Three States of Counter--Rotating Turbulent Taylor--Couette Flow

Physics of Fluids, 2010

We experimentally study the turbulent flow between two coaxial and independently rotating cylinders. We determined the scaling of the torque with Reynolds numbers at various angular velocity ratios (Rotation numbers), and the behaviour of the wall shear stress when varying the Rotation number at high Reynolds numbers. We compare the curves with PIV analysis of the mean flow and show the peculiar role of perfect counterrotation for the emergence of organised large scale structures in the mean part of this very turbulent flow that appear in a smooth and continuous way: the transition resembles a supercritical bifurcation of the secondary mean flow.

Journal of Fluid Mechanics, 2007

We analyze the global transport properties of turbulent Taylor-Couette flow in the strongly turbulent regime for independently rotating outer and inner cylinders, reaching Reynolds numbers of the inner and outer cylinders of Rei = 2 × 10 6 and Reo = ±1.4 × 10 6 , respectively. For all Rei, Reo, the dimensionless torque G scales as a function of the Taylor number Ta (which is proportional to the square of the difference between the angular velocities of the inner and outer cylinders) with a universal effective scaling law G ∝ Ta 0.88 , corresponding to Nuω ∝ Ta 0.38 for the Nusselt number characterizing the angular velocity transport between the inner to the outer cylinders. The exponent 0.38 corresponds to the ultimate regime scaling for the analogous Rayleigh-Bénard system. The transport is most efficient for the counterrotating case along the diagonal in phase space with ωo ≈ −0.4ωi.

Journal of Fluid Mechanics, 2014

Torque measurements in Taylor-Couette flow, with large radius ratio and large aspect ratio, over a range of velocities up to a Reynolds number of 24 000 are presented. Following a specific procedure, nine states with distinct number of vortices along the axis were found and the aspect ratio of the vortices were measured. The relationship between the speed and the torque for a given number of vortices is reported. In the turbulent Taylor vortex flow regime, at relatively high Reynolds number, a change in behaviour is observed corresponding to intersections of the torque-speed curves for different states. Before each intersection, the torque for a state with larger number of vortices is higher. After each intersection, the torque for a state with larger number of vortices is lower. The exponent, from the scaling laws of the torque, always depends on the aspect ratio of the vortices. When the Reynolds number is rescaled using the mean aspect ratio of the vortices, only a partial collapse of the exponent data is found. †

Journal of Fluid Mechanics, 2014

Direct numerical simulations of Taylor–Couette flow, i.e. the flow between two coaxial and independently rotating cylinders, were performed. Shear Reynolds numbers of up to $3\times 10^{5}$, corresponding to Taylor numbers of $\mathit{Ta}=4.6\times 10^{10}$, were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws (with logarithmic corrections) for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios, different aspect ratios and different rotation ratios. It is shown that the transition is approximately independent of the aspect and rotation ratios, but depends significantly on the radius ratio. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the...

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.

Physical Review Letters, 2012

The flow structure of strongly turbulent Taylor-Couette flow with Reynolds numbers up to Re i ¼ 2 Â 10 6 of the inner cylinder is experimentally examined with high-speed particle image velocimetry (PIV). The wind Reynolds numbers Re w of the turbulent Taylor-vortex flow is found to scale as Re w / Ta 1=2 , exactly as predicted by Grossmann and Lohse [Phys. Fluids 23, 045108 (2011).] for the ultimate turbulence regime, in which the boundary layers are turbulent. The dimensionless angular velocity flux has an effective scaling of Nu ! / Ta 0:38 , also in correspondence with turbulence in the ultimate regime. The scaling of Nu ! is confirmed by local angular velocity flux measurements extracted from high-speed PIV measurements: though the flux shows huge fluctuations, its spatial and temporal average nicely agrees with the result from the global torque measurements.