Do Finite-Size Lyapunov Exponents Detect Coherent Structures?

TL;DR

This paper establishes a rigorous mathematical connection between FSLE ridges and Lagrangian Coherent Structures, clarifying when FSLE effectively detects hyperbolic LCSs and highlighting limitations such as false positives and computational sensitivities.

Contribution

It provides the first rigorous proof linking FSLE ridges to FTLE ridges and hyperbolic LCSs, and identifies key limitations of FSLE in coherence detection.

Findings

FSLE ridges can indicate FTLE ridges under certain conditions

Some FSLE ridges are false positives for LCSs

FSLE has limitations like ill-posedness and sensitivity to parameters

Abstract

Ridges of the Finite-Size Lyapunov Exponent (FSLE) field have been used as indicators of hyperbolic Lagrangian Coherent Structures (LCSs). A rigorous mathematical link between the FSLE and LCSs, however, has been missing. Here we prove that an FSLE ridge satisfying certain conditions does signal a nearby ridge of some Finite-Time Lyapunov Exponent (FTLE) field, which in turn indicates a hyperbolic LCS under further conditions. Other FSLE ridges violating our conditions, however, are seen to be false positives for LCSs. We also find further limitations of the FSLE in Lagrangian coherence detection, including ill-posedness, artificial jump-discontinuities, and sensitivity with respect to the computational time step.