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Ultimate-state transition of turbulent Rayleigh-Bénard convection

Guenter Ahlers^1,2,*, Eberhard Bodenschatz^2,3,4,*, and Xiaozhou He^5,*

¹Department of Physics, University of California, Santa Barbara, California 93106, USA
²Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
³Institute for Nonlinear Dynamics, University of Göttingen, 37077 Göttingen, Germany
⁴Laboratory of Atomic and Solid-State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA
⁵Institute for Turbulence-Noise-Vibration Interaction and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China

^*Member of the International Collaboration for Turbulence Research.

Phys. Rev. Fluids 2, 054603 – Published 3 May, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.054603

Abstract

Recently Schumacher et al. [Phys. Rev. Fluids 1, 084402 (2016)] used direct numerical simulation to calculate the shear stress exerted on the top and bottom viscous boundary layers (BLs) of Rayleigh-Bénard convection with a Prandtl number $\Pr = 0.021$ and aspect ration $Γ = 1$ for Rayleigh numbers $Ra$ up to $4 \times 10^{8}$ . By extrapolating their results to larger $Ra$ , they concluded that the sample would undergo a transition to turbulent BLs and enter the “ultimate state” at ${Ra}^{*} ≃ 10^{11}$ for $\Pr = 0.021$ . Here we show that their result is consistent with the experimentally determined ${Ra}^{*} = 2 \times 10^{13}$ for $\Pr = 0.82$ by He et al. [Phys. Rev. Lett. 108, 024502 (2012); He et al., New J. Phys. 17, 063028 (2015)] and the $\Pr$ dependence of ${Ra}^{*}$ predicted by Grossmann and Lohse [Phys. Rev. E 66, 016305 (2002)]. Thus the numerical results of Schumacher et al. support the interpretation of the experimentally observed transition at ${Ra}^{*} = 2 \times 10^{13}$ for $\Pr = 0.82$ as the ultimate-state transition.

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References (23)

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Ultimate-state transition of turbulent Rayleigh-Bénard convection

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