A Reynolds number Re_(eff) was measured in turbulent Rayleigh-Benard convection (RBC) of a cylindrical sample over the Rayleigh-number range 10~(12) ≤ Ra ≤ 10~(15) and for Prandtl numbers Pr near 0.8 (He et al., 2012). The aspect ratio Γ ≡ D/L of the cylindrical sample was 0.50 (D = 1.12 m was the diameter and L = 2.24 m was the height). The measurements of Re_(eff) were conducted at a distance L/4 above the bottom plate and 1.0 cm away from the sidewall inside the sample. For Ra {approx.＜} 10~(13) the results showed Re_(eff) ∝ Ra~(ζ_(eff)) with ζ_(eff) {approx =} 0.43, consistent with classical turbulent RBC. After a transition region for 10~(13) {approx.＜} Ra {approx.＜} 5×10~(14), where multi-stability occurred, we found an exponent ζ {approx =} 0.50, in agreement with the predictions of Grossmann and Lohse (2011) for the large-Ra asymptotic state. We believe that our measurements revealed the transition of RBC to the ultimate state predicted by Kraichnan (1962).
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