Geometry of transient chaos in streamwise-localized pipe flow turbulence

TL;DR

This paper investigates the geometric structure of transient chaos in localized pipe flow turbulence, revealing how homoclinic tangles and fractal boundaries influence the transition to sustained turbulence.

Contribution

It uncovers the state space structure involving homoclinic orbits and fractal boundaries that underlie transient chaos in localized pipe flow turbulence.

Findings

Identification of transverse homoclinic orbits and tangles

Demonstration of fractal laminar-turbulent boundaries

Mapping of gateways facilitating turbulence escape

Abstract

In pipes and channels, the onset of turbulence is initially dominated by localized transients, which lead to sustained turbulence through their collective dynamics. In the present work, we study the localized turbulence in pipe flow numerically and elucidate a state space structure that gives rise to transient chaos. Starting from the basin boundary separating laminar and turbulent flow, we identify transverse homoclinic orbits, the presence of which necessitates a homoclinic tangle and chaos. A direct consequence of the homoclinic tangle is the fractal nature of the laminar-turbulent boundary, which was conjectured in various earlier studies. By mapping the transverse intersections between the stable and unstable manifold of a periodic orbit, we identify the 'gateways' that promote an escape from turbulence.