Transition to shear-driven turbulence in Couette-Taylor flow

Daniel P. Lathrop, Jay Fineberg, and Harry L. Swinney

Center for Nonlinear Dynamics, University of Texas, Austin, Texas 78712

Department of Physics, University of Texas, Austin, Texas 78712

Received 27 March 1992

Turbulent flow between concentric cylinders is studied in experiments for Reynolds numbers 800<R<1.23×106 for a system with radius ratio η=0.7246. Despite predictions for the torque scaling as a power law of the Reynolds number, high-precision torque measurements reveal no Reynolds-number range with a fixed power law. A well-defined nonhysteretic transition at R=1.3×104 is marked by a change in the Reynolds-number dependence of the torque. Flow quantities such as the axial turbulent diffusivity, the time scales asociated with the fluctuations of the wall shear stress, and the root-mean-square fluctuations of the wall shear stress and its time derivative are all shown to be simply related to the global torque measurements. Above the transition, the torque measurements and observed time scales indicate a close correspondence between this closed-flow system and open-wall–bounded-shear flows such as pipe flow, duct flow, and flow over a flat plate.