Objective Eulerian coherent structures

Serra, Mattia; Haller, George

doi:10.1063/1.4951720

Cited by 97 publications

(131 citation statements)

References 36 publications

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“…3. The scalar field calculations using (a) the finite-time Lyapunov exponent [37], (b) the trajectory-normal repulsion rate [20], (c) minimum eigenvalue of S from the objective Eulerian coherent structure approach [35], and (d) the trajectory divergence rate. Panels (a) and (b) were calculated by integrating trajectories over an integration time T = −0.33.…”

Section: Approximation Of Hyperbolic Lagrangian Coherent Structuresmentioning

confidence: 99%

Trajectory-free approximation of phase space structures using the trajectory divergence rate

2019

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This paper introduces the trajectory divergence rate, a scalar field which locally gives the instantaneous attraction or repulsion of adjacent trajectories. This scalar field may be used to find highly attracting or repelling invariant manifolds, such as slow manifolds, to rapidly approximating hyperbolic Lagrangian coherent structures, or to provide the local stability of invariant manifolds. This work presents the derivation of the trajectory divergence rate and the related trajectory divergence ratio for 2-dimensional systems, investigates their properties, shows their application to several example systems, and presents their extension to higher dimensions.

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Section: Approximation Of Hyperbolic Lagrangian Coherent Structuresmentioning

confidence: 99%

Trajectory-free approximation of phase space structures using the trajectory divergence rate

2019

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“…Variational arguments show that elliptic OCSs can be located as null-geodesics of suitably defined Lorentzian metrics ( [11,16]). Their computation, however, requires a number of non-standard steps that complicate its implementation.…”

Section: Introductionmentioning

confidence: 99%

Efficient computation of null geodesics with applications to coherent vortex detection

Serra¹,

Haller²

2017

Proc. R. Soc. A.

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Recent results suggest that boundaries of coherent fluid vortices (elliptic coherent structures) can be identified as closed null-geodesics of appropriate Lorentzian metrics defined on the flow domain.Here we derive an automated method for computing such null-geodesics based on the geometry of the underlying geodesic flow. Our approach simplifies and improves existing procedures for computing variationally defined Eulerian and Lagrangian vortex boundaries. As an illustration, we compute objective vortex boundaries from satellite-inferred ocean velocity data. A MATLAB implementation of our method is available as supplementary material. *

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“…Haller [Hal15] considered the outermost elliptic LCS, of a family of nested elliptic LCSs, as the boundary of a coherent vortex. Serra and Haller [SH16b] used the variational framework to find objective Eulerian vortex boundaries as closed instantaneous (per time step) curves across which the averaged material stretching rate shows no leading-order variability. Based on these (instantaneous) curves, they forecasted the Lagrangian persistence of a vortex [SH16a].…”

Section: Extraction Of Vortex Boundariesmentioning

confidence: 99%

The State of the Art in Vortex Extraction

Günther

Theisel

2018

Computer Graphics Forum

106

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Vortices are commonly understood as rotating motions in fluid flows. The analysis of vortices plays an important role in numerous scientific applications, such as in engineering, meteorology, oceanology, medicine and many more. The successful analysis consists of three steps: vortex definition, extraction and visualization. All three have a long history, and the early themes and topics from the 1970s survived to this day, namely, the identification of vortex cores, their extent and the choice of suitable reference frames. This paper provides an overview over the advances that have been made in the last 40 years. We provide sufficient background on differential vector field calculus, extraction techniques like critical point search and the parallel vectors operator, and we introduce the notion of reference frame invariance. We explain the most important region‐based and line‐based methods, integration‐based and geometry‐based approaches, recent objective techniques, the selection of reference frames by means of flow decompositions, as well as a recent local optimization‐based technique. We point out relationships between the various approaches, classify the literature and identify open problems and challenges for future work.

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Objective Eulerian coherent structures

Cited by 97 publications

References 36 publications

Trajectory-free approximation of phase space structures using the trajectory divergence rate

Trajectory-free approximation of phase space structures using the trajectory divergence rate

Efficient computation of null geodesics with applications to coherent vortex detection

The State of the Art in Vortex Extraction

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