Measurements of the Nusselt number Nu and of a Reynolds number Re(eff) for Rayleigh-Bénard convection (RBC) over the Rayleigh-number range 10(12)≲Ra≲10(15) and for Prandtl numbers Pr near 0.8 are presented. The aspect ratio Γ≡D/L of a cylindrical sample was 0.50. For Ra≲10(13) the data yielded Nu∝Ra(γ(eff)) with γ(eff)≃0.31 and Re(eff)∝Ra(ζ(eff)) with ζ(eff)≃0.43, consistent with classical turbulent RBC. After a transition region for 10(13)≲Ra≲5×10(14), where multistability occurred, we found γ(eff)≃0.38 and ζ(eff)=ζ≃0.50, in agreement with the results of Grossmann and Lohse for the large-Ra asymptotic state with turbulent boundary layers which was first predicted by Kraichnan.

We report results for the temperature profiles of turbulent Rayleigh-Bénard convection (RBC) in the interior of a cylindrical sample of aspect ratio Γ≡D/L=0.50 (D and L are the diameter and height, respectively). Both in the classical and in the ultimate state of RBC we find that the temperature varies as A×ln(z/L)+B, where z is the distance from the bottom or top plate. In the classical state, the coefficient A decreases in the radial direction as the distance from the side wall increases. For the ultimate state, the radial dependence of A has not yet been determined. These findings are based on experimental measurements over the Rayleigh-number range 4×10(12)≲Ra≲10(15) for a Prandtl number Pr≃0.8 and on direct numerical simulation at Ra=2×10(12), 2×10(11), and 2×10(10), all for Pr=0.7.

We report on the experimental results for heat-transport measurements, in the form of the Nusselt number N u, by turbulent Rayleigh-Bénard convection (RBC) in a cylindrical sample of aspect ratio ≡ D/L = 0.50 (D = 1.12 m is the diameter and L = 2.24 m the height). The measurements were made using sulfur hexafluoride at pressures up to 19 bar as the fluid. They are for the Rayleigh-number range 3 × 10 12 Ra 10 15 and for Prandtl numbers Pr between 0.79 and 0.86. For Ra < Ra * 1 1.4 × 10 13 we find N u = N 0 Ra γ eff with γ eff = 0.312 ± 0.002, which is consistent with classical turbulent RBC in a system with laminar boundary layers below the top and above the bottom 7

We report experimental results for heat-transport measurements, in the form of the Nusselt number N u, by turbulent Rayleigh-Bénard convection (RBC) in a cylindrical sample of aspect ratio ≡ D/L = 1.00 (D = 1.12 m is the diameter and L = 1.12 m the height) and compare them with previously reported results for = 0.50. The measurements were made using sulfur hexafluoride at pressures up to 19 bars as the fluid. They are for the Rayleighnumber range 4 × 10 11 Ra 2 × 10 14 and for Prandtl numbers Pr between 0.79 and 0.86. For Ra < Ra * 1 2 × 10 13 we find N u = N 0 Ra γ eff with γ eff = 0.321 ± 0.002 and N 0 = 0.0776, consistent with classical turbulent RBC in a system with laminar boundary layers (BLs) below the top and above the bottom 6 International Collaboration for Turbulence Research. 2 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 = 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 = 0.50. This differs from an earlier estimate by Roche et al (2010 New J. Phys. 12 085014), which yielded a transition at Ra U 1.3 × 10 11 −2.5±0.5 . A -independent Ra * 1 would suggest that the BL shear transition is induced by fluctuations on a scale less than the sample dimensions rather than by a global -dependent flow mode. Within the resolution of the measurements the heat transport above Ra * 1 is equal for the two values, suggesting a universal aspect of the ultimate-state transition and properties. The enhanced scatter of N u in the transition region, which exceeds the experimental resolution, indicates an intrinsic irreproducibility of the state of the system. Several previous measurements for = 1.00 are re-examined and compared with the present results. None of them identified the ultimate-state transition.

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