Comparing Finite-Time Lyapunov Exponents and Lagrangian Descriptors for identifying phase space structures in a simple two-dimensional, time-periodic double-gyre model

TL;DR

This paper compares Finite-Time Lyapunov Exponents and Lagrangian Descriptors in identifying phase space structures like manifolds and tori in a simple 2D time-periodic double-gyre flow model, highlighting their advantages and limitations.

Contribution

It provides a detailed comparison of FTLEs and LDs for detecting Lagrangian Coherent Structures in a specific flow model, including theoretical background and practical examples.

Findings

FTLEs effectively identify stable and unstable manifolds.

LDs offer complementary insights into phase space structures.

Both methods have specific advantages and limitations depending on the context.

Abstract

This paper compares the advantages, limitations, and computational considerations of using Finite-Time Lyapunov Exponents (FTLEs) and Lagrangian Descriptors (LDs) as tools for identifying barriers and mechanisms of fluid transport in two-dimensional time-periodic flows. These barriers and mechanisms of transport are often referred to as "Lagrangian Coherent Structures," though this term often changes meaning depending on the author or context. This paper will specifically focus on using FTLEs and LDs to identify stable and unstable manifolds of hyperbolic stagnation points, and the Kolmogorov-Arnold-Moser (KAM) tori associated with elliptic stagnation points. The background and theory behind both methods and their associated phase space structures will be presented, and then examples of FTLEs and LDs will be shown based on a simple, periodic, time-dependent double-gyre toy model with varying parameters.