Curvature Fields, Topology, and the Dynamics of Spatiotemporal Chaos

TL;DR

This paper investigates how curvature fields derived from particle trajectories reveal the topological dynamics and transition to chaos in a two-dimensional fluid flow, highlighting the role of hyperbolic and elliptic points.

Contribution

It introduces a method to measure curvature fields from trajectories to analyze flow topology and characterizes the transition to chaos through topological point interactions.

Findings

Hyperbolic and elliptic points are identified and tracked.

Topological changes correlate with the transition to chaos.

Flow topology undergoes a two-stage transition with distinct phases.

Abstract

The curvature field is measured from tracer particle trajectories in a two-dimensional fluid flow that exhibits spatiotemporal chaos, and is used to extract the hyperbolic and elliptic points of the flow. These special points are pinned to the forcing when the driving is weak, but wander over the domain and interact in pairs at stronger driving, changing the local topology of the flow. Their behavior reveals a two-stage transition to spatiotemporal chaos: a gradual loss of spatial and temporal order followed by an abrupt onset of topological changes.