Lagrangian Coherent Set Detection with Topological Advection

Lagrangian coherent structures (LCSs) determine the transport properties and mixing dynamics of general aperiodic fluid flows, much as invariant manifolds and periodic orbits do for autonomous or periodic systems. Due to the prevalence of LCSs in nature and industry, there exist many successful techniques for detecting them in data. However, these approaches typically require very fine trajectory data to reconstruct velocity fields and compute Cauchy-Green-tensor-related quantities (such as FTLE fields). We use topological techniques to help detect coherent trajectory sets in relatively sparse 2D advection problems. In particular, we use a new, computationally efficient algorithm which evolves topological loops (material curves) forward in time due to the movement of sets of advected particles. Starting with simple loops, and their future state - given by the topological advection algorithm, we systematically combine them to form the boundary of LCSs. We then show how this approach effectively and efficiently reveals coherent sets of trajectories in models flows.