Lagrangian Coherent Structure Detection using Natural Tracers in Particle-Laden Surface Flows*

Surface flows exist in a variety contexts, with modern examples including the motion of drifting buoys, ice floes, and plastic pollution in the ocean, and the advection of debris in rivers. An open problem in the study of such flows is the characterization of coherent particle behavior without direct access to underlying velocity fields or a dense distribution of tracers. This work proposes the finite-time Q criterion as an objective metric for detecting Lagrangian coherent structures and develops a trajectory-based algorithm for its sparse approximation. The tool will be demonstrated on analytical and experimental data for flows representative of real-world applications.