Coherent Lagrangian vortices: The black holes of turbulence

TL;DR

This paper introduces a variational principle for identifying coherent vortices in 2D turbulence, revealing mathematical parallels with black hole photon spheres and applying the method to real oceanic eddies for transport analysis.

Contribution

It presents a novel variational approach to define vortex boundaries in turbulence, linking fluid dynamics with cosmological concepts, and demonstrates its effectiveness on ocean data.

Findings

Identified super-coherent eddies in the South Atlantic.

Derived explicit differential equations for vortex boundaries.

Provided Lagrangian transport estimates for Agulhas rings.

Abstract

We introduce a simple variational principle for coherent material vortices in two-dimensional turbulence. Vortex boundaries are sought as closed stationary curves of the averaged Lagrangian strain. Solutions to this problem turn out to be mathematically equivalent to photon spheres around black holes in cosmology. The fluidic photon spheres satisfy explicit differential equations whose outermost limit cycles are optimal Lagrangian vortex boundaries. As an application, we uncover super-coherent material eddies in the South Atlantic, which yield specific Lagrangian transport estimates for Agulhas rings.