Transition to the Ultimate State of Turbulent Rayleigh-Bénard Convection

Measurements of the Nusselt number Nu and of a Reynolds number Reeff for Rayleigh-B\'enard convection (RBC) over the Rayleigh-number range 10¹²Ra10¹⁵ and for Prandtl numbers Pr near 0.8 are presented. The aspect ratio Γ≡D/L of a cylindrical sample was 0.50. For Ra10¹³ the data yielded Nu∝Ra^γeff with γeff0.31 and Reeff∝Ra^ζeff with ζeff0.43, consistent with classical turbulent RBC. After a transition region for 10¹³Ra5×10¹⁴, where multistability occurred, we found γeff0.38 and ζeff=ζ0.50, in agreement with the results of Grossmann and Lohse for the large-Ra asymptotic state with turbulent boundary layers which was first predicted by Kraichnan.