Reynolds number scaling in cryogenic turbulent Rayleigh-Benard convection in a cylindrical aspect ratio one cell
Abstract
We perform an experimental study of turbulent Rayleigh-Benard convection up to very high Rayleigh number, 10(8) < Ra < 10(14), in a cylindrical aspect ratio one cell, 30 cm in height, filled with cryogenic helium gas. We monitor temperature fluctuations in the convective flow with four small (0.2 mm) sensors positioned in pairs 1.5 cm from the sidewalls and 2.5 cm vertically apart and symmetrically around the mid-height of the cell.
Based on one-point and two-point correlations of the temperature fluctuations, we determine different types of Reynolds numbers, Re, associated with the large-scale circulation (LSC). We observe a transition between two types of Re.
Ra/scaling around Ra = 10(10)-10(11), which is accompanied by a scaling change of the skewness of the probability distribution functions (PDFs) of the temperature fluctuations. The Re.
Ra/dependencies measured near the sidewall at Prandtl number Pr similar to 1 are consistent with the (RaPr2/3)-Pr-4/9 scaling above the transition, while for Ra < 10(10), the Re. Ra/dependencies are steeper.
It seems likely that this change in Re. Ra/scaling is linked to the previously reported change in the Nusselt number Nu.
Ra/scaling. This behaviour is in agreement with independent cryogenic laboratory experiments with Pr similar to 1, but markedly different from the Re scaling obtained in water experiments (Pr similar to 3: 3-5: 6).
We discuss the results in comparison with different versions of the Grossmann-Lohse theory.