Turbulence strength in ultimate Taylor–Couette turbulence

We provide experimental measurements for the effective scaling of the Taylor–Reynolds number within the bulk (Formula presented.), based on local flow quantities as a function of the driving strength (expressed as the Taylor number (Formula presented.)), in the ultimate regime of Taylor–Couette flow. We define (Formula presented.), where (Formula presented.) is the bulk-averaged standard deviation of the azimuthal velocity, (Formula presented.) is the bulk-averaged local dissipation rate and (Formula presented.) 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 (Formula presented.) 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 (Formula presented.), (corresponding to (Formula presented.) for the dimensionless local angular velocity transfer), which is nearly the same as for the global energy dissipation rate obtained from both torque measurements ((Formula presented.)) and direct numerical simulations ((Formula presented.)). The resulting Kolmogorov length scale is then found to scale as (Formula presented.) and the turbulence intensity as (Formula presented.). With both the local dissipation rate and the local fluctuations available we finally find that the Taylor–Reynolds number effectively scales as (Formula presented.) in the present parameter regime of (Formula presented.).