Torque Scaling in Turbulent Taylor-Couette Flow with Co- and Counterrotating Cylinders

We analyze the global transport properties of turbulent Taylor-Couette flow in the strongly turbulent regime for independently rotating outer and inner cylinders, reaching Reynolds numbers of the inner and outer cylinders of Rei=2×106 and Reo=±1.4×106, respectively. For all Rei, Reo, the dimensionless torque G scales as a function of the Taylor number Ta (which is proportional to the square of the difference between the angular velocities of the inner and outer cylinders) with a universal effective scaling law G∝Ta0.88, corresponding to Nuω∝Ta0.38 for the Nusselt number characterizing the angular velocity transport between the inner and outer cylinders. The exponent 0.38 corresponds to the ultimate regime scaling for the analogous Rayleigh-Bénard system. The transport is most efficient for the counterrotating case along the diagonal in phase space with ωo≈-0.4ωi.