Coherent Lagrangian vortices: the black holes of turbulence
By G. Haller, Francisco J. Beron-Vera. Journal of Fluid Mechanics, 2013
240 citations recorded by the source corpus.
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.
Subfields: Computational Mechanics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/5ae5b3b7226eb423196a527f1eca16b14b925fd7
How researchers see this paper
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In Computational Mechanics
- Yisheng Gao
- Chaoqun Liu
- Mohammad Farazmand
- Xiangrui Dong
- Shuling Tian
- Alireza Hadjighasem
- Florian Huhn
- L. Zanna
In Nuclear and High Energy Physics
- Yisheng Gao
- Chaoqun Liu
- Shuling Tian
- Xiangrui Dong
- Mohammad Farazmand
- Alireza Hadjighasem
- Florian Huhn
- G. Haller
Citations in the corpus
- Defining coherent vortices objectively from the vorticity (2015, methodology): “We integrate the vorticity deviation norm separately (as opposed to solving the combined ODE (9.1)), using 1200 vorticity values along each trajectory, equally spaced in time.”
- Lagrangian Coherent Structures (2015, background): “As shown by Haller & Beron-Vera (2013, 2014), stationary curves of the tangential stretching functional coincide with null geodesics of the Lorentzian metric family, gλ(u, v) = 〈u, Eλv〉 , λ > 0, (13) with the generalized Green-Lagrange strain tensor Eλ(x0) defined in Equation 8.”
- Definitions of vortex vector and vortex (2017, methodology): “To objectively study the vortex structures in the rotating reference frame, objective Eulerian criteria are also proposed (Haller 2005; Haller & Beron-Vera 2013; Karrasch, Huhn & Haller 2014; Haller 2015; Haller et al. 2016; Haller 2016).”
- Lagrangian ocean analysis: Fundamentals and practices (2018, methodology): “886 Definitions of parabolic and elliptic LCSs, corresponding to jet cores and vortex 887 boundaries, can similarly be made using the tools of differential geometry 888 (123, 120).”