Stability and turbulent transport in rotating shear flows: prescription from analysis of cylindrical and plane Couette flows data

摘要

This paper provides a prescription for the turbulent viscosity in rotatingshear flows for use e.g. in geophysical and astrophysical contexts. Thisprescription is the result of the detailed analysis of the experimental dataobtained in several studies of the transition to turbulence and turbulenttransport in Taylor-Couette flow. We first introduce a new set of controlparameters, based on dynamical rather than geometrical considerations, so thatthe analysis applies more naturally to rotating shear flows in general and notonly to Taylor-Couette flow. We then investigate the transition thresholds inthe supercritical and the subcritical regime in order to extract their generaldependencies on the control parameters. The inspection of the mean profilesprovides us with some general hints on the mean to laminar shear ratio. Thenthe examination of the torque data allows us to propose a decomposition of thetorque dependence on the control parameters in two terms, one completely givenby measurements in the case where the outer cylinder is at rest, the other onebeing a universal function provided here from experimental fits. As a result,we obtain a general expression for the turbulent viscosity and compare it toexisting prescription in the literature. Finally, throughout all the paper wediscuss the influence of additional effects such as stratification or magneticfields.