On star-convex volumes in 2-D hydrodynamical flows and their relevance for coherent transport

Oceanic surface flows are dominated by finite-time mesoscale structures that separate two-dimensional flows into volumes of qualitatively different dynamical behavior. Among these, the transport boundaries around eddies are of particular interest since the enclosed volumes show a notable stability with respect to filamentation while being transported over significant distances with consequences for a multitude of different oceanic phenomena. In this paper, we present a novel method to analyze coherent transport in oceanic flows. The presented approach is purely based on convexity and aims to uncover maximal persistently star-convex (MPSC) volumes, volumes that remain star-convex with respect to a chosen reference point during a predefined time window. Since these volumes do not generate filaments, they constitute a sub-class of finite-time coherent volumes. The new perspective yields definitions for filaments, which enables the study of MPSC volume formation and dissipation. We discuss the underlying theory and present an algorithm, the material star-convex structure search, that yields comprehensible and intuitive results. In addition, we apply our method to different velocity fields and illustrate the usefulness of the method for interdisciplinary research by studying the generation of filaments in a real-world example.