Journal of Fluid Mechanics


Coherent Lagrangian vortices: the black holes of turbulence

G. Hallera1 and F. J. Beron-Veraa2 c1

a1 Institute for Mechanical Systems, ETH Zurich, 8092 Zurich, Switzerland

a2 Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL 33149, USA


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.

(Received May 13 2013)

(Revised July 18 2013)

(Accepted July 25 2013)

Key words

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


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