Automated computation of material barriers to diffusive and stochastic transport

Lagrangian coherent structures (LCS) are distinguished, time-evolving surfaces that shape conservative tracer patterns in complex dynamical systems. The objective (observer-independent) identification of such structures has recently been extended to uncover the material skeletons of diffusive and stochastic tracer patterns. In this extended theory, diffusion barriers are identified as material surfaces that inhibit the diffusion of passive scalars more than neighbouring surfaces do. Here, we describe a computational algorithm based on these new results. The algorithm offers a fully automated detection of conservative, diffusive and stochastic transport barriers without reliance on user input or fine-tuning of parameters, as other coherent-structure-detection algorithms typically do. Moreover, we extend the new, diffusive LCS theory to uncover objectively defined instantaneous (Eulerian) barriers to diffusive transport. We also introduce a publicly available Matlab graphical user interface (GUI) that implements all these results for general, two-dimensional unsteady flow data. We close by demonstrating the use of this GUI on a satellite-based oceanic surface velocity data set.