Ultimate Turbulent Taylor-Couette Flow

TL;DR

This study experimentally investigates highly turbulent Taylor-Couette flow at very high Reynolds numbers, confirming theoretical predictions about turbulence scaling laws and boundary layer behavior in the ultimate turbulence regime.

Contribution

It provides experimental evidence for turbulence scaling laws in the ultimate regime of Taylor-Couette flow using high-speed PIV at unprecedented Reynolds numbers.

Findings

Re_w scales as Ta^{1/2}, matching predictions for ultimate turbulence.

Nu_ω scales as Ta^{0.38}, consistent with ultimate turbulence theory.

Local flux measurements agree with global torque results despite fluctuations.

Abstract

The flow structure of strongly turbulent Taylor-Couette flow with Reynolds numbers up to Re_i = 2*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 for the ultimate turbulence regime, in which the boundary layers are turbulent. The dimensionless angular velocity flux has an effective scaling of Nu_{\omega} ~ Ta^0.38, also in correspondence with turbulence in the ultimate regime. The scaling of Nu_{\omega} 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.