Angular momentum transport and flow organisation in Taylor-Couette flow at radius ratio of $\eta =0.357$

Abstract

We experimentally and numerically investigate the angular momentum transport in turbulent Taylor-Couette flow for independently rotating cylinders at a small radius ratio of $\eta =0.357$ for various shear Reynolds numbers ($4.5\times 10^3\le R{e}_S\le 1.2\times 10^5$) and ratios of angular velocities ($-0.5\le \mu \le 0.2$). \red{The momentum transport in terms of the pseudo-Nusselt number ${Nu}_{\omega }$ does not show a pure power law scaling with the forcing $R{e}_S$ and features non-constant effective scaling between $1.3\times 10^4\le R{e}_S\le 4\times 10^4$. This transition lies in the classical turbulent regime and is caused by the curvature-dependent limited capacity of the outer cylinder to emit small-scale plumes at a sufficient rate to equalize the angular momentum in the bulk.} For counter-rotating cylinders, a maximum in the torque occurs at ${\mu }_{\max }=-0.123\pm 0.030$. The origin of this maximum can be attributed to a strengthening of turbulent Taylor vortices, which is revealed by the flow visualization technique. In addition, different flow states at ${\mu }_{\max }$ concerning the wavelength of the large-scale vortices have been detected. The experimental and numerical results for the Nusselt number show a very good agreement.