Finite-time Lyapunov exponents in the instantaneous limit and material transport

Nolan, Peter J.; Serra, Mattia; Ross, Shane D.

doi:10.1007/s11071-020-05713-4

Cited by 32 publications

(34 citation statements)

References 90 publications

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“…For , the instantaneous of limit of the FTLE field is the maximal rate-of-strain eigenvalue with the rate-of-strain tensor defined in (7.25 a , b ), as noted by Serra & Haller (2016) and Nolan, Serra & Ross (2020). This eigenvalue field can, in principle, be used to detect objective Eulerian coherent structures (OECS) as instantaneous limits of LCS.…”

Section: Practical Implementation Of Active Barrier Identificationmentioning

confidence: 99%

Objective barriers to the transport of dynamically active vector fields

et al. 2020

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Section: Practical Implementation Of Active Barrier Identificationmentioning

confidence: 99%

Objective barriers to the transport of dynamically active vector fields

et al. 2020

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“…Superimposed on the Q s field are the attracting (blue) and repelling (red) instantaneous hyperbolic LCSs, material lines within the flow where the attraction and repulsion of each species will be maximized. These features were obtained using a ridge detection algorithm [36] (an averaging or coarse-graining procedure could be performed, revealing fewer structures [11,44,45]). In the top center, we show the species amount for water vapor 3 h later, at 18:00, with the 15:00 −s 1 and s 2 ridgelines advected to 18:00.…”

Section: Resultsmentioning

confidence: 99%

“…In [35], it was shown that the Eulerian rate-of-strain tensor can provide an instantaneous approximation of the Lagrangian dynamics of a fluid flow and states that one should seek objective Eulerian coherent structures (OECSs) based on it, as short-term limits of LCSs. Further work on this topic [36] also showed that in two-dimensional flows, the minimum and maximum eigenvalues of the Eulerian rate-of-strain tensor are the limits of the backward-time and forward-time FTLE fields, respectively, as integration (advection) time goes to zero. Nolan et al [36] posited that the trenches of the minimum eigenvalue field can be identified as instantaneous attracting LCSs and the ridges of the maximum eigenvalue field can be identified as instantaneous repelling LCSs.…”

Section: Eulerian-lagrangian Analysismentioning

confidence: 98%

“…Further work on this topic [36] also showed that in two-dimensional flows, the minimum and maximum eigenvalues of the Eulerian rate-of-strain tensor are the limits of the backward-time and forward-time FTLE fields, respectively, as integration (advection) time goes to zero. Nolan et al [36] posited that the trenches of the minimum eigenvalue field can be identified as instantaneous attracting LCSs and the ridges of the maximum eigenvalue field can be identified as instantaneous repelling LCSs. For the remainder of the paper, we shall refer to the minimum and maximum eigenvalues of the Eulerian rate-of-strain tensor as the attraction and repulsion rates, respectively, and both can be considered as instantaneous, rather than finite-time, Lyapunov exponents.…”

Section: Eulerian-lagrangian Analysismentioning

confidence: 98%

“…The FTLE measures the rate of separation of two nearby fluid parcels in a flow over the time horizon T. Ridges of the σ s [t 0 ,t 0 +T] (x 0 ) field for T < 0 identify regions of the flow that are the most attracting over the time interval [t 0 , t 0 + T]. Furthermore, in [36], it was demonstrated that the −s s 1 (x 0 , t 0 ) field (with the minus sign) was the limit of the σ s [t 0 ,t 0 +T] (x 0 ) field as T → 0. Thus, the attraction rate field, −s s 1 (x 0 , t 0 ), provides a computationally inexpensive instantaneous approximation of the main attracting curves, as it is based on a single velocity snapshot, and no particle trajectory integration is necessary.…”

Section: Computation Of the Lagrangian Trajectory-averaged Attractionmentioning

confidence: 99%

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Finite-time Lyapunov exponents in the instantaneous limit and material transport

Cited by 32 publications

References 90 publications

Objective barriers to the transport of dynamically active vector fields

Objective barriers to the transport of dynamically active vector fields

Pollution Transport Patterns Obtained Through Generalized Lagrangian Coherent Structures

Climate change in mechanical systems: the snapshot view of parallel dynamical evolutions

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