Azimuthal diffusion of the large-scale-circulation plane, and absence of significant non-Boussinesq effects, in turbulent convection near the ultimate-state transition. (17th February 2016)

• Record Type: Journal Article
• Authors: He, Xiaozhou; Bodenschatz, Eberhard; Ahlers, Guenter
• Is Part Of: Journal of fluid mechanics. Volume 791(2016:Mar.)
• Publication Date: 2016-02-17
• Subjects: Bénard convection, -- turbulent convection; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2016.56
• Languages: English
• ISSNs: 0022-1120

Abstract

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'.