Torque scaling in turbulent Taylor-Couette flow with co- and counterrotating cylinders

• Published in: Physical review letters 2011-01, Vol.106 (2), p.024502-024502, Article 024502
• Main Authors: van Gils, Dennis P M, Huisman, Sander G, Bruggert, Gert-Wim, Sun, Chao, Lohse, Detlef
• Format: Article
• Language: English
• ISSN: 0031-9007; 1079-7114
• DOI: 10.1103/PhysRevLett.106.024502

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 Re(i) = 2×10(6) and Re(o) = ±1.4×10(6), respectively. For all Re(i), Re(o), 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 ∝ Ta(0.88), corresponding to Nu(ω) ∝ Ta(0.38) 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 ω(o) ≈ -0.4ω(i).