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Free keywords:
Bénard convection; Turbulent convection
Abstract:
We present measurements of the orientation θ0 and temperature amplitude δ of the large-scale circulation in a cylindrical sample of turbulent Rayleigh–Bénard convection (RBC) with aspect ratio Γ≡D/L=1.00 (D and L are the diameter and height respectively) and for the Prandtl number Pr≃0.8. The results for θ0 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 Dθ and a corresponding Reynolds number Reθ for Rayleigh numbers over the range 2×1012≲Ra≲1.5×1014. In the classical state (Ra≲2×1013) the results were consistent with the measurements by Brown & Ahlers (J. Fluid Mech., vol. 568, 2006, pp. 351–386) for Ra≲1011 and Pr=4.38, which gave Reθ∝Ra0.28, and with the Prandtl-number dependence Reθ∝Pr−1.2 as found previously also for the velocity-fluctuation Reynolds number ReV (He et al., New J. Phys., vol. 17, 2015, 063028). At larger Ra the data for Reθ(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 ReV(Ra) at Ra∗1≃2×1013 and Ra∗2≃8×1013. In the ultimate state we found Reθ∝Ra0.40±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 Göttingen experiments and discussed in the present paper is indeed to a new state of RBC referred to as ‘ultimate’.
