Lagrangian coherent structures separate dynamically distinct regions in fluid flows

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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“…It was found that shrink lines delineate regions where energy moves up and down the energy cascade. 46 …”

Section: Applications Of the Geometric Approachmentioning

confidence: 99%

Lagrangian based methods for coherent structure detection

Allshouse

Peacock

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…FTLE and FSLE methods have seen wide usage in both experimental [37,38,39,40] and observational [42,43,47,83,84,85,46,49,50,51] contexts.…”

Section: Lcs Diagnostic Methodsmentioning

confidence: 99%

“…The key point is whatever the definitions of LCSs, their formulation is typically (with a few exceptions, such as, for example, the burning manifolds of [32,33,34,35,36]) based solely on the Lagrangian trajectories associated with (1), and the goal is to identify fluid parcel groups that behave similarly, and are thus 'coherent.' This has been a rich area of study using both experimental [37,38,39,40] and observational [41,42,43,44,45,46,47,48,49,50,51,52,53] data.…”

Section: Introductionmentioning

confidence: 99%

Generalized Lagrangian coherent structures

Balasuriya

Ouellette

Rypina

2018

Physica D: Nonlinear Phenomena

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The notion of a Lagrangian Coherent Structure (LCS) is by now well established as a way to capture transient coherent transport dynamics in unsteady and aperiodic fluid flows that are known over finite time. We show that the concept of an LCS can be generalized to capture coherence in other quantities of interest that are transported by, but not fully locked to, the fluid. Such quantities include those with dynamic, biological, chemical, or thermodynamic relevance, such as temperature, pollutant concentration, vorticity, kinetic energy, plankton density, and so on. We provide a conceptual framework for identifying the Generalized Lagrangian Coherent Structures (GLCSs) associated with such evolving quantities. We show how LCSs can be seen as a special case within this framework, and provide an overarching discussion of various methods for identifying LCSs. The utility of this more general viewpoint is highlighted through a variety of examples. We also show that although LCSs approximate GLCSs in certain limiting situations under restrictive assumptions on how the velocity field affects the additional quantities of interest, LCSs are not in general sufficient to describe their coherent transport.

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“…Lagrangian stretching and FTLEs have been used extensively to approximate the locations of barriers to the movement of non-reacting species [37][38][39][40] and are closely related to Lagrangian Coherent Structures, 41,42 which are also calculated using C tþT t . FTLEs have also been considered in ARD systems.…”

Section: Introductionmentioning

confidence: 99%

Optimal stretching in the reacting wake of a bluff body

Wang

Tithof

Nevins

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We experimentally study spreading of the Belousov-Zhabotinsky reaction behind a bluff body in a laminar flow. Locations of reacted regions (i.e., regions with high product concentration) correlate with a moderate range of Lagrangian stretching and that range is close to the range of optimal stretching previously observed in topologically different flows [T. D. Nevins and D. H. Kelley, Phys. Rev. Lett. 117, 164502 (2016)]. The previous work found optimal stretching in a closed, vortex dominated flow, but this article uses an open flow and only a small area of appreciable vorticity. We hypothesize that optimal stretching is common in advection-reaction-diffusion systems with an excitation threshold, including excitable and bistable systems, and that the optimal range depends on reaction chemistry and not on flow shape or characteristic speed. Our results may also give insight into plankton blooms behind islands in ocean currents.

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Lagrangian coherent structures separate dynamically distinct regions in fluid flows

Cited by 34 publications

References 23 publications

Lagrangian based methods for coherent structure detection

Lagrangian based methods for coherent structure detection

Generalized Lagrangian coherent structures

Optimal stretching in the reacting wake of a bluff body

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