Measurements of Reynolds number near the transition to the ultimate-state of turbulent Rayleigh-Bénard convection

A Reynolds number Re_!"" was measured in turbulent Rayleigh-Bénard convection (RBC) of a cylindrical sample over the Rayleigh-number range 10¹² = Ra = 10¹⁵ and for Prandtl numbers Pr near 0.8 (He et al., 2012). The aspect ratio G = 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_!"" were conducted at a distance L/4 above the bottom plate and 1.0 cm away from the sidewall inside the sample. For Ra ? 10^!" the results showed Re_!"" ? Ra^!!"" with !_!"" ? 0.43, consistent with classical turbulent RBC. After a transition region for 10^!" ? Ra ? 5×10^!", where multi-stability occurred, we found an exponent ? ? 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).