Lagrange2D

A Mathematica package for the Lagrangian analysis of fluid flows

Example "Double Gyre" Flow Field	Pathlines for particles in flow

Transport field	Maximum finite-time Lyapunov exponents

Kaplan-Yorke Fractal Dimension	Flushing time distribution

Installation

Download this repository. In your working notebook, make sure that lagrange2d.wl is on the path. The package can then be imported as follows:

SetDirectory[NotebookDirectory[]]
<< lagrange2d.wl

Functions and usage

Please refer to the notebook demos.nb for example problems utilizing the various functions in the package. Briefly, capabilities include: Numerical integration of a "blob" of neighboring points, calculation of finite-time Lyapunov exponents and the spatial field of Kaplan-Yorke dimensions, and animation and plotting tools.

See figures above for examples of output plots.

If you find this code useful, please consider citing the accompanying paper

Gilpin, William. "Lagrange2D: A Mathematica package for Lagrangian analysis of two-dimensional fluid flows" https://arxiv.org/abs/1908.00717

Theoretical background

The FTLE function in this package is based on research developed by the Haller lab at ETH Zurich. For theoretical background, please refer to the review of Lagrangian coherent structures. For a MATLAB package that finds Lagrangian coherent structures using FTLE, please refer to LCSTool

Files included in this repository

'lagrange2d.wl' the main package file demos.nb a notebook containing executable examples and outputs /resources contains example output images /dev contains temporary versions used for development README.md contains documentation .gitignore version control auxiliary file