Classical 1/3 scaling of convection holds up to Ra = 10¹⁵

The global transport of heat and momentum in turbulent convection is constrained by thin thermal and viscous boundary layers at the heated and cooled boundaries of the system. This bottleneck is thought to be lifted once the boundary layers themselves become fully turbulent at very high values of the Rayleigh number Ra-the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells for Ra & 10¹² have reported different outcomes on the putative heat transport law. Here we show, by direct numerical simulations of three-dimensional turbulent Rayleigh-Bénard convection flows in a slender cylindrical cell of aspect ratio 1/10, that the Nusselt number-the dimensionless measure of heat transport-follows the classical power law of Nu = (0.0525 ± 0.006) × Ra^0.331+0.002 up to Ra = 10¹⁵. Intermittent fluctuations in the wall stress, a blueprint of turbulence in the vicinity of the boundaries, manifest at all Ra considered here, increasing with increasing Ra, and suggest that an abrupt transition of the boundary layer to turbulence does not take place.