Detection of evolving Lagrangian coherent structures: A multiple object tracking approach

MacMillan, Theodore; Ouellette, Nicholas T.; Richter, David H.

doi:10.1103/physrevfluids.5.124401

Cited by 5 publications

(5 citation statements)

References 18 publications

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“…The evolving network approach works well when sufficiently strong spectral gaps exist such that short-term variations due to systematic errors or noise do not cause the recent clustering to deviate strongly from the preceding one, such as also required in Ref. 35.…”

Section: B Evolving Cluster Approachmentioning

confidence: 99%

“…These similarity measures quickly become meaningless due to turbulent dispersion, causing Lagrangian approaches to fail for long-term investigations in fully turbulent flows. One first attempt to overcome this problem is to follow coherent sets from short-time computations by means of a multiple object tracking method 35 . However, such procedure strongly relies on the capability of the underlying clustering algorithm to identify reliable structures.…”

Section: Introductionmentioning

confidence: 99%

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Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows

Schneide,

Vieweg,

Schumacher

et al. 2021

Preprint

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We explore the transport mechanisms of heat in two-and three-dimensional turbulent convection flows by means of the long-term evolution of Lagrangian coherent sets. They are obtained from the spectral clustering of trajectories of massless fluid tracers that are advected in the flow. Coherent sets result from trajectories that stay closely together under the dynamics of the turbulent flow. For longer times, they are always destroyed by the intrinsic turbulent dispersion of material transport. Here, this constraint is overcome by the application of evolutionary clustering algorithms that add a time memory to the coherent set detection and allow individual trajectories to leak in or out of evolving clusters. Evolutionary clustering thus also opens the possibility to monitor the splits and mergers of coherent sets. These rare dynamic events leave clear footprints in the evolving eigenvalue spectrum of the Laplacian matrix of the trajectory network in both convection flows. The Lagrangian trajectories reveal the individual pathways of convective heat transfer across the fluid layer.We identify the long-term coherent sets as those fluid flow regions that contribute least to heat transfer. Thus, our evolutionary framework defines a complementary perspective on the slow dynamics of turbulent superstructure patterns in convection flows that were recently discussed in the Eulerian frame of reference. The presented framework might be well suited for studies in natural flows which are typically based on sparse information from drifters and probes.

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Section: B Evolving Cluster Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows

Schneide,

Vieweg,

Schumacher

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The question of determining when coherent structures are born and when they die is largely unaddressed in the dynamical systems literature. To quote MacMillan et al [45]: "One major shortcoming of these (LCS) techniques, however, is the lack of an objective procedure for identifying time scales of interest, or an ability to characterise the lives, deaths, or age of coherent structures, especially when relevant flow time scales are larger than the time scales associated with coherence." Several previous studies have investigated lifetimes in the context of ocean eddies, for example, Froyland et al [20] first identified a suitable timescale and then carried out a series of FTCS computations on time windows sliding forward in time, Andrade et al [3] exhaustively search a discretised twoparameter space (𝑡, 𝑇) where 𝑡 is the initial time and 𝑇 is the flow duration, using these pairs as variable inputs to many separate LCS computations.…”

Section: Introductionmentioning

confidence: 99%

“…To quote MacMillan et al. [45]: “One major shortcoming of these (LCS) techniques, however, is the lack of an objective procedure for identifying time scales of interest, or an ability to characterise the lives, deaths, or age of coherent structures, especially when relevant flow time scales are larger than the time scales associated with coherence.” Several previous studies have investigated lifetimes in the context of ocean eddies, for example, Froyland et al. [20] first identified a suitable timescale and then carried out a series of FTCS computations on time windows sliding forward in time, Andrade et al.…”

Section: Introductionmentioning

confidence: 99%

Detecting the birth and death of finite‐time coherent sets

Froyland

Koltai

2023

Comm Pure Appl Math

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Finite‐time coherent sets (FTCSs) are distinguished regions of phase space that resist mixing with the surrounding space for some finite period of time; physical manifestations include eddies and vortices in the ocean and atmosphere, respectively. The boundaries of FTCSs are examples of Lagrangian coherent structures (LCSs). The selection of the time duration over which FTCS and LCS computations are made in practice is crucial to their success. If this time is longer than the lifetime of coherence of individual objects then existing methods will fail to detect the shorter‐lived coherence. It is of clear practical interest to determine the full lifetime of coherent objects, but in complicated practical situations, for example a field of ocean eddies with varying lifetimes, this is impossible with existing approaches. Moreover, determining the timing of emergence and destruction of coherent sets is of significant scientific interest. In this work we introduce new constructions to address these issues. The key components are an inflated dynamic Laplace operator and the concept of semi‐material FTCSs. We make strong mathematical connections between the inflated dynamic Laplacian and the standard dynamic Laplacian, showing that the latter arises as a limit of the former. The spectrum and eigenfunctions of the inflated dynamic Laplacian directly provide information on the number, lifetimes, and evolution of coherent sets.

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“…The question of determining when coherent structures are born and when they die is largely unaddressed in the dynamical systems literature. To quote MacMillan et al [MOR20]: "One major shortcoming of these (LCS) techniques, however, is the lack of an objective procedure for identifying time scales of interest, or an ability to characterise the lives, deaths, or age of coherent structures, especially when relevant flow time scales are larger than the time scales associated with coherence." Several previous studies have investigated lifetimes in the context of ocean eddies, e.g.…”

Section: Introductionmentioning

confidence: 99%

Detecting the birth and death of finite-time coherent sets

Froyland¹,

Koltai²

2021

Preprint

View full text Add to dashboard Cite

Finite-time coherent sets (FTCSs) are distinguished regions of phase space that resist mixing with the surrounding space for some finite period of time; physical manifestations include eddies and vortices in the ocean and atmosphere, respectively. The boundaries of finite-time coherent sets are examples of Lagrangian coherent structures (LCSs). The selection of the time duration over which FTCS and LCS computations are made in practice is crucial to their success. If this time is longer than the lifetime of coherence of individual objects then existing methods will fail to detect the shorter-lived coherence. It is of clear practical interest to determine the full lifetime of coherent objects, but in complicated practical situations, for example a field of ocean eddies with varying lifetimes, this is impossible with existing approaches. Moreover, determining the timing of emergence and destruction of coherent sets is of significant scientific interest. In this work we introduce new constructions to address these issues. The key components are an inflated dynamic Laplace operator and the concept of semi-material FTCSs. We make strong mathematical connections between the inflated dynamic Laplacian and the standard dynamic Laplacian [Fro15], showing that the latter arises as a limit of the former. The spectrum and eigenfunctions of the inflated dynamic Laplacian directly provide information on the number, lifetimes, and evolution of coherent sets.

show abstract

Detection of evolving Lagrangian coherent structures: A multiple object tracking approach

Cited by 5 publications

References 18 publications

Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows

Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows

Detecting the birth and death of finite‐time coherent sets

Detecting the birth and death of finite-time coherent sets

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