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

We present experimental results for the Reynolds number ReU based on the horizontal mean-flow velocity U and for ReV based on the root-mean-square horizontal fluctuation velocity V for turbulent Rayleigh–Bénard convection in a cylindrical sample of aspect ratio Γ = 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× 10⁵ to 2× 10⁷ . We find that ReU 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 Γ = 1. 00 and attribute this difference to averaging caused by lateral random diffusion of the large-scale circulation cells in large- Γ samples. For the fluctuations we found ReV = R̃ ₀ Prα Raη , with R̃ ₀ = 0. 31 , α = - 0. 53± 0. 11 and η = 0. 45± 0. 03 . That result agrees well with the GL model. The close agreement of the coefficient R̃ ₀ must be regarded as a coincidence because the GL model was for Γ = 1. 00 and for a mean-flow velocity U .