# Quantifying the role of folding in nonautonomous flows: the unsteady Double-Gyre

## TL;DR

This paper investigates the role of folding in chaos within the nonautonomous Double-Gyre flow, introducing a novel approach to identify chaos through manifold curvature and folding analysis.

## Contribution

It demonstrates how folding can be used to prove chaos in nonautonomous flows without classical homoclinic structures, extending the understanding of chaotic mechanisms.

## Key findings

- Folding is crucial for chaos in the Double-Gyre system.
- Manifold curvature helps identify fold points.
- The method applies to general 2D nonautonomous flows.

## Abstract

We analyze chaos in the well-known nonautonomous Double-Gyre system. A key focus is on folding, which is possibly the less-studied aspect of the "stretching + folding = chaos" mantra of chaotic dynamics. Despite the Double-Gyre not having the classical homoclinic structure for the usage of the Smale-Birkhoff theorem to establish chaos, we use the concept of folding to prove the existence of an embedded horseshoe-map. We also show how curvature of manifolds can be used to identify fold points in the Double-Gyre. This method is applicable to general nonautonomous flows in two dimensions, defined for either finite or infinite times.