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

Abstract

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 sigma = 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 Gamma = 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 ~= 10^12 and Nusselt number N ~= 600 were reached for Gamma = 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_infty for plates with infinite conductivity. The results for N_infty and Gamma >= 0.43 are nearly independent of Gamma. For Gamma = 0.275 N_infty falls about 2.5 % below the other data. For R ~<= 10^11, the effective exponent gamma_eff of N_infty = N_0 R^gamma_eff 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 Gamma = 0.98, 0.67, and 0.43, gamma_eff saturates at the asymptotic value gamma = 1/3 of the Grossmann-Lohse model. The data do not reveal any crossover to a Kraichnan regime with gamma_eff > 1/3.