Ultimate turbulent Taylor-Couette flow.

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 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(ω)∝Ta(0.38), also in correspondence with turbulence in the ultimate regime. The scaling of Nu(ω) 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.