An autonomous dynamical system captures all LCSs in three-dimensional unsteady flows

Oettinger, David; Haller, George

doi:10.1063/1.4965026

Cited by 8 publications

(6 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A simplified algorithm for computing geodesic LCSs without the use of the direction field is now available 70 , but will not be used in this paper. There is no general extension of geodesic LCS theory to three dimensional flows, but related local variational principles for hyperbolic and elliptic LCSs are now available in three dimensions as well 71,72 . Farazmand & Haller 73 introduce the notion of rotationally coherent LCSs as tubular material surfaces whose elements exhibit identical mean material rotation over a finite time interval [t 0 , t 1 ].…”

Section: Stationary Curves Of the Average Strain: Elliptic Lcssmentioning

confidence: 99%

Section: Stationary Curves Of the Average Strain: Elliptic Lcssmentioning

confidence: 99%

See 1 more Smart Citation

A critical comparison of Lagrangian methods for coherent structure detection

Hadjighasem

Farazmand

Blazevski³

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

202

230

View full text Add to dashboard Cite

We review and test twelve different approaches to the detection of finite-time coherent material structures in two-dimensional, temporally aperiodic flows. We consider both mathematical methods and diagnostic scalar fields, comparing their performance on three benchmark examples: the quasiperiodically forced Bickley jet, a two-dimensional turbulence simulation, and an observational wind velocity field from Jupiter's atmosphere. A close inspection of the results reveals that the various methods often produce very different predictions for coherent structures, once they are evaluated beyond heuristic visual assessment. As we find by passive advection of the coherent set candidates, false positives and negatives can be produced even by some of the mathematically justified methods due to the ineffectiveness of their underlying coherence principles in certain flow configurations. We summarize the inferred strengths and weaknesses of each method, and make general recommendations for minimal self-consistency requirements that any Lagrangian coherence detection technique should satisfy.Keywords: Lagrangian coherent structures; nonlinear dynamical systems; vortex dynamics Coherent Lagrangian (material) structures are ubiquitous in unsteady fluid flows, often observable indirectly from tracer patterns they create, for example, in the atmosphere and the ocean. Despite these observations, a direct identification of these structures from the flow velocity field (without reliance on seeding passive tracers) has remained a challenge. Several heuristic and mathematical detection methods have been developed over the years, each promising to extract materially coherent domains from arbitrary unsteady velocity fields over a finite time interval of interest. Here we review a number of these methods and compare their performance systematically on three benchmark velocity data sets. Based on this comparison, we discuss the strengths and weaknesses of each method, and recommend minimal self-consistency requirements that Lagrangian coherence detection tools should satisfy.

show abstract

Section: Stationary Curves Of the Average Strain: Elliptic Lcssmentioning

confidence: 99%

Section: Stationary Curves Of the Average Strain: Elliptic Lcssmentioning

confidence: 99%

A critical comparison of Lagrangian methods for coherent structure detection

Hadjighasem

Farazmand

Blazevski³

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

202

230

View full text Add to dashboard Cite

show abstract

“…In the next section, we recall the terminology used for the definition of LCSs [13] and OECSs [12] in two-dimensional flows. Variational definitions of LCSs are now available also for threedimensional flows [11], but these definitions do not lead to geodesic problems, and hence are not covered by the computational approach developed here. A similar conclusion holds for OECS definitions obtained as short-term limits of three-dimensional LCS definitions.…”

Section: Null Geodesics and The Computation Of Objective Coherent Structuresmentioning

confidence: 99%

“…In light of this, several methods for the identification of coherent structures (CSs) have been developed [1][2][3][4][5][6]. Only recent mathematical results [7][8][9][10][11][12], however, offer a rigorous and objective (frame-invariant) definition of CSs, uncovering the skeletons behind these wellorganized regions.…”

Section: Introductionmentioning

confidence: 99%

Efficient computation of null geodesics with applications to coherent vortex detection

Serra¹,

Haller²

2017

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

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. *

show abstract

“…While the focus of the present study was on assessing two-dimensional flow structures, the LCS approach can, in principle, be extended to three-dimensional (3D) studies with a vertical component, and LCS methods are increasingly becoming established for 3D applications [20]. Of course, 3D studies will be geometrically more complex and thus can be more challenging to both calculate and visualize.…”

Section: Discussionmentioning

confidence: 99%

Uncovering Fine-Scale Wave-Driven Transport Features in a Fringing Coral Reef System via Lagrangian Coherent Structures

Leclair

Lowe

Zhang

et al. 2020

Fluids

View full text Add to dashboard Cite

Understanding the transport and exchange of water masses both within a reef and between a reef and the surrounding ocean is needed to describe a wide-range of ecosystem processes that are shaped by the movement of material and heat. We show how novel Lagrangian data processing methods, specifically developed to reveal key and often hidden transport structures, can help visualize flow transport patterns within and around morphologically complex reef systems. As an example case study, we consider the wave-driven flow transport within the Ningaloo Reef in Western Australia. We show that a network of attracting, repelling, and trapping flow transport structures organizes the flow transport into, around, and out of the reef. This approach is broadly applicable to coral reef systems, since the combination of well-defined bathymetry and persistent flow-forcing mechanisms (e.g., by wave breaking or tides) is conducive to the existence of persistent Lagrangian transport structures that organize material transport.

show abstract

An autonomous dynamical system captures all LCSs in three-dimensional unsteady flows

Cited by 8 publications

References 24 publications

A critical comparison of Lagrangian methods for coherent structure detection

A critical comparison of Lagrangian methods for coherent structure detection

Efficient computation of null geodesics with applications to coherent vortex detection

Uncovering Fine-Scale Wave-Driven Transport Features in a Fringing Coral Reef System via Lagrangian Coherent Structures

Contact Info

Product

Resources

About