A note on power-law scaling in a Taylor–Couette flow

Recent studies [Lathrop et al., Phys. Rev. A 46, 6390 (1992); Lewis et al., Phys. Rev. E 59, 5457 (1999)] on Taylor–Couette flow, where the inner cylinder is rotating and the outer one is at rest, show that, despite earlier predictions [Wendt, Ing. Arch. 4, 557 (1933); Tong et al., Phys. Rev. Lett. 65, 2780 (1990)], the non-dimensional torque (G=T/ρν2L) does not follow a fixed power-law scaling (i.e., G∼Reα, where α is a constant value) for 800<Re<1.23×106. Here, we perform simultaneous flow visualization and high precision torque measurements of the same flow configuration using a Haake RS-75 Rheometer to establish if this is also true in the lower Reynolds number range (Re<800). Results show that, although α varies with the Reynolds number, it can be approximated reasonably well with a constant value α=1 for Re/Rec<1 and α=1.5 for 1.5<Re/Rec<6.32. The latter finding is in good agreement with that of Wendt [Ing. Arch. 4, 557 (1933)]. A possible explanation for the differences with the results of earlier studies is provided in this paper.