Performance of Lagrangian Descriptors and their variants in incompressible flows

TL;DR

This paper evaluates the effectiveness of Lagrangian descriptors in incompressible flows, revealing limitations in their ability to identify transport barriers and suggesting they are less useful in linear systems.

Contribution

The study critically assesses the performance of Lagrangian descriptors in incompressible flows and challenges previous assumptions about their ability to detect transport barriers.

Findings

Barriers are not always indicated by singular features of the M function.

Lagrangian descriptors are less effective in most linear systems.

The techniques are applicable beyond incompressible flows.

Abstract

The method of Lagrangian descriptors has been already applied in many different contexts, specially in geophysical flows. In this paper we analyze the performance of this methodology in incompressible flows. We demonstrate that barriers to transport are not always coded by singular features of the $M$ function as Mancho, Wiggins and their co-workers conjectured. The techniques presented here are not restricted to incompressible flows. In fact, by our approach, one can infer that the method of Lagrangian descriptors is not useful in most linear systems.