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Coherent Lagrangian vortices: the black holes of turbulence

  • G. Haller (a1) and F. J. Beron-Vera (a2)

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.

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L. M. Beal , W. P. M. De Ruijter , A. Biastoch , R. Zahn & SCOR/WCRP/IAPSO Working Group 2011 On the role of the Agulhas system in ocean circulation and climate. Nature 472, 429436.

J. K. Beem , P. L. Ehrlich & L. E. Kevin 1996 Global Lorentzian Geometry. CRC Press.

F. J. Beron-Vera , M. J. Olascoaga & G. J. Goni 2008 Oceanic mesoscale vortices as revealed by Lagrangian coherent structures. Geophys. Res. Lett. 35, L12603.

F. J. Beron-Vera , Y. Wang , M. J. Olascoaga , G. J. Goni & G. Haller 2013 Objective detection of oceanic eddies and the Agulhas leakage. J. Phys. Oceanogr. 43, 14261438.

D. B. Chelton , M. G. Schlax & R. M. Samelson 2011 Global observations of nonlinear mesoscale eddies. Prog. Oceanogr. 91, 167216.

K. L. Denman & A. E. Gargett 1983 Time and space scales of vertical mixing and advection of phytoplankton in the upper ocean. Limnol. Oceanogr. 28, 801815.

G. J. Goni , S. L. Garzoli , A. J. Roubicek , D. B. Olson & O. B. Brown 1997 Agulhas ring dynamics from TOPEX/Poseidon satellite altimeter data. J. Mar. Res. 55, 861883.

G. Haller & T. Sapsis 2008 Where do inertial particles go in fluid flows? Physica D 237, 573583.

J. Jeong & F. Hussain 1985 On the identification of a vortex. J. Fluid Mech. 285, 6994.

A. Provenzale 1999 Transport by coherent barotropic vortices. Annu. Rev. Fluid Mech. 31, 5593.

C. Truesdell & W. Noll 2004 The Nonlinear Field Theories of Mechanics. Springer.

H. M. van Aken , A. K. van Veldhovena , C. Vetha , W. P. M. de Ruijterb , P. J. van Leeuwenb , S. S. Drijfhoutc , C. P. Whittled & M. Rouaultd 2003 Observations of a young Agulhas ring, Astrid, during MARE in March 2000. Deep-Sea Res. II 50, 167195.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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