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

TL;DR

This study investigates the torque scaling in highly turbulent Taylor-Couette flow with independently rotating cylinders, revealing a universal scaling law and optimal transport conditions in the counterrotating regime.

Contribution

It provides the first comprehensive analysis of torque scaling laws in turbulent Taylor-Couette flow at very high Reynolds numbers with independent cylinder rotation.

Findings

Torque G scales as Ta^{0.88} across all Re_i, Re_o.

Nusselt number Nu_omega scales as Ta^{0.38}, indicating ultimate regime behavior.

Maximum transport efficiency occurs in counterrotation near omega_o ≈ -0.4 omega_i.

Abstract

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.