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

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

2010-10-05

arxiv.org/abs/1010.0922v2

Phys. Rev. Lett. 106, 024502 (2011)

Physics

Fluid Dynamics

3 pages, 4 figures

Scientific paper

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 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.

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