# High Reynolds number Taylor-Couette turbulence

## TL;DR

This review summarizes recent advances in understanding fully developed Taylor-Couette turbulence, focusing on torque behavior, flow structures, transitions, and astrophysical relevance, highlighting progress in experiments, simulations, and theory since the 2000s.

## Contribution

It provides a comprehensive overview of recent experimental, numerical, and theoretical insights into high Reynolds number Taylor-Couette turbulence, emphasizing parameter dependence and flow transitions.

## Key findings

- Global torque varies with Reynolds numbers and geometry.
- Flow organization includes velocity profiles and boundary layers.
- Transitions between turbulent flow states are characterized.

## Abstract

Taylor-Couette flow -- the flow between two coaxial co- or counter-rotating cylinders -- is one of the paradigmatic systems in physics of fluids. The (dimensionless) control parameters are the Reynolds numbers of the inner and outer cylinder, the ratio of the cylinder radii, and the aspect ratio. The response of the system is the torque required to retain constant angular velocities, which can be connected to the angular velocity transport through the gap. While the low Reynolds number regime has been very well explored in the '80s and '90s of the last century, in the fully turbulent regime major research activity only developed in the last decade. In this paper we review this recent progress in our understanding of fully developed Taylor-Couette turbulence, from the experimental, numerical, and theoretical point of view. We will focus on the parameter dependence of the global torque and on the local flow organisation, including velocity profiles and boundary layers. Next, we will discuss transitions between different (turbulent) flow states. We will also elaborate on the relevance of this system for astrophysical disks (Keplerian flows). The review ends with a list of challenges for future research on turbulent Taylor-Couette flow. The published version in ARFM: Annu. Rev. Fluid Mech. 48:53-80 (2016).