Azimuthal diffusion of the large-scale-circulation plane, and absence of significant non-Boussinesq effects, in turbulent convection near the ultimate-state transition

Abstract

We present measurements of the orientation $\theta_0$ and temperature amplitude $\delta$ of the large-scale circulation in a cylindrical sample of turbulent Rayleigh-Benard convection (RBC) with aspect ratio $\Gamma \equiv D/L = 1.00$ ($D$ and $L$ are the diameter and height respectively) and for the Prandtl number $Pr \simeq 0.8$. Results for $\theta_0$ revealed a preferred orientation with upflow in the West, consistent with a broken azimuthal invariance due to Earth's Coriolis force [see \cite{BA06b}]. They yielded the azimuthal diffusivity $D_\theta$ and a corresponding Reynolds number $Re_{\theta}$ for Rayleigh numbers over the range $2\times 10^{12} < Ra < 1.5\times 10^{14}$. In the classical state ($Ra < 2\times 10^{13}$) the results were consistent with the measurements by \cite{BA06a} for $Ra < 10^{11}$ and $Pr = 4.38$ which gave $Re_{\theta} \propto Ra^{0.28}$, and with the Prandtl-number dependence $Re_{\theta} \propto Pr^{-1.2}$ as found previously also for the velocity-fluctuation Reynolds number $Re_V$ \cite[]{HGBA15b}. At larger $Ra$ the data for $Re_{\theta}(Ra)$ 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 $Ra^*_1 \simeq 2\times 10^{13}$ and $Ra^*_2 \simeq 8\times 10^{13}$. In the ultimate state we found $Re_{\theta} \propto Ra^{0.40\pm 0.03}$. Recently \cite{SU15} 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 G\"ottingen experiments and discussed in the present paper is indeed to a new state of RBC referred to as "ultimate".