Turbulent Rayleigh–Bénard convection for a Prandtl number of 0.67

Abstract

For the Rayleigh-number range 107 ≲ Ra ≲ 1011 we report measurements of the Nusselt number Nu and of properties of the large-scale circulation (LSC) for cylindrical samples of helium gas (Prandtl number Pr = 0.674) that have aspect ratio Γ ≡ D/L = 0.50 (D and L are the diameter and the height respectively) and are heated from below. The results for Nu are consistent with recent direct numerical simulations. We measured the amplitude δ of the azimuthal temperature variation induced by the LSC at the sidewall, and the LSC circulation-plane orientation θ0, at three vertical positions. For the entire Ra range the LSC involves a convection roll that is coherent over the height of the system. However, this structure frequently collapses completely at irregular time intervals and then reorganizes from the incoherent flow. At small δ the probability distribution p(δ) increases linearly from zero; for Γ = 1 and Pr = 4.38 this increase is exponential. No evidence of a two-roll structure, with one above the other, was observed. This differs from recent direct numerical simulations for Γ = 0.5 and Pr = 0.7, where a one-roll LSC was found to exist only for Ra ≲ 109 to 1010, and from measurements for Γ = 0.5 and Pr ≃ 5, where one- and two-roll structures were observed with transitions between them at random time intervals.