Logarithmic temperature profiles in the ultimate regime of thermal convection

Abstract

We report on the theory of logarithmic temperature profiles in very strongly developed thermal convection in the geometry of a Rayleigh-Benard cell with aspect ratio one and discuss the degree of agreement with the recently measured profiles in the ultimate state of very large Rayleigh number flow. The parameters of the log-profile are calculated and compared with the measure ones. Their physical interpretation as well as their dependence on the radial position are discussed.

14 pages, no figure

References in corpus (3)

• Logarithmic temperature 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 $\Gamma =0.50$

Cited by in corpus (20)

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• Optimal Taylor-Couette flow: Radius ratio dependence
• Direct numerical simulation of Taylor-Couette flow with grooved walls: torque scaling and flow structure
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• Logarithmic temperature profiles of turbulent Rayleigh-Bénard convection in the classical and ultimate state for a Prandtl number of 0.8
• Logarithmic mean temperature profiles and their connection to plume emissions in turbulent Rayleigh-Bénard convection
• Logarithmic Spatial Variations and Universal $f^{-1}$ Power Spectra of Temperature Fluctuations in Turbulent Rayleigh-Bénard Convection
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• Azimuthal diffusion of the large-scale-circulation plane, and absence of significant non-Boussinesq effects, in turbulent convection near the ultimate-state transition
• On the logarithmic profile of temperature in the atmospheric convective boundary layers
• Velocity fluctuations and boundary layer structure in a rough Rayleigh-B{é}nard cell filled with water
• Boundary layer structure in turbulent Rayleigh-Bénard convection in a slim box
• Calculation of the mean velocity profile for strongly turbulent Taylor--Couette flow and arbitrary radius ratios
• Turbulent Rayleigh-Bénard convection described by projected dynamics in phase space
• A Lagrangian fluctuation-dissipation relation for scalar turbulence, III. Turbulent Rayleigh-Bénard convection
• Physical Mechanism behind the Early Onset of the Ultimate State in Supergravitational Centrifugal Thermal Convection