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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

Published online by Cambridge University Press:  17 February 2016

Xiaozhou He ,
Eberhard Bodenschatz  and
Guenter Ahlers
Xiaozhou He
Affiliation:
Max Planck Institute for Dynamics and Self Organization (MPIDS), D-37073 Göttingen, Germany Institute for Turbulence–Noise–Vibration Interaction and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China International Collaboration for Turbulence Research
Eberhard Bodenschatz
Affiliation:
Max Planck Institute for Dynamics and Self Organization (MPIDS), D-37073 Göttingen, Germany Institute for Nonlinear Dynamics, University of Göttingen, D-37073 Göttingen, Germany Laboratory of Atomic and Solid-State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA International Collaboration for Turbulence Research
Guenter Ahlers*
Affiliation:
Max Planck Institute for Dynamics and Self Organization (MPIDS), D-37073 Göttingen, Germany Department of Physics, University of California, Santa Barbara, CA 93106, USA International Collaboration for Turbulence Research
*
†Email address for correspondence: guenter@physics.ucsb.edu
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Abstract

We present measurements of the orientation ${\it\theta}_{0}$ and temperature amplitude ${\it\delta}$ of the large-scale circulation in a cylindrical sample of turbulent Rayleigh–Bénard convection (RBC) with aspect ratio ${\it\Gamma}\equiv D/L=1.00$ ( $D$ and $L$ are the diameter and height respectively) and for the Prandtl number $Pr\simeq 0.8$ . The results for ${\it\theta}_{0}$ revealed a preferred orientation with up-flow in the west, consistent with a broken azimuthal invariance due to the Earth’s Coriolis force (see Brown & Ahlers (Phys. Fluids, vol. 18, 2006, 125108)). They yielded the azimuthal diffusivity $D_{{\it\theta}}$ and a corresponding Reynolds number $Re_{{\it\theta}}$ for Rayleigh numbers over the range $2\times 10^{12}\lesssim Ra\lesssim 1.5\times 10^{14}$ . In the classical state ( $Ra\lesssim 2\times 10^{13}$ ) the results were consistent with the measurements by Brown & Ahlers (J. Fluid Mech., vol. 568, 2006, pp. 351–386) for $Ra\lesssim 10^{11}$ and $Pr=4.38$ , which gave $Re_{{\it\theta}}\propto Ra^{0.28}$ , and with the Prandtl-number dependence $Re_{{\it\theta}}\propto Pr^{-1.2}$ as found previously also for the velocity-fluctuation Reynolds number $Re_{V}$ (He et al., New J. Phys., vol. 17, 2015, 063028). At larger $Ra$ the data for $Re_{{\it\theta}}(Ra)$ revealed a transition to a new state, known as the ‘ultimate’ state, which was first seen in the Nusselt number $Nu(Ra)$ and in $Re_{V}(Ra)$ at $Ra_{1}^{\ast }\simeq 2\times 10^{13}$ and $Ra_{2}^{\ast }\simeq 8\times 10^{13}$ . In the ultimate state we found $Re_{{\it\theta}}\propto Ra^{0.40\pm 0.03}$ . Recently, Skrbek & Urban (J. Fluid Mech., vol. 785, 2015, pp. 270–282) claimed that non-Oberbeck–Boussinesq effects on the Nusselt and Reynolds numbers of turbulent RBC may have been interpreted erroneously as a transition to a new state. We demonstrate that their reasoning is incorrect and that the transition observed in the Göttingen experiments and discussed in the present paper is indeed to a new state of RBC referred to as ‘ultimate’.

JFM classification

Turbulent Flows: Turbulent convection

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Rapids
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Journal of Fluid Mechanics , Volume 791 , 25 March 2016 , R3
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© 2016 Cambridge University Press 

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