Lagrange2D
A Mathematica package for the Lagrangian analysis of fluid flows
| Example "Double Gyre" Flow Field | Pathlines for particles in flow |
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| Transport field | Maximum finite-time Lyapunov exponents |
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| Kaplan-Yorke Fractal Dimension | Flushing time distribution |
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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