Heat transport by turbulent Rayleigh-Bénard Convection in cylindrical cells with aspect ratio one and less

We present high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of water (Prandtl number σ = 4.4) with a diameter D of 49.7 cm and heights L = 116.3, 74.6, and 50.6 cm, as well as for D = 24.8 cm and L = 90.2 cm. For each aspect ratio Γ ≡ D/L = 0.28, 0.43, 0.67, and 0.98 the data cover a range of a little over a decade of R. The maximum R ≃ 10 and Nusselt number N ≃ 600 were reached for Γ = 0.43 and D = 49.7. The data were corrected for the influence of the finite conductivity of the top and bottom plates on the heat transport in the fluid to obtain estimates of N∞ for plates with infinite conductivity. The results for N∞ and Γ ≥ 0.43 are nearly independent of Γ. For Γ = 0.275 N∞ falls about 2.5 % below the other data. For R < ∼ 10 , the effective exponent γeff of N∞ = N0R γeff is about 0.321, larger than those of the Grossmann-Lohse model with its current parameters by about 0.01. For the largest Rayleigh numbers covered for Γ = 0.98, 0.67, and 0.43, γeff saturates at the asymptotic value γ = 1/3 of the Grossmann-Lohse model. The data do not reveal any crossover to a Kraichnan regime with γeff > 1/3.