Automated detection of coherent Lagrangian vortices in two-dimensional unsteady flows

Karrasch, Daniel; Huhn, Florian; Haller, George

doi:10.1098/rspa.2014.0639

Cited by 50 publications

(94 citation statements)

References 36 publications

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“…The presence of closed orbits is linked to the existence of singularities in the CG tensor field, which is used as a means for identifying their location. 44 By virtue of their transport properties, these are also considered elliptical LCS. There are two elliptic barriers in the double-gyre system, and they are presented as green lines in Figure 2.…”

Section: A Finite-time Lyapunov Exponentsmentioning

confidence: 99%

Lagrangian based methods for coherent structure detection

Allshouse

Peacock

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows. The transport of material by advection in fluid systems is a process of vital and ubiquitous importance, underlying scenarios as diverse as pollutant distribution and searchand-rescue operations in the ocean to blood flow in the human body. The rapidly advancing field of Lagrangian based methods for studying flow transport has demonstrated an effective ability to find robust and significant transport features that underly the organization of flow transport in complex, unsteady flow fields. In this review, we present an overview of four of the leading Lagrangian approaches, each with their own strengths and challenges. Details of each method are presented along with an example application to the same model system, the double-gyre flow. Furthermore, we highlight a number of exciting applications and future directions to bring Lagrangian based analysis closer to implementation in real-time, real-world decision making strategies.

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Section: A Finite-time Lyapunov Exponentsmentioning

confidence: 99%

Lagrangian based methods for coherent structure detection

Allshouse

Peacock

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The algorithms are developed as part of the open-source CoherentStructures.jl project. These methods in principle scale well with the size of the domain, but existing implementations related to the publications [32,29,20,38] failed to fully leverage this; we therefore had to make significant conceptual and implementation modifications.…”

Section: Introductionmentioning

confidence: 99%

“…Conceptually, our work is based on the index-theory-based methodology developed in [29], whose implementation was a mixture of methods implemented in [11,32,20]. In [38], Serra & Haller identified (i) the detection of tensor field singularities (points of repeated tensor eigenvalues) of tensor fields and (ii) the identification of their topological type as major computational bottlenecks in the implementation of [29]. Moreover, these steps required a number of parameters whose choice had-at times-unpredictable impact on the computational outcome.…”

Section: Introductionmentioning

confidence: 99%

“…In our implementation, we have carefully addressed the issues raised by [38] regarding the implementation of [29]. Specifically, we have improved a number of aspects related to the (inherently robust) topological index-theory-based methods.…”

Section: Introductionmentioning

confidence: 99%

“…

We describe a new method for computing coherent Lagrangian vortices in two-dimensional flows according to any of the following approaches: blackhole vortices [23], objective Eulerian Coherent Structures (OECSs) [37], material barriers to diffusive transport [24,25], and constrained diffusion barriers [25]. The method builds on ideas developed previously in [29], but our implementation alleviates a number of shortcomings and allows for the fully automated detection of such vortices on unprecedentedly challenging real-world flow problems, for which specific human interference is absolutely infeasible. Challenges include very large domains and/or parameter spaces.

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mentioning

confidence: 99%

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Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains

Karrasch¹,

Schilling²

2020

The SMAI Journal of Computational Mathematics

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The life cycle of a coherent Lagrangian Agulhas ring

2016

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Abstract. We document the long-term evolution of an Agulhas ring detected from satellite altimetry using a technique from nonlinear dynamical systems that enables objective (i.e., observer-independent) eddy framing. Such objectively detected eddies have Lagrangian (material) boundaries that remain coherent (unfilamented) over the detection period. The ring preserves a quite compact material entity for a period of about 2 years even after most initial coherence is lost within 5 months after detection. We attribute this to the successive development of short-term coherent material boundaries around the ring. These boundaries provide effective short-term shielding for the ring, which prevents a large fraction of the ring's interior from being mixed with the ambient turbulent flow. We show that such coherence regain events cannot be inferred from Eulerian analysis. This process is terminated by a ring-splitting event which marks the ring demise, near the South American coast. The genesis of the ring is characterized by a ring-merging event away from the Agulhas retroflection, followed by a 4-month-long partial coherence stage, scenario that is quite different than a simple current occlusion and subsequent eddy pinch off.

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Automated detection of coherent Lagrangian vortices in two-dimensional unsteady flows

Cited by 50 publications

References 36 publications

Lagrangian based methods for coherent structure detection

Lagrangian based methods for coherent structure detection

Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains

The life cycle of a coherent Lagrangian Agulhas ring

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