Fluids typically produce highly complicated dynamics. With suitable mathematical methods, however, we can uncover key structures that act as invisible walls for particles inside such flows. Detecting the transport barriers therefore provides a simplified picture that reveals the essential parts of the dynamics. Applied to, e.g., the ocean, this helps understanding oil spills, or locating and tracking mesoscale eddies.
At the moment, we develop theories and numerical methods for locating transport barriers in three-dimensional flows with arbitrary time dependence. As a continuation of recent work on Lagrangian coherent structures carried out in the group of Prof. G. Haller, the most important ingredients are concepts from dynamical systems theory, geometry and fluid mechanics.