Simplifying the complexity of pipe flow

TL;DR

This paper models transitional pipe flow as a one-dimensional excitable and bistable medium, capturing key phenomena like puff-slug transition, puff splitting, and turbulence onset through continuous and discrete models.

Contribution

It introduces novel simplified models that replicate large-scale features of transitional pipe flow, including metastable puffs and the transition to sustained turbulence.

Findings

Models reproduce puff-slug transition and metastable puffs

Discrete model captures turbulence spreading and intermittency

Transition to turbulence aligns with directed percolation theory

Abstract

Transitional pipe flow is modeled as a one-dimensional excitable and bistable medium. Models are presented in two variables, turbulence intensity and mean shear, that evolve according to established properties of transitional turbulence. A continuous model captures the essence of the puff-slug transition as a change from excitability to bistability. A discrete model, that additionally incorporates turbulence locally as a chaotic repeller, reproduces almost all large-scale features of transitional pipe flow. In particular it captures metastable localized puffs, puff splitting, slugs, a continuous transition to sustained turbulence via spatiotemporal intermittency (directed percolation), and a subsequent increase in turbulence fraction towards uniform, featureless turbulence.