Anomalous Reynolds-number scaling in turbulent Rayleigh-Benard convection

This paper reports measurements of Reynolds numbers R p e corresponding to the turnover time of thermal excitations ('plumes') and R. e corresponding to the twisting-oscillation period of the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection over the Rayleigh-number range 2 x 10(8) less than or similar to R less than or similar to 10(11) and Prandtl-number range 3.3 less than or similar to sigma less than or similar to 29 for cylindrical samples of aspect ratio Gamma = 1. For R < R* similar or equal to 3 x 10(9) both periods, and hence both Reynolds numbers, were the same and scaled as R-e similar to R-gamma eff with gamma(eff) similar or equal to 0.45 < 1/2. Here both the sigma- and R-dependences were quantitatively consistent with the Grossmann-Lohse (GL) prediction. For R > R* the results could be represented by R-e(p) = 0.138 sigma(-0.82) R-0.493 for the plume turnover time and R-e(omega) = 0.17 sigma(-0.81) R-0.480 for the twisting oscillation, both of which differ significantly from the GL prediction as well as from each other. A relatively sharp transition at R* to the large-R regime and the separation of the two Reynolds numbers from each other suggest a qualitative and sudden change that renders the measured quantities inapplicable to the GL prediction. Combining R-e(p) and previously reported measurements of the Nusselt number N yielded the kinetic energy-dissipation epsilon(u) = (N - 1) R/sigma(2) as a function of R p e. For R less than or similar to R* these results were in excellent agreement with the corresponding GL prediction, and both approached closely to the (Re)(3)- dependence that is expected at large Re where the bulk contribution to epsilon(u) dominates. For R > R* the data were consistent with epsilon(u). proportional to (Re) (8/ 3). This di. ers from the expected large Re behavior and suggests that R p e no longer is the Reynolds number relevant to epsilon (u).