We present measurements of the angular momentum flux (torque) in Taylor-Couette flow of water between independently rotating cylinders for all regions of the (Ω1, Ω2) parameter space at high Reynolds numbers, where Ω1 (Ω2) is the inner (outer) cylinder angular velocity. We find that the Rossby number Ro = (Ω1 - Ω2)/Ω2 fully determines the state and torque G as compared to G(Ro = ∞) ≡ G∞. The ratio G/G∞ is a linear function of Ro(-1) in four sections of the parameter space. For flows with radially increasing angular momentum, our measured torques greatly exceed those of previous experiments [Ji et al., Nature (London), 444, 343 (2006)], but agree with the analysis of Richard and Zahn [Astron. Astrophys. 347, 734 (1999)].
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