We present an experimental study of turbulent Rayleigh-Bénard convection (RBC) in a cylindrical cell of height 0.3 m, diameter 0.3 m. It is designed to minimize the influence of its structure on the convective flow of cryogenic ${}^4\mathrm{He}$ gas of Prandtl number $\mathrm{Pr}\approx 1$, with the aim of resolving existing contradictions in Nusselt (Nu) versus Rayleigh number (Ra) scaling. For $7.2\times {10}^6\le \mathrm{Ra}\lesssim {10}^{11}$ our data agree with suitably corrected data from similar cryogenic experiments and are consistent with $\mathrm{Nu}\propto {\mathrm{Ra}}^{2/7}$. On approaching $\mathrm{Ra}\approx {10}^{11}$ our data display a crossover to $\mathrm{Nu}\propto {\mathrm{Ra}}^{1/3}$ that approximately holds up to $\mathrm{Ra}\cong 4.6\times {10}^{13}$; there is no sign of a transition to the ultimate Kraichnan regime. Differences in Nu(Ra) scaling observed in similar RBC experiments for $\mathrm{Ra}\gtrsim {10}^{11}$ cannot be explained due to the difference in Pr, but seem to depend also on experimental details.

• Received 20 December 2010

DOI:https://doi.org/10.1103/PhysRevLett.107.014302