Using sparse trajectory data to find Lagrangian Coherent Structures (LCS) in fluid flows

Video by Tanner Harms, based on "Lagrangian Gradient Regression for the Detection of Coherent Structures from Sparse Trajectory Data"
by Tanner D. Harms, Steven L. Brunton, Beverley J. McKeon
arxiv.org/abs/2310.10994
The method of Lagrangian Coherent Structures (LCS) uses particle trajectories in fluid flows to identify coherent structures that govern the behavior of the flow. The typical methods employed to identify LCS rely on a dense grid of numerical tracers which are seeded onto the pre-computed vector fields and advected through time and space. However, in many systems, dense flow field information is not available, and researchers must perform their analyses on a sparse set of tracers that already exist in the flow. For example, if we wish our flow observer to autonomously make decisions based on the flow field information, then the computational expense of the normal LCS identification pipeline is too costly to use. It will need to use only the trajectories of the tracers that it sees in the flow. Motivated by the desire to study flow fields autonomously, this video shows how sparse trajectory data can be leveraged to identify key flow quantities including the velocity gradient, Finite-Time Lyapunov Exponent (FTLE), and Lagrangian-Averaged Vorticity Deviation (LAVD), which are often used to identify LCS.
Key links:
• Lagrangian Coherent St...
arxiv.org/abs/2310.10994
pubs.aip.org/aip/cha/article-...
www.amazon.com/Transport-Barr...
pubs.aip.org/aip/cha/article/...

[@mode-lab]

Awesome work Tanner - and beatiful video!

[@thatkidJM0808]

This was amazing!

[@okhan5087]

Excellent video as usual!

[@veganphilosopher1975]

I'm a simple man. I see Lagrangian coherent structures, I hit like.

[@andrewli6260]

Great tutorial. Dr. brunton would you pls make more tutorial videos in LCS? Love that topic

[@tedmsxu]

Awesome work.

[@JeniferHarms]

I love that guy!

[@soyagricola7526]

Love your videos ,it wpukd be great that you make a series of videos of the finite element method i understand that now taking big attentiom from mechanics fluids invetigators, at least thats why zienkiewitzs says

[@GeoffryGifari]

Hmmm... along with the improvements, are there some extra "costs" for LGR compared to the alternative?

[@GeoffryGifari]

Are the wooden spheres used to emphasize the "sparse" part?