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

• Published in: arXiv.org 2011-02
• Main Authors: Dennis P M van Gils, Huisman, Sander G, Gert-Wim Bruggert, Sun, Chao, Lohse, Detlef
• Format: Article
• Language: English
• Subjects: Angular velocity; Couette flow; Cylinders; Fluid dynamics; Fluid flow; Rotating cylinders; Scaling laws; Torque; Transport properties; Turbulent flow
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1010.0922

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 x 10^6 and Re_o = 1.4 x 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 \propto Ta^{0.88}, corresponding to Nu_omega \propto 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-Benard system. The transport is most efficient for the counterrotating case along the diagonal in phase space with omega_o \approx -0.4 omega_i.