FTLE from 2-D/3-D Noisy and Sparse Trajectories (MATLAB)

Lagrangian coherent structures from Noisy and Sparse Trajectories for flows in 2-D/3-D Euclidean spaces

The MATLAB code to compute FTLE for flows defined on Euclidean spaces is available at this link. The following tutorial provides instructions on how to use the code. We use the numerical method described in [1].

Pre-requisites

The code was built on MATLAB R2025b in a Windows 10 system. We have tested these codes on a Mac OSX 15 and Ubuntu 20 operating systems. The most straightforwrd Installation method, is using Git, as all the code is hosted on GitHub. We assume that Git is installed and set up on the system. If not, we refer you to this link.

Installation

To install the code, navigate to the path where you would want to install it on the terminal and clone the GitHub repository using the code

git clone  https://github.com/SreejithSanthosh/flow_coherent_structure.git

This will generate a directory called flow_coherent_structure, which contains all the code. To check if all the necessary components navigate to the ftle_from_sparse_trajec folder and make it your root directory in MATLAB and run example_sparsetrajec2d.m on MATLAB. This runs the deformation analysis, presenting the results below for the double-gyre velocity field.

Result of FTLE Analaysis

\(\Lambda\) is the FTLE field, \(\xi\) is the axis of maximum deformation.

Further development of this code is currently ongoing to improve the robustness of the method and increase its speed. To get those updates, use the command

git pull

Performing deformation analysis for your data

The two example code example_sparsetrajec2d.m is written for a specific flow field. To use this analysis for your data, you need for a 2D flow, the two coordinates of the intial position of the trajectories x0, y0 at time \(t_0\) and its final position xf,yf at time \(t_f\). The Lagrangian analysis is done over the time-interval \(t_0\rightarrow t_f\). The function compute_deform_sparsetrajec.m computes the singular values and its associated axis from x0,y0,xf,yf formatted as r0 and rf. From the results of this function, the FTLE can be visualized using the code described in %% Visualize the result in example_sparsetrajec2d.m. The function compute_deform_sparsetrajec.m can also compute the deformation metrics for trajectories in 3D where r0 and rf are formatted as a double array of size Nq x 3 where Nq is the trajectory index an the second axis is the 3 coordinates of the trajectory.

References

[1] : Mowlavi, S., Serra, M., Maiorino, E., & Mahadevan, L. (2022). Detecting Lagrangian coherent structures from sparse and noisy trajectory data. Journal of Fluid Mechanics, 948, A4.