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 Nu_ω∝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-B\'enard system. The transport is most efficient for the counterrotating case along the diagonal in phase space with ωₒ≈-0.4ωᵢ.