# Laminar-turbulent coexistence in annular Couette flow

## TL;DR

This study uses direct numerical simulations to explore laminar-turbulent coexistence in annular Couette flow, revealing different regimes based on radius ratio and highlighting localized turbulence with short-range fluctuations.

## Contribution

It identifies and characterizes three distinct flow regimes in annular Couette flow, including a novel localized turbulence regime at low radius ratios, and discusses implications for phase transition.

## Key findings

- High-radius ratio regime shows helical turbulent patches coexisting with laminar flow.
- Moderate-radius ratio regime lacks clear laminar-turbulent coexistence.
- Low-radius ratio regime exhibits localized turbulence with short-range fluctuations.

## Abstract

Annular Couette flow is the flow between two coaxial cylinders driven by the axial translation of the inner cylinder. It is investigated using direct numerical simulation in long domains, with an emphasis on the laminar-turbulent coexistence regime found for marginally low values of the Reynolds number. Three distinct flow regimes are demonstrated as the radius ratio $\eta$ is decreased from 0.8 to 0.5 and finally to 0.1. The high-$\eta$ regime features helically-shaped turbulent patches coexisting with laminar flow, as in planar shear flows. The moderate-$\eta$ regime does not feature any marked laminar-turbulent coexistence. In an effort to discard confinement effects, proper patterning is however recovered by artificially extending the azimuthal span beyond 2$\pi$. Eventually, the low-$\eta$ regime features localised turbulent structures different from the puffs commonly encountered in transitional pipe flow. In this new coexistence regime, turbulent fluctuations are surprisingly short-ranged. Implications are discussed in terms of phase transition and critical scaling.