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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 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.