Momentum transport in Taylor-Couette flow with vanishing curvature

TL;DR

This study numerically investigates the transition from turbulent Taylor-Couette flow to rotating plane Couette flow as the radii tend to infinity, revealing common turbulent behaviors and new torque maxima at high radius ratios.

Contribution

It provides a continuous analysis of the TCF to RPCF transition at high radius ratios, identifying new torque maxima and their origins, and linking boundary layer dynamics to flow stability.

Findings

Flow results collapse for radius ratios ≥ 0.9, indicating common turbulence characteristics.

Disappearance of intermittent bursts and torque maximum as radius ratio approaches 1.

Emergence of two new torque maxima at high radius ratios, linked to flow structures.

Abstract

We numerically study turbulent Taylor-Couette flow (TCF) between two independently rotating cylinders and the transition to rotating plane Couette flow (RPCF) in the limit of infinite radii. By using the shear Reynolds number $Re_S$ and rotation number $R_\Omega$ as dimensionless parameters, the transition from TCF to RPCF can be studied continuously without singularities. Already for radius ratios $\eta\geq0.9$ we find that the simulation results for various radius ratios and for RPCF collapse as a function of $R_\Omega$, indicating a turbulent behaviour common to both systems. We observe this agreement in the torque, mean momentum transport, mean profiles, and turbulent fluctuations. Moreover, the central profiles in TCF and RPCF for $R_\Omega>0$ are found to conform with inviscid neutral stability. Intermittent bursts that have been observed in the outer boundary layer and have been linked to the formation of a torque maximum for counter-rotation are shown to disappear as $\eta \rightarrow 1$. The corresponding torque maximum disappears as well. Instead, two new maxima of different origin appear for $\eta\geq0.9$ and RPCF, a broad and a narrow one, in contrast to the results for smaller $\eta$. The broad maximum at $R_\Omega=0.2$ is connected with a strong vortical flow and can be reproduced by streamwise invariant simulations. The narrow maximum at $R_\Omega=0.02$ only emerges with increasing $Re_S$ and is accompanied by an efficient and correlated momentum transport by the mean flow. Since the narrow maximum is of larger amplitude for $Re_S=2\cdot10^4$, our simulations suggest that it will dominate at even higher $Re_S$.