Investigating the connection between complexity of isolated trajectories and Lagrangian coherent structures

Abstract

It is argued that the complexity of fluid particle trajectories provides the basis for a new method, referred to as the Complexity Method (CM), for estimation of Lagrangian coherent structures in aperiodic flows that are measured over finite time intervals. The basic principles of the CM are explained and the CM is tested in a variety of examples, both idealized and realistic, and in different reference frames. Two measures of complexity are explored in detail: the correlation dimension of trajectory, and a new measure – the ergodicity defect. Both measures yield structures that strongly resemble Lagrangian coherent structures in all of the examples considered. Since the CM uses properties of individual trajectories, and not separation rates between closely spaced trajectories, it may have advantages for the analysis of ocean float and drifter data sets in which trajectories are typically widely and non-uniformly spaced.