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We report experimental results for heat-transport measurements, in the formof the Nusselt number \Nu, by turbulent Rayleigh-B\'enard convection in acylindrical sample of aspect ratio $\Gamma \equiv D/L = 0.50$ ($D = 1.12$ m isthe diameter and $L = 2.24$ m the height). The measurements were made usingsulfur hexafluoride at pressures up to 19 bars as the fluid. They are for theRayleigh-number range $3\times 10^{12} \alt \Ra \alt 10^{15}$ and for Prandtlnumbers \Pra\ between 0.79 and 0.86. For $\Ra < \Ra^*_1 \simeq 1.4\times10^{13}$ we find $\Nu = N_0 \Ra^{\gamma_{eff}}$ with $\gamma_{eff} = 0.312 \pm0.002$, consistent with classical turbulent Rayleigh-B\'enard convection in asystem with laminar boundary layers below the top and above the bottom plate.For $\Ra^*_1 < \Ra < \Ra^*_2$ (with $\Ra^*_2 \simeq 5\times 10^{14}$)$\gamma_{eff}$ gradually increases up to $0.37\pm 0.01$. We argue that above$\Ra^*_2$ the system is in the ultimate state of convection where the boundarylayers, both thermal and kinetic, are also turbulent. Several previousmeasurements for $\Gamma = 0.50$ are re-examined and compared with the presentresults.

new journal of physics

Heat transport by turbulent Rayleigh-B\'enard convection for $\Pra\  \simeq 0.8$ and $3\times 10^{12} \alt \Ra\ \alt 10^{15}$: Aspect ratio  $\Gamma = 0.50$