Reynolds number measurements in Rayleigh-Benard convection

We determined the Reynolds number $R_e$ in cylindrical cells of aspect ratio $\Gamma \equiv D/L = 1$ ($D =$ diameter, $L = $ height) filled with water at a mean temperature of 40$^\circ$C and heated from below for Rayleigh numbers $R$ from $10^9$ to $10^{11}$. It is well known that the main flow structure in this system is a collection of hot and cold plumes and an associated large-scale circulation (LSC). We measured the temperature of the cell side-wall as a function of time at eight azimuthal locations on the horizontal mid-plane. The cross-correlation functions of temperatures on opposite sides of the cell indicate that localized hot or cold volumes associated with the LSC survive for a time comparable to the turnover time $\tau$ as they follow the LSC. >From maxima of the cross-correlation functions we find $\tau$, and from it the Reynolds number $R_e \equiv (4L/\tau)(L/\nu)$ ($\nu$ is the kinematic viscosity), of the LSC. The results are consistent with measurements by others \footnote{X.-L. Qiu and P. Tong, Phys. Rev. E {\bf 66}, 026308 (2002).} for $R \alt 10^ {10}$ and with the prediction of Grossmann and Lohse footnote{S. Grossmann and D. Lohse, Phys. Rev. E {\bf 66}, 016305 (2002).}.