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Addendum to ‘Coherent Lagrangian vortices: the black holes of turbulence’

Published online by Cambridge University Press:  14 August 2014

G. Haller  and
F. J. Beron-Vera
G. Haller*
Affiliation:
Institute of Mechanical Systems, ETH Zurich, 8092 Zurich, Switzerland
F. J. Beron-Vera
Affiliation:
Department of Atmospheric Sciences, RSMAS, University of Miami, Miami, FL 33149, USA
*
†Email address for correspondence: [email protected]
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Abstract

In Haller & Beron-Vera (J. Fluid Mech., vol. 731, 2013, R4) we developed a variational principle for the detection of coherent Lagrangian vortex boundaries. The solutions of this variational principle turn out to be closed null geodesics of the Lorentzian metric induced by a generalized Green–Lagrange strain tensor family. This metric interpretation implies a mathematical analogy between coherent Lagrangian vortex boundaries and photon spheres in general relativity. Here, we give an improved discussion of this analogy.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Geophysical and Geological Flows: Ocean circulation
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 755 , 25 September 2014 , R3
Copyright
© 2014 Cambridge University Press 

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References

Beem, J. K., Ehrlich, P. L. & Kevin, L. E. 1996 Global Lorentzian Geometry. CRC Press.Google Scholar
Claudel, C.-M., Virbhadra, K. S. & Ellis, G. F. R. 2001 The geometry of photon surfaces. J. Math. Phys. 42, 818–838.Google Scholar
Haller, G. & Beron-Vera, F. J. 2013 Coherent Lagrangian vortices: the black holes of turbulence. J. Fluid Mech. 731, R4.Google Scholar