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

Recent studies [Lathrop , Phys. Rev. A 46, 6390 (1992); Lewis , 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 , Phys. Rev. Lett. 65, 2780 (1990)], the non-dimensional torque (G=T/rhonu(2)L) does not follow a fixed power-law scaling (i.e., Gsimilar toRe(alpha), where alpha is a constant value) for 800<Re<1.23x10(6). 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 alpha varies with the Reynolds number, it can be approximated reasonably well with a constant value alpha=1 for Re/Re-c<1 and alpha=1.5 for 1.5<Re/Re-c<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. (C) 2004 American Institute of Physics.