Turbulence strength in ultimate Taylor-Couette turbulence

Abstract

We provide experimental measurements for the effective scaling of the Taylor-Reynolds number within the bulk ReQλbulk, based on local flow quantities as a function of the driving strength (expressed as the Taylor number Ta), in the ultimate regime of Taylor-Couette flow. We define Reλbulk =Qbulk(μθ))2(15/vϵbulk)1/2, where bulk.u/is the bulk-averaged standard deviation of the azimuthal velocity,bulk is the bulk-averaged local dissipation rate and is the liquid kinematic viscosity. The data are obtained through flow velocity field measurements using particle image velocimetry. We estimate the value of the local dissipation rate.r/using the scaling of the second-order velocity structure functions in the longitudinal and transverse directions within the inertial range-without invoking Taylor's hypothesis. We find an effective scaling of ϵbulk/(v3d-4∼Ta1.40, (corresponding to Nuωbulk ∼Ta0:40 for the dimensionless local angular velocity transfer), which is nearly the same as for the global energy dissipation rate obtained from both torque measurements (Nuω ∼Ta0.40) and direct numerical simulations (Nuω∼ Ta0.38). The resulting Kolmogorov length scale is then found to scale as Iθbulk=dTa.0:35 and the turbulence intensity as Ibulk ∼Ta-0.061. With both the local dissipation rate and the local fluctuations available we finally find that the Taylor-Reynolds number effectively scales as ReLemda;bulk ∼ Ta0.18 in the the present parameter regime of 0× 108