Search for the ``ultimate state" in turbulent Rayleigh-B\'enard convection*

Measurements of the Nusselt number $Nu$ will be reported for turbulent Rayleigh-B\'enard convection of a cylindrical sample. They cover the Rayleigh-number range $10^{11} \alt Ra \alt 2\times 10^{15}$ using N$_2$ ($Pr = 0.72$) and SF$_6$ ($Pr = 0.79$ to 0.84) at pressures up to 19 bars and near-ambient temperatures. The sample had a height $L=2.24$m and diameter $D = 1.12$m and utilized the high-pressure vessel known as the ``Uboot of G\"ottingen" at the Max Planck Institute for Dynamics and Self-Organization in G\"ottingen, Germany. For $Ra \alt 4\times 10^{13}$ the data yielded $Nu \propto Ra^{\gamma_{eff}}$ with $\gamma_{eff} = 0.308$ and did not show the transition near $Ra = 10^{11}$ to an ``ultimate regime" that was reported by Chavanne et al. At $Ra = 4\times 10^{13}$ there is a well defined but continuous transition to a regime where $\gamma_{eff}$ is smaller than 0.30.