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

Abstract

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.