# Lagrange2D: A Mathematica package for Lagrangian analysis of two-dimensional fluid flows

## TL;DR

Lagrange2D is a Mathematica package designed for analyzing two-dimensional fluid flows using Lagrangian metrics, facilitating visualization, structure identification, and flow characterization.

## Contribution

The paper introduces Lagrange2D, a comprehensive open-source Mathematica package for Lagrangian analysis of 2D fluid flows, including trajectory integration, visualization, and structure detection.

## Key findings

- Enables rapid flow characterization and visualization.
- Supports calculation of finite-time Lyapunov exponents and other metrics.
- Facilitates identification of Lagrangian coherent structures.

## Abstract

We introduce Lagrange2D, a Mathematica package for analysis and characterization of complex fluid flows using Lagrangian transport metrics. Lagrange2D includes built-in functions for integrating ensembles of trajectories subject to time-varying two-dimensional flows, as well as utilities for calculating various quantities of interest, such as finite-time Lyapunov exponents, stretching vector fields, the fractal dimension, and flushing times. The package also includes tools for visualizing transport and pathlines, as well as for generating videos. This package aims to ease rapid characterization of arbitrary flows, by allowing identification of Lagrangian coherent structures and other quantities of interest. The open-source code for the package is available on GitHub at: \url{https://github.com/williamgilpin/lagrange2d}