Capturing deviation from ergodicity at different scales

Scott, Sherry E.; Redd, Thomas C.; Kuznetsov, L.; Mezić, Igor; Jones, Christopher K. R. T.

doi:10.1016/j.physd.2009.05.003

Cited by 23 publications

(23 citation statements)

References 11 publications

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“…Other options include the combined function g • b being the instantaneous eigenvector field of the variational equation [41], or a set of indicator functions over spatial boxes in order to define trajectory's "correlation dimension" or "ergodicity defect" [64,50]. Averages of the form (4) are also relevant to determining dispersion statistics [65], which are expected to be different in different coherent regions of a fluid.…”

Section: Lcs Diagnostic Methodsmentioning

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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Section: Lcs Diagnostic Methodsmentioning

confidence: 99%

Generalized Lagrangian coherent structures

Balasuriya

Ouellette

Rypina

2018

Physica D: Nonlinear Phenomena

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“…Our results confirm the importance of studying coherent structures in zones in addition to focusing on finding the location of the barriers. Applying the recent results of geodesic LCS theory [19] or using the probabilistic approach based on transfer operators [20] to improve the objectivity in domain partitions may bring further insights on the statistics we obtain here. Such studies will be reported elsewhere.…”

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confidence: 85%

Finite-time statistics of scalar diffusion in Lagrangian coherent structures

Tang

Walker

2012

Phys. Rev. E

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We study the variability of passive scalar diffusion via the statistics of stochastic particle dispersion in a chaotic flow. We find that at intermediate times when the statistics of individual trajectories start to exhibit scaling-law behaviors, scalar variance over the entire domain exhibits multimodal structure. We demarcate the domain based on Lagrangian coherent structures and find that the conditional statistics exhibit strong unimodal behavior, indicating coherence of effective diffusion among each Lagrangian partition of the flow.

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“…The second complexity measure considered here is the ergodicity defect d that was recently introduced by Scott et al (2009). d measures the extent to which the dynamical system and the corresponding map falls short of being ergodic using the "time average equals space average" view of ergodicity (Petersen, 1983;Lasota and Mackey, 1994).…”

Section: Two Complexity Measures and The Relationship Between Themmentioning

confidence: 99%

“…d measures the extent to which the dynamical system and the corresponding map falls short of being ergodic using the "time average equals space average" view of ergodicity (Petersen, 1983;Lasota and Mackey, 1994). The ergodicity defect was originally introduced in the context of illustrative (mathematical) maps in Scott et al (2009) and the theory behind it is further developed in (Scott, 2010(Scott, , 2011b. Here we extend the notion of ergodicity defect to fluid particle trajectories in geophysical fluid flows.…”

Section: Two Complexity Measures and The Relationship Between Themmentioning

confidence: 99%

Investigating the connection between complexity of isolated trajectories and Lagrangian coherent structures

Rypina

Scott

Pratt

et al. 2011

Nonlin. Processes Geophys.

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Abstract. It is argued that the complexity of fluid particle trajectories provides the basis for a new method, referred to as the Complexity Method (CM), for estimation of Lagrangian coherent structures in aperiodic flows that are measured over finite time intervals. The basic principles of the CM are explained and the CM is tested in a variety of examples, both idealized and realistic, and in different reference frames. Two measures of complexity are explored in detail: the correlation dimension of trajectory, and a new measure -the ergodicity defect. Both measures yield structures that strongly resemble Lagrangian coherent structures in all of the examples considered. Since the CM uses properties of individual trajectories, and not separation rates between closely spaced trajectories, it may have advantages for the analysis of ocean float and drifter data sets in which trajectories are typically widely and non-uniformly spaced.

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Capturing deviation from ergodicity at different scales

Cited by 23 publications

References 11 publications

Generalized Lagrangian coherent structures

Generalized Lagrangian coherent structures

Finite-time statistics of scalar diffusion in Lagrangian coherent structures

Investigating the connection between complexity of isolated trajectories and Lagrangian coherent structures

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