Heat transport by turbulent Rayleigh-B\'enard convection for $Pr \simeq 0.8$ and $4 \times 10^{11} < Ra < 2 \times 10^{14}$: ultimate-state transition for aspect ratio $\Gamma$ = 1.00~

We report experimental results for heat transport by Rayleigh-B\'enard convection (RBC) in a cylindrical sample with aspect ratio $\Gamma \equiv D/L = 1.00$ ($D= 1.12$ m is the diameter and $L = 1.12$ m is the height) over the range $4 \times 10^{11} < Ra < 2 \times 10^{14}$ at $Pr \simeq 0.8$. For $Ra < Ra_1^* \simeq 2 \times 10^{13}$ we find $Nu = N_0 Ra^{\gamma_{\mathrm{eff}}}$ with $\gamma_{\mathrm{eff}}$ = 0.321 $\pm$ 0.002 and $N_0 = 0.0776$, consistent with classical turbulent RBC in a system with laminar boundary layers (BLs) below the top and above the bottom plate and with the prediction of Grossmann and Lohse$^{(1)}$. For $Ra > Ra_1^*$ the data rise above the classical-state power-law and show greater scatter. In analogy to similar behavior observed for $\Gamma = 0.50$$^{(2)}$, we interpret this phenomenon as the onset of the transition to the ultimate state. Within our resolution this onset occurs at nearly the same value of $Ra_1^*$ as it does for $\Gamma = 0.50$.