How does flow in a pipe become turbulent?

TL;DR

This paper investigates the complex transition to turbulence in pipe flow, highlighting the role of transient structures, stable manifolds, and the sensitive dependence on initial conditions, which differ from classical transition scenarios.

Contribution

It reveals that pipe flow turbulence is supported by transient three-dimensional waves and is governed by the stable manifold of an invariant chaotic state, differing from classical linear stability.

Findings

Turbulence in pipe flow can decay spontaneously without external triggers.

Transient three-dimensional travelling waves are key to turbulence sustenance.

The boundary between laminar and turbulent states is shaped by a stable manifold of a chaotic attractor.

Abstract

The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when the flow speed is high enough and the perturbation sufficiently strong such that turbulent flow is established, it can return to the laminar state without any indication of the imminent decay. In this parameter range, the lifetimes of perturbations show a sensitive dependence on initial conditions and an exponential distribution. The turbulence seems to be supported by three-dimensional travelling waves which appear transiently in the flow field. The boundary between laminar and turbulent dynamics is formed by the stable manifold of an invariant chaotic state. We will also discuss the relation between observations in short, periodically continued domains, and the dynamics in fully extended puffs.