Turbulent convection at high Rayleigh numbers and aspect ratio 4

We report measurements of the Nusselt number, $\hbox{\it Nu}$, in turbulent thermal convection in a cylindrical container of aspect ratio 4. The highest Rayleigh number achieved was $\hbox{\it Ra} \,{=}\, 2 \,{\times}\, 10^{13}$. Except for the last half a decade or so of $\hbox{\it Ra}$, experimental conditions obey the Boussinesq approximation accurately. For these conditions, the data show that the $\log\hbox{\it Nu}$–$\log\hbox{\it Ra}$ slope saturates at a value close to 1/3, as observed previously by us in experiments with smaller aspect ratios. The increasing slope over the last half a decade of $\hbox{\it Ra}$ is inconclusive because the corresponding conditions are non-Boussinesq. Finally, we report a modified scaling relation between the plume advection frequency and ${\hbox{\it Ra}}$ that collapses data for different aspect ratios.