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 [Formula: see text]-the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells for [Formula: see text] 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 [Formula: see text], that the Nusselt number-the dimensionless measure of heat transport-follows the classical power law of [Formula: see text] up to [Formula: see text] Intermittent fluctuations in the wall stress, a blueprint of turbulence in the vicinity of the boundaries, manifest at all [Formula: see text] considered here, increasing with increasing [Formula: see text], and suggest that an abrupt transition of the boundary layer to turbulence does not take place.