Turbulent Rayleigh–Bénard convection in a cylindrical container with aspect ratio Γ = 0.50 and Prandtl number Pr = 4.38

Measurements of the Nusselt number and properties of the large-scale circulation (LSC) are presented for turbulent Rayleigh–Bénard convection in water-filled cylindrical containers (Prandtl number Pr = 4.38) with aspect ratio Γ = 0.50. They cover the range 2 × 10 8 ≲ Ra ≲ 1 × 10 11 of the Rayleigh number Ra . We confirm the occurrence of a double-roll state (DRS) of the LSC and focus on the statistics of the transitions between the DRS and a single-roll state (SRS). The fraction of the run time when the SRS existed varied continuously from about 0.12 near Ra = 2 × 10 8 to about 0.8 near Ra = 10 11 , while the fraction of the run time when the DRS could be detected changed from about 0.4 to about 0.06 over the same range of Ra . We determined separately the Nusselt number of the SRS and the DRS, and found the former to be larger than the latter by about 1.6% (0.9%) at Ra = 10 10 (10 11 ). We report a contribution to the dynamics of the SRS from a torsional oscillation similar to that observed for cylindrical samples with Γ = 1.00. Results for a number of statistical properties of the SRS are reported, and some are compared with the cases Γ = 0.50, Pr = 0.67 and Γ = 1.00, Pr = 4.38. We found that genuine cessations of the SRS were extremely rare and occurred only about 0.3 times per day, which is less frequent than for Γ = 1.00; however, the SRS was disrupted frequently by roll-state transitions and other less well-defined events. We show that the time derivative of the LSC plane orientation is a stochastic variable which, at constant LSC amplitude, is Gaussian distributed. Within the context of the LSC model of Brown & Ahlers ( Phys. Fluids , vol. 20, 2008 b , art. 075101), this demonstrates that the stochastic force due to the small-scale fluctuations that is driving the LSC dynamics has a Gaussian distribution.