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Coherent Lagrangian vortices: the black holes of turbulence

Published online by Cambridge University Press:  03 September 2013

G. Haller  and
F. J. Beron-Vera
G. Haller
Affiliation:
Institute for Mechanical Systems, ETH Zurich, 8092 Zurich, Switzerland
F. J. Beron-Vera*
Affiliation:
Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL 33149, USA
*
†Email address for correspondence: georgehaller@ethz.ch
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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.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Vortex Flows: Vortex Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 731 , 25 September 2013 , R4
Copyright
©2013 Cambridge University Press 

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