Finite-Time Transport Structures of Flow Fields

Shi, Kuangyu; Theisel, Holger; Weinkauf, Tino; Hege, Hans Christian; Seide, H.-P.

doi:10.1109/pacificvis.2008.4475460

Cited by 6 publications

(3 citation statements)

References 27 publications

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“…In a fundamental article, Haller used FTLE to explore velocity fields of the fluid flow and discovered their link to LCS; this link may offer information on flow separation akin to the separatrices of vector field topology [47,48]. Analyses by Green et al [49] and Shi et al [50] provide evidence for this claim. It is revealed that FTLEs deliver more information than LCS in a number of analytical and numerical flow disciplines, and it has also been discovered that FTLEs generate more detail than LCS.…”

Section: Finite-time Lyapunov Exponentsmentioning

confidence: 99%

Understanding Flow around Planetary Moons via Finite-Time Lyapunov Exponent Maps

Canales,

Howell

2024

Preprint

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This contribution focuses on the use of finite-time Lyapunov exponent (FTLE) maps to investigate spacecraft motion within the context of the circular restricted three-body problem. The authors expose some of the advantages and shortcomings of FTLE maps and illustrate their use by examining the motion in the vicinity of a moon; in particular, the Jovian moons, Ganymede and Europa. The behavior of trajectories in the vicinity of the moons and the factors that influence their construction are examined. The authors also explore the symmetry relationships of the Lagrangian coherent structures that are defined within the FTLE maps. It is useful to establish relationships between initial conditions within the FTLE maps to understand particular trajectory behaviors in the neighborhoods of moons. The results demonstrate that, by utilizing FTLE maps, a better understanding of spacecraft behavior in the vicinity of celestial bodies emerges, enabling more accurate mission planning and execution.

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Section: Finite-time Lyapunov Exponentsmentioning

confidence: 99%

Understanding Flow around Planetary Moons via Finite-Time Lyapunov Exponent Maps

Canales,

Howell

2024

Preprint

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“…Theisel et al [TWHS04] and Shi et al [STW*06] analyzed the behavior of path lines and suggested a definition of time‐dependent VFT for the special case of periodic vector fields. Shi et al [STW*08] suggest to analyze the Poincaré map of the velocity field, which allows to find critical points in time‐periodic data sets such as the Petri Dish and the Double Gyre example discussed later.…”

Section: Related Workmentioning

confidence: 99%

Toward a Lagrangian Vector Field Topology

Fuchs

Kemmler

Schindler

et al. 2010

Computer Graphics Forum

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In this paper we present an extended critical point concept which allows us to apply vector field topology in the case of unsteady flow. We propose a measure for unsteadiness which describes the rate of change of the velocities in a fluid element over time. This measure allows us to select particles for which topological properties remain intact inside a finite spatio-temporal neighborhood. One benefit of this approach is that the classification of critical points based on the eigenvalues of the Jacobian remains meaningful. In the steady case the proposed criterion reduces to the classical definition of critical points. As a first step we show that finding an optimal Galilean frame of reference can be obtained implicitly by analyzing the acceleration field. In a second step we show that this can be extended by switching to the Lagrangian frame of reference. This way the criterion can detect critical points moving along intricate trajectories. We analyze the behavior of the proposed criterion based on two analytical vector fields for which a correct solution is defined by their inherent symmetries and present results for numerical vector fields.

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“…Researchers are primarily focused on visualization methodologies 23–25; the LCS location is calculated through ridge detection algorithms but no characterization of the structure is provided. Shi et al 26 adopt a path‐line integral convolution approach to calculate the LCS location and uncover the dynamical information of flow transport. Pekiert and Sadlo 27 present an algorithm able to detect ridge points without using eigenvalues; this approach can have a beneficial impact on the computation time.…”

Section: Introductionmentioning

confidence: 99%

Detection and characterization of transport barriers in complex flows via ridge extraction of the finite time Lyapunov exponent field

Senatore

Ross

2010

Numerical Meth Engineering

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SUMMARYThis paper proposes an algorithm to detect and characterize ridges in the finite time Lyapunov exponent (FTLE) field obtained from a continuous dynamical system or flow. These ridges represent time-dependent separatrices of the flow and are also called Lagrangian coherent structures (LCS). LCS have been demonstrated to be an effective way to analyze realistic time-chaotic flows, although they can be quite complex. Therefore, in order to exploit the information that LCS can provide it is important to locate and characterize these structures in a systematic way. This can be accomplished by interpreting the FTLE as a height field and detecting the LCS as ridges of this graph. Methodologies developed in the image processing framework are integrated with dynamical system inspired approaches in order to characterize ridge strength and location. The main novel contribution of the proposed algorithm is a scheme to connect sets of points into curves or surfaces (rather than distributions of points around a ridge axis) and classify these curves or surfaces using a dynamical systems measure of strength. This approach provides the capability to track ranked LCS in space and time. The results are presented for a simple analytical model and noisy LCS from realistic three-dimensional geophysical fluid data.

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Finite-Time Transport Structures of Flow Fields

Cited by 6 publications

References 27 publications

Understanding Flow around Planetary Moons via Finite-Time Lyapunov Exponent Maps

Understanding Flow around Planetary Moons via Finite-Time Lyapunov Exponent Maps

Toward a Lagrangian Vector Field Topology

Detection and characterization of transport barriers in complex flows via ridge extraction of the finite time Lyapunov exponent field

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