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

Abstract

We present measurements of the orientation theta(0) and temperature amplitude delta of the large-scale circulation in a cylindrical sample of turbulent Rayleigh-Benard convection (RBC) with aspect ratio Gamma equivalent to D/L = 1.00 (D and L are the diameter and height respectively) and for the Prandtl number Pr similar or equal to 0.8. The results for theta(0) 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 D-theta and a corresponding Reynolds number Re-theta for Rayleigh numbers over the range 2 x 10(12) less than or similar to Ra less than or similar to 1.5 less than or similar to 10(14). In the classical state (Ra less than or similar to 2 x 10(13)) the results were consistent with the measurements by Brown & Ahlers (J. Fluid Mech., vol. 568, 2006, pp. 351-386) for Ra less than or similar to 10(11) and Pr = 4.38, which gave Re-theta alpha Ra-0.28, and with the Prandtl-number dependence Re-theta alpha Pr-1.2 as found previously also for the velocity-fluctuation Reynolds number Re-V (He et al., New J. Phys., vol. 17, 2015, 063028). At larger Ra the data for Re-theta (Ra) revealed a transition to a new state, known as the 'ultimate' state, which was first seen in the Nusselt number Nu(Ra) and in Re-V(Ra) at Ra-1 similar or equal to 2 x 10(13) and Ra-2 similar or equal to 8 x 10(13). In the ultimate state we found Re-theta alpha Ra-0.40 +/- 0.03. Recently, Skrbek & 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 Gottingen experiments and discussed in the present paper is indeed to a new state of RBC referred to as 'ultimate'.