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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 \, =\, 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 \, \, 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 \, =\, 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 \, \, 0. 43 are nearly independent of. For \, =\, 0. 275 N_ falls about 2. 5% below the other data. For R \, \, 10^11, the effective exponent ₄₅₅ of N_ \, =\, N₀ R^ ₄₅₅ is about 0. 32, larger than those of the Grossmann–Lohse model with its current parameters by about 0. 01. For the largest Rayleigh numbers covered for \, =\, 0. 98, 0. 67, and 0. 43, ₄₅₅ saturates at the asymptotic value \, =\, 1/3 of the Grossmann–Lohse model. The data do not reveal any crossover to a Kraichnan regime with ₄₅₅ \, >\, 1/3.
Nikolaenko et al. (Fri,) studied this question.