Lagrangian Coherent Structures: Application to Unsteady Oceanic and Laboratory Flows

Abstract

In this thesis we study several spatio-temporal transport problems in two-dimensional time-dependent flows that generate chaotic advection. We aim to clarify the role of advective transport for passive and also for reactive tracers. Therefore, we characterize transport in these flows in the very detail with Lagrangian coherent structures (LCS) that reveal the geometry of irregular fluid motion, and especially emphasize lines of separation and merging of fluid patches. In particular, (1) we study the spreading of a phytoplankton plankton patch in a numerical NPZ model, (2) we examine the role of advection for the Madagascar plankton bloom , (3) we extract flow patterns in the surface flow of the Ria de Vigo, an estuary in NW Spain, and (4) we analyze transport patterns in a turbulent laboratory flow induced by Faraday waves and relate the resulting Lagrangian coherent structures with the filamentous wave front of a chemical reaction. The results show that LCS are a very useful method to visualize the fluid transport in different chaotic flows.