Measurement of angular momentum transport in turbulent flow between independently rotating cylinders

TL;DR

This study measures angular momentum transport in turbulent Taylor-Couette flow with independently rotating cylinders, revealing the Rossby number's role in determining torque and confirming theoretical predictions.

Contribution

The paper provides comprehensive torque measurements across all rotation regimes at high Reynolds numbers, establishing the Rossby number as a key parameter and comparing results with previous experiments and theories.

Findings

Torque ratio G/Gi depends linearly on inverse Rossby number

Radially-increasing angular momentum flows have higher torque than previous experiments

Results align with Richard and Zahn's theoretical analysis

Abstract

We present measurements of the angular momentum flux (torque) in Taylor-Couette flow of water between independently rotating cylinders for all regions of the $\(\Omega_1, \Omega_2\)$ parameter space at high Reynolds numbers, where $\Omega_1$ $\(\Omega_2\)$ is the inner (outer) cylinder angular velocity. We find that the Rossby number $Ro = \(\Omega_1 - \Omega_2\)/\Omega_2$ fully determines the state and torque $G$ as compared to $G(Ro = \infty) \equiv \Gi$. The ratio $G/\Gi$ 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 \textit{et al.}, Nature, \textbf{444}, 343 (2006)], but agree with the analysis of Richard and Zahn [Astron. Astrophys., \textbf{347}, 734 (1999)].