Spatio-temporal organization of dynamics in a two-dimensional periodically driven vortex flow: a Lagrangian flow network perspective

TL;DR

This paper introduces a network-based method to analyze the complex Lagrangian dynamics in a driven 2D vortex flow, revealing invariant structures and flow regimes through transfer operator approximations.

Contribution

It presents a novel approach using flow networks derived from transfer operators to identify invariant structures and regimes in Lagrangian flow dynamics.

Findings

Network measures correlate with Lyapunov exponents

Identified flow regimes and invariant structures

Validated approach with ROC analysis

Abstract

We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a directed network that characterizes the exchange of mass between distinct regions of the flow domain. By studying different measures characterizing flow network connectivity at different time-scales, we are able to identify the location of dynamically invariant structures and regions of maximum dispersion. Specifically, our approach allows to delimit co-existing flow regimes with different dynamics. To validate our findings, we compare several network characteristics to the well-established finite-time Lyapunov exponents and apply a receiver operating characteristic (ROC) analysis to identify network measures that are particularly useful for unveiling the skeleton of Lagrangian chaos.