Towards boiling Taylor-Couette turbulence

Abstract

We provide experimental measurements for the effective scaling of the Taylor-Reynolds number within the bulk Re λ,bulk , 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. The data are obtained through flow velocity field measurements using Particle Image Velocimetry (PIV). We estimate the value of the local dissipation rate ϵ(r) using the scaling of the second order velocity structure functions in the longitudinal and transverse direction within the inertial range-without invoking Taylor's hypothesis. We find an effective scaling of ϵ bulk /(ν 3 d −4) ∼ Ta 1.40 , (corresponding to Nu ω,bulk ∼ Ta 0.40 for the dimensionless local angular velocity transfer), which is nearly the same as for the global energy dissipation rate obtained from both torque measurements (Nu ω ∼ Ta 0.40) and Direct Numerical Simulations (Nu ω ∼ Ta 0.38). The resulting Kolmogorov length scale is then found to scale as η bulk /d ∼ Ta −0.35 and the turbulence intensity as I θ,bulk ∼ 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 Re λ,bulk ∼ Ta 0.18 in the present parameter regime of 4.0 × 10 8 < Ta < 9.0 × 10 10 .