# Lagrangian Flow Network approach to an open flow model

## TL;DR

This paper extends the Lagrangian Flow Network framework to open chaotic flows, demonstrating its effectiveness in identifying key structures like the chaotic saddle and manifolds in a jet flow model.

## Contribution

It applies network theory tools to open flows, revealing how network metrics can locate chaotic structures, which was previously limited to closed flows.

## Key findings

- High out-degree and forward-time entropy identify the chaotic saddle and stable manifold.
- High in-degree and backward-time entropy highlight the saddle and unstable manifold.
- Cyclic clustering coefficient indicates the presence of periodic orbits at the saddle.

## Abstract

Concepts and tools from network theory, the so-called Lagrangian Flow Network framework, have been successfully used to obtain a coarse-grained description of transport by closed fluid flows. Here we explore the application of this methodology to open chaotic flows, and check it with numerical results for a model open flow, namely a jet with a localized wave perturbation. We find that network nodes with high values of out-degree and of finite-time entropy in the forward-in-time direction identify the location of the chaotic saddle and its stable manifold, whereas nodes with high in-degree and backwards finite-time entropy highlight the location of the saddle and its unstable manifold. The cyclic clustering coefficient, associated to the presence of periodic orbits, takes non-vanishing values at the location of the saddle itself.