Directed percolation describes lifetime and growth of turbulent puffs and slugs

TL;DR

This paper demonstrates that Directed Percolation simulations in a 3+1D pipe geometry accurately model the complex transition to turbulence, including puff formation, relaminarization, and slug expansion, with quantitative agreement to experiments.

Contribution

It introduces a DP-based model that captures the full phenomenology of turbulence transition in pipes, providing a unified theoretical framework.

Findings

DP simulations reproduce puff and slug behaviors.

Characteristic lifetime diverges superexponentially below transition.

Active clusters expand with velocity scaling consistent with experiments.

Abstract

We show that Directed Percolation (DP) simulations in a pipe geometry in 3+1 dimensions fully capture the observed complex phenomenology of the transition to turbulence. At low Reynolds numbers (Re), turbulent puffs form and spontaneously relaminarize. At high Re, turbulent slugs expand uniformly into the laminar regions. In a spatiotemporally intermittent state between these two regimes of Re, puffs split and turbulent regions exhibit laminar patches. DP also captures the main quantitative features of the transition, with a superexponentially diverging characteristic lifetime below the transition. Above the percolation threshold, active (turbulent) clusters expand into the inactive (laminar) phase with a well-defined velocity whose scaling with control parameter (Reynolds number or percolation probability) is consistent with experimental results. Our results provide strong evidence in favor of a conjecture of Pomeau.