Addendum to "Coherent Lagrangian vortices: The black holes of turbulence"
G. Haller, F. J. Beron-Vera
TL;DR
This paper refines the analogy between coherent Lagrangian vortex boundaries in fluid dynamics and photon spheres in general relativity, based on a variational principle involving Lorentzian metrics.
Contribution
It provides an improved discussion on the mathematical analogy between vortex boundaries and photon spheres, building on previous variational principles.
Findings
Vortex boundaries are null-geodesics of a Lorentzian metric.
The analogy with photon spheres is mathematically clarified.
The variational principle identifies vortex boundaries as special geodesics.
Abstract
In Haller and Beron-Vera (2013) we developed a variational principle for the detection of coherent Lagrangian vortex boundaries. The solutions of this variational principle turn out to be closed null-geodesics of the Lorentzian metric associated with a generalized Green-Lagrange strain tensor family. This metric interpretation implies a mathematical analogy between coherent Lagrangian vortex boundaries and photon spheres in general relativity. Here we give an improved discussion on this analogy.
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