Search for the ``ultimate state" in turbulent Rayleigh-B\'enard convection for Rayleigh numbers up to $4\times 10^{13}$ and Prandtl numbers near 0.8.*

Measurements of the Nusselt number $Nu$ over the Rayleigh-number range $10^{10} < Ra < 4\times 10^{13}$ for N$_2$ (Prandtl number $Pr = 0.72$) and SF$_6$ ($Pr = 0.78$ to 0.82) are reported. They were made at pressures up to 15 bars and near-ambient temperatures for a cylindrical sample of height $L=2.2$ m and diameter $D = 1.1$ m in a new High-Pressure Convection Facility (HPCF) constructed at the Max Planck Institute for Dynamics and Self-Organization in G\"ottingen, Germany. The data can be represented well by a power law with an effective exponent of 0.31. They do not show the transition to an ``ultimate regime" reported by Chavanne et al.