Reynolds-number measurements for low-Prandtl-number turbulent convection of large-aspect-ratio samples

We present experimental results for the Reynolds number Re-U based on the horizontal mean-flow velocity U and for Re-V based on the root-mean-square horizontal fluctuation velocity V for turbulent Rayleigh-Benard convection in a cylindrical sample of aspect ratio Gamma = 10.9 over the Prandtl number range 0.18 <= Pr <= 0.88. The results were derived from space-time cross-correlation functions of shadowgraph images, using the elliptic approximation of He & Zhang (Phys. Rev. E, vol. 73, 2006, 055303). The data cover the Rayleigh number range from 3 x 10(5) to 2 x 10(7). We find that Re-U is nearly two orders of magnitude smaller than the values given by the Grossmann-Lohse (GL) model (Grossmann & Lohse, Phys. Rev. E, vol. 66, 2002, 016305) for Gamma = 1.00 and attribute this difference to averaging caused by lateral random diffusion of the large-scale circulation cells in large-Gamma samples. For the fluctuations we found Re-V = (R) over tilde (0PrRa eta)-Ra-alpha, with (R) over tilde (0) = 0.31, alpha = -0.53 +/- 0.11 and eta = 0.45 +/- 0.03. That result agrees well with the GL model. The close agreement of the coefficient (R) over tilde (0) must be regarded as a coincidence because the GL model was for Gamma = 1.00 and for a mean-flow velocity U.