Time-Dependent 2-D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures

TL;DR

This paper introduces a novel method for analyzing 2-D time-dependent vector fields by extending classical topology concepts using generalized streak lines, closely related to Lagrangian coherent structures, and demonstrates its effectiveness on synthetic and CFD data.

Contribution

It generalizes vector field topology to unsteady fields using generalized streak lines, linking it to Lagrangian coherent structures, and provides a practical evaluation on synthetic and CFD data.

Findings

Effective in identifying regions of different behavior in unsteady vector fields.

Successfully applied to synthetic and CFD data for validation.

Provides a new perspective on analyzing time-dependent flow structures.

Abstract

This paper presents an approach to a time-dependent variant of the concept of vector field topology for 2-D vector fields. Vector field topology is defined for steady vector fields and aims at discriminating the domain of a vector field into regions of qualitatively different behaviour. The presented approach represents a generalization for saddle-type critical points and their separatrices to unsteady vector fields based on generalized streak lines, with the classical vector field topology as its special case for steady vector fields. The concept is closely related to that of Lagrangian coherent structures obtained as ridges in the finite-time Lyapunov exponent field. The proposed approach is evaluated on both 2-D time-dependent synthetic and vector fields from computational fluid dynamics.