Turbulent convection at high Rayleigh numbers and aspect ratio 4

We report measurements of the Nusselt number, Nu, in turbulent thermal convection in a cylindrical container of aspect ratio 4. The highest Rayleigh number achieved was Ra \, =\, 2 \, \, 10^13. Except for the last half a decade or so of Ra, experimental conditions obey the Boussinesq approximation accurately. For these conditions, the data show that the Nu – 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 Ra is inconclusive because the corresponding conditions are non-Boussinesq. Finally, we report a modified scaling relation between the plume advection frequency and Ra that collapses data for different aspect ratios.