Improved characterization of Lagrangian coherent structures through time-scale analysis

TL;DR

This paper introduces a continuous time-scale framework for Lagrangian coherent structures that automatically determines the optimal temporal scale at each location, improving the detection of significant structures in various fields.

Contribution

The paper presents a novel continuous time-scale approach for LCS extraction that adapts to local features, enhancing structural detection in vector, tensor, and map fields.

Findings

Improved detection of LCS in fluid dynamics, medical imaging, and orbital mechanics.

Method reveals structures missed by existing techniques.

Applicable to vector, tensor, and discrete map fields.

Abstract

The computation of Lagrangian coherent structures (LCS) has established itself as a prominent means to reveal significant geometric structures in time-dependent vector fields. Their characterization, however, requires the selection of a suitable time parameter for the construction of the flow map that may not be known in advance. We present in this paper a continuous time-scale framework for LCS extraction and visualization. Specifically, we treat the time axis as a continuum from which a best temporal scale is automatically determined at each spatial location for the extraction of LCS. Beyond its effectiveness with vector fields we show that this method can be successfully applied to improve the characterization of salient structures in tensor fields and discrete maps. We present applications of our method to problems spanning fluid dynamics, medical imaging, and orbital mechanics. The results show that our approach can reveal important structural features that are missed by existing LCS extraction methods.