Self-Replication of Turbulent Puffs: On the edge between chaotic saddles

TL;DR

This paper investigates the self-replication mechanism of turbulent puffs in pipe flow, identifying an edge state that mediates the transition from one to two puffs, enhancing understanding of turbulence sustenance.

Contribution

It reveals the role of an edge state in the self-replication process of turbulent puffs, confirming a proposed mechanism through direct numerical simulations.

Findings

Identified an edge state mediating puff self-replication

Demonstrated the transition mechanism from one to two puffs

Confirmed the theoretical mechanism with numerical evidence

Abstract

Pipe flow is a canonical example where turbulence first appears intermittently in space and time, taking the form of localized structures termed puffs. Turbulence spreads via puff self-replication, which must out-compete puff decays to sustain it. Here we study the self-replication process, a transition from one to two puffs, using direct numerical simulations. We identify an edge state on the phase space boundary between the two states, demonstrate that it mediates the transition, and show that self-replication follows a previously proposed mechanism, with the edge state as its tipping point.