Attracting and repelling Lagrangian coherent structures from a single computation

TL;DR

This paper presents a method to compute both attracting and repelling Lagrangian Coherent Structures simultaneously from a single flow data set, overcoming limitations of previous approaches that required separate forward and backward computations.

Contribution

It introduces a novel approach to identify both types of hyperbolic LCSs at the same time instance from a single computation, improving analysis of aperiodic flows.

Findings

Both attracting and repelling LCSs can be computed from a single flow run.

LCSs are derived as surfaces normal to eigenvectors of the Cauchy-Green strain tensor.

The method works for temporally aperiodic dynamical systems.

Abstract

Hyperbolic Lagrangian Coherent Structures (LCSs) are locally most repelling or most attracting material surfaces in a finite-time dynamical system. To identify both types of hyperbolic LCSs at the same time instance, the standard practice has been to compute repelling LCSs from future data and attracting LCSs from past data. This approach tacitly assumes that coherent structures in the flow are fundamentally recurrent, and hence gives inconsistent results for temporally aperiodic systems. Here we resolve this inconsistency by showing how both repelling and attracting LCSs are computable at the same time instance from a single forward or a single backward run. These LCSs are obtained as surfaces normal to the weakest and strongest eigenvectors of the Cauchy-Green strain tensor.