Characterizing fluid dynamical systems using Euler characteristic surface and Euler metric

Euler characteristic (chi), a topological invariant, helps to understand the topology of a network or complex. We demonstrate that the multiscale topological information of dynamically evolving fluid flow systems can be crystallized into their Euler characteristic surfaces chi(s)(r, t). Furthermore, we demonstrate the Euler Metric (EM), introduced by the authors, can be utilized to identify the stability regime of a given flow pattern, besides distinguishing between different flow systems. The potential of the Euler characteristic surface and the Euler metric have been demonstrated first on analyzing a simulated deterministic dynamical system before being applied to analyze experimental flow patterns that develop in micrometer sized drying droplets.