A homoclinic tangle on the edge of shear turbulence

TL;DR

This paper demonstrates the existence of a flow homoclinic to a time-periodic edge state, providing a new explanation for turbulent bursting in shear flows through the classical Smale-Birkhoff theorem.

Contribution

It introduces a flow homoclinic to a time-periodic edge state, linking edge states to turbulent bursts and advancing understanding of subcritical transition to turbulence.

Findings

Existence of a flow homoclinic to a time-periodic edge state

Turbulent bursting explained via Smale-Birkhoff theorem

Localized vortical structures during bursts

Abstract

Experiments and simulations lend mounting evidence for the edge state hypothesis on subcritical transition to turbulence, which asserts that simple states of fluid motion mediate between laminar and turbulent shear flow as their stable manifolds separate the two in state space. In this Letter we describe a flow homoclinic to a time-periodic edge state. Its existence explains turbulent bursting through the classical Smale-Birkhoff theorem. During a burst, vortical structures and the associated energy dissipation are highly localized near the wall, in contrast to the familiar regeneration cycle.