Azimuthal diffusion of the large-scale-circulation plane, and absence of significant non-Boussinesq effects, in turbulent convection near the ultimate-state transition

We present measurements of the orientation and temperature amplitude of the large-scale circulation in a cylindrical sample of turbulent Rayleigh-Bénard convection (RBC) with aspect ratio ( and are the diameter and height respectively) and for the Prandtl number . The results for revealed a preferred orientation with up-flow in the west, consistent with a broken azimuthal invariance due to the Earth's Coriolis force (see Brown & Ahlers (Phys. Fluids, vol. 18, 2006, 125108)). They yielded the azimuthal diffusivity and a corresponding Reynolds number for Rayleigh numbers over the range . In the classical state the results were consistent with the measurements by Brown & Ahlers (J. Fluid Mech., vol. 568, 2006, pp. 351-386) for and , which gave , and with the Prandtl-number dependence as found previously also for the velocity-fluctuation Reynolds number (He et al., New J. Phys., vol. 17, 2015, 063028). At larger the data for revealed a transition to a new state, known as the 'ultimate' state, which was first seen in the Nusselt number and in at and . In the ultimate state we found . Recently, Skrbek and Urban (J. Fluid Mech., vol. 785, 2015, pp. 270-282) claimed that non-Oberbeck-Boussinesq effects on the Nusselt and Reynolds numbers of turbulent RBC may have been interpreted erroneously as a transition to a new state. We demonstrate that their reasoning is incorrect and that the transition observed in the Göttingen experiments and discussed in the present paper is indeed to a new state of RBC referred to as 'ultimate'.