Plume Statistics in Turbulent Rayleigh-B\'enard Convection*

We report spatial statistics of thermal plumes based on an analysis of shadowgraph images for a cylindrical Rayleigh-B\'enard sample of height $L = 9.5$ mm and aspect ratio $\Gamma = 10.6$. The fluids consisted of pure gases with Prandtl- numbers $Pr\approx0.7$ and gas mixtures with $0.17 \leq Pr < 0.7$. The Rayleigh-number range was $3\times10^{5} \leq Ra \leq 5\times10^{6}$. We found the plume-length probability-density functions to be well fit by lognormal distributions with fit parameters which revealed a sharp transition from patterns to turbulence. In the turbulent range the mean spacing between plumes was found to scale as $Ra^{-0.33}$, suggesting that the Kolmogorov length $\eta_K$ is the relevant length scale, rather than the thermal boundary-layer thickness.