Reynolds numbers of the large-scale flow in turbulent Rayleigh-Bénard convection

We measured Reynolds numbers Re of turbulent Rayleigh-Bénard convection over the Rayleighnumber range 2×10 <∼ R <∼ 10 11 and Prandtl-number range 3.3 <∼ σ <∼ 29 for cylindrical samples of aspect ratio Γ = 1. For R <∼ Rc ≃ 3× 10 9 we found Re ∼ R βeff with βeff ≃ 0.46 < 1/2. Here both the σand R-dependences are quantitatively consistent with the Grossmann-Lohse (GL) prediction. For R > Rc we found Re = 0.106 σ R, which differs from the GL prediction. The relatively sharp transition at Rc to the large-R regime suggests a qualitative and sudden change that renders the GL prediction inapplicable.