Heat transport by turbulent Rayleigh-B\'enard convection for $\Pra\   \simeq 0.8$ and $4\times 10^{11} \alt \Ra\ \alt 2\times10^{14}$:   Ultimate-state transition for aspect ratio $\Gamma = 1.00$
  We report experimental results for heat-transport measurements by turbulent Rayleigh-B\'enard convection in a cylindrical sample of aspect ratio $\Gamma \equiv D/L = 1.00$ ($D = 1.12$ m is the diameter and $L = 1.12$ m the height). They are for the Rayleigh-number range $4\times10^{11} \alt \Ra \alt 2\times10^{14}$ and for Prandtl numbers \Pra\ between 0.79 and 0.86.   For $\Ra < \Ra^*_1 \simeq 2\times 10^{13}$ we find $\Nu = N_0 \Ra^{\gamma_{eff}}$ with $\gamma_{eff} = 0.321 \pm 0.002$ and $N_0 = 0.0776$, consistent with classical turbulent Rayleigh-B\'enard convection in a system with laminar boundary layers below the top and above the bottom plate and with the prediction of Grossmann and Lohse.   For $\Ra > \Ra_1^*$ the data rise above the classical-state power-law and show greater scatter. In analogy to similar behavior observed for $\Gamma = 0.50$, we interpret this observation as the onset of the transition to the ultimate state. Within our resolution this onset occurs at nearly the same value of $\Ra_1^*$ as it does for $\Gamma = 0.50$. This differs from an earlier estimate by Roche {\it et al.} which yielded a transition at $\Ra_U \simeq 1.3\times 10^{11} \Gamma^{-2.5\pm 0.5}$. A $\Gamma$-independent $\Ra^*_1$ would suggest that the boundary-layer shear transition is induced by fluctuations on a scale less than the sample dimensions rather than by a global $\Gamma$-dependent flow mode. Within the resolution of the measurements the heat transport above $\Ra_1^*$ is equal for the two $\Gamma$ values, suggesting a universal aspect of the ultimate-state transition and properties. The enhanced scatter of \Nu\ in the transition region, which exceeds the experimental resolution, indicates an intrinsic irreproducibility of the state of the system. 
Xiaozhou He, Denis Funfschilling, Eberhard Bodenschatz, and Guenter   Ahlers
physics.flu-dyn nlin.CD