Coherent Lagrangian vortices: The black holes of turbulence

G. Haller, F. J. Beron-Vera

Research output: Contribution to journalArticlepeer-review

132 Scopus citations


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.

Original languageEnglish (US)
Article numberR4
JournalJournal of Fluid Mechanics
StatePublished - Sep 25 2013


  • geophysical and geological flows
  • nonlinear dynamical systems
  • vortex flows

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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