Quasi-Objective Coherent Structure Diagnostics from Single Trajectories

Abstract: We derive measures of local material stretching and rotation that are computable from individual trajectories without reliance on other trajectories or on an underlying velocity field. Both measures are quasi-objective: they approximate objective (i.e., observer-independent) coherence diagnostics in frames satisfying a certain condition. This condition requires the trajectory accelerations to dominate the angular acceleration induced by the spatial mean vorticity. We illustrate in examples how quasi-objective coherence diagnostics highlight elliptic and hyperbolic Lagrangian coherent structures even from very sparse trajectory data.