Studying edge geometry in transiently turbulent shear flows

TL;DR

This paper investigates the edge of chaos in shear flows, revealing it is not a global separator but wrapped around turbulence structures, affecting decay paths in transitional turbulence.

Contribution

It provides a detailed statistical analysis of decay paths in shear flows and demonstrates the edge of chaos is part of the chaotic saddle, not a separate global boundary.

Findings

The edge of chaos is wrapped around turbulence structures.

Decaying trajectories can circumnavigate the edge without crossing it.

The edge of chaos is part of the chaotic saddle, not a global separator.

Abstract

In linearly stable shear flows at moderate Re, turbulence spontaneously decays despite the existence of a codimension-one manifold, termed the edge of chaos, which separates decaying perturbations from those triggering turbulence. We statistically analyse the decay in plane Couette flow, quantify the breaking of self-sustaining feedback loops and demonstrate the existence of a whole continuum of possible decay paths. Drawing parallels with low-dimensional models and monitoring the location of the edge relative to decaying trajectories we provide evidence, that the edge of chaos separates state space not globally. It is instead wrapped around the turbulence generating structures and not an independent dynamical structure but part of the chaotic saddle. Thereby, decaying trajectories need not cross the edge, but circumnavigate it while unwrapping from the turbulent saddle.