# Heteroclinic path to spatially localized chaos in pipe flow

## TL;DR

This paper uncovers a heteroclinic connection between localized solutions in pipe flow, revealing a dynamical mechanism for puff generation and advancing understanding of turbulence transition.

## Contribution

It introduces a novel combination of symmetry reduction and Poincaré sections to analyze heteroclinic connections in shear flows, linking localized solutions to turbulence phenomena.

## Key findings

- Uncovered heteroclinic connection between localized solutions
- Connection persists above bifurcation point, influencing puff formation
- Provides a dynamical explanation for localized turbulence in pipe flow

## Abstract

In shear flows at transitional Reynolds numbers, localized patches of turbulence, known as puffs, coexist with the laminar flow. Recently, Avila et al., Phys. Rev. Let. 110, 224502 (2013) discovered two spatially localized relative periodic solutions for pipe flow, which appeared in a saddle-node bifurcation at low speeds. Combining slicing methods for continuous symmetry reduction with Poincar\'e sections for the first time in a shear flow setting, we compute and visualize the unstable manifold of the lower-branch solution and show that it contains a heteroclinic connection to the upper branch solution. Surprisingly this connection even persists far above the bifurcation point and appears to mediate puff generation, providing a dynamical understanding of this phenomenon.