Efficient Computation of Null-Geodesic with Applications to Coherent Vortex Detection

TL;DR

This paper introduces an automated, efficient method for computing null-geodesics to identify coherent vortex boundaries in fluid flows, improving accuracy and simplicity over previous techniques, with practical applications demonstrated on ocean data.

Contribution

The paper presents a novel, automated approach for computing null-geodesics that define vortex boundaries, enhancing existing methods through geometric simplification and improved robustness.

Findings

Successfully computed vortex boundaries from satellite ocean data.

Provided a MATLAB implementation for practical use.

Enhanced the accuracy and efficiency of vortex detection methods.

Abstract

Recent results suggest that boundaries of coherent fluid vortices (elliptic coherent structures) can be identified as closed null-geodesics of appropriate Lorentzian metrics defined on the flow domain. Here we derive an automated method for computing such null-geodesics based on the geometry of the underlying geodesic flow. Our approach simplifies and improves existing procedures for computing variationally defined Eulerian and Lagrangian vortex boundaries. As an illustration, we compute objective vortex boundaries from satellite-inferred ocean velocity data. A MATLAB implementation of our method is available as supplementary material.