiles in the ultimate regime of thermal convection
• Logarithmic Spatial Variations and Universal $f^{-1}$ Power Spectra of Temperature Fluctuations in Turbulent Rayleigh-Bénard Convection

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