Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data

This paper provides discussion and prescription about stability and transport in the Taylor–Couette experiment, a rotating shear flow with shear perpendicular to the rotation axis. Such geometry frequently occurs in geophysical or astrophysical context. The prescriptions we obtain are the result of a detailed analysis of the experimental data obtained in several studies of the transition to turbulence and turbulent transport in Taylor–Couette flow. We first introduce a new set of control parameters, based on dynamical rather than geometrical considerations, so that they may be relevant to any rotating shear flows in general and not only to Taylor–Couette flow. We then investigate the transition thresholds in the supercritical and the subcritical regime in order to extract their general dependencies on the control parameters. The inspection of the mean profiles provides us with some general hints on the turbulent to laminar shear ratio. Then the examination of the torque data allows us to propose a decomposition of the torque dependence on the control parameters in two terms, one completely determined by measurements in the case where the outer cylinder is at rest, the other one being a universal function deduced here from experimental fits. As a result, we obtain a general expression for the turbulent viscosity and compare it to existing prescriptions in the literature. Finally, throughout the paper we discuss the influence of additional effects such as stratification or magnetic fields.