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

Abstract

This paper provides a prescription for the turbulent viscosity in rotating shear flows for use e.g. in geophysical and astrophysical contexts. This prescription is the result of the 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 the analysis applies more naturally to 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 mean 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 given by measurements in the case where the outer cylinder is at rest, the other one being a universal function provided here from experimental fits. As a result, we obtain a general expression for the turbulent viscosity and compare it to existing prescription in the literature. Finally, throughout all the paper we discuss the influence of additional effects such as stratification or magnetic fields.

Angular momentum transport and turbulence in laboratory models of Keplerian flows

“…To further study the scaling of angular momentum transport in rotating shear flows, we compare our measurements to those of Wendt (1933), Taylor (1936) and Richard (2001), Dubrulle et al (2005). We find a universal scaling of the torque for various rotation profiles that captures the effects of the various geometries used in the experiments summarized here.…”

Compressible Taylor–Couette flow – instability mechanism and codimension 3 points

“…Similarities between astrophysical disks and fluid flows bounded by concentric differentially rotating cylinders have motivated a number of theoretical and experimental studies of hydrodynamic and magnetohydrodynamic Taylor-Couette flows (see, e.g. Goodman & Ji 2002;Dubrulle et al 2005;Hersant, Dubrulle & Huré 2005;Stefani et al 2006). One problem of considerable interest is, for instance, the controversial question of subcritical hydrodynamic turbulence in Keplerian-like Taylor-Couette flows.…”

Experimental Analysis of the Stratorotational Instability in a Cylindrical Couette Flow

“…Most of these studies were performed with a stationary outer cylinder and all concluded that stable vertical stratification stabilizes the flow and reduces the axial wavelength of the unstable modes which bifurcate through Hopf bifurcations. In astrophysics, Keplerian flows whose angular velocity is Ω(r) ∼ r −3/2 , are always stable to infinitely small perturbations in respect to the Rayleigh criterion [8]. As a consequence of this stability, several scenarios have been recently proposed to justify the existence of turbulence in accretion disk flows.…”

“…Ingredients other than pure shear then need to be taken into account in order to trigger instabilities and transition to turbulence in these flows. One of the most popular scenarios relies on the MagnetoRotational Instability [9] but other instabilities such as the elliptical instability [10] or non linear shear instabilities [8] have also been suggested. In 2001, Molemaker et al [11] and Yavneh et al [12] predicted that cylindrical Couette flows in a stratified fluid may become unstable even if the Rayleigh criterion for stability was verified, i.e.…”