  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.
