  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.
