Refining and classifying finite-time Lyapunov exponent ridges

TL;DR

This paper improves methods for extracting and classifying FTLE ridges in 2D flows, analyzing their role in flow transport, with practical application to ocean surface velocity data.

Contribution

It introduces a refined method for FTLE ridge extraction, adapts a classification scheme for deformation types, and assesses effects of discretization and noise.

Findings

FTLE ridge extraction method enhances accuracy

Classification scheme clarifies deformation types

Application to ocean data demonstrates practical utility

Abstract

While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of an FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by an FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model.