Finite-Time Lyapunov Exponents and Lagrangian Coherent Structures in Uncertain Unsteady Flows

The objective of this paper is to understand transport behavior in uncertain time-varying flow fields by redefining the finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structure (LCS) as stochastic counterparts of their traditional deterministic definitions. Three new concepts are intro...

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Veröffentlicht in:IEEE transactions on visualization and computer graphics Jg. 22; H. 6; S. 1672 - 1682
Hauptverfasser: Hanqi Guo, Wenbin He, Peterka, Tom, Han-Wei Shen, Collis, Scott M., Helmus, Jonathan J.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.06.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Atmospheric measurements
Behavior
Coherence
Computer simulation
Data visualization
Divergence
Lagrangian coherent structures
Liapunov exponents
Lyapunov exponents
Meteorology
Particle measurements
Probability density functions
Ridges
Statistical analysis
stochastic particle tracing
Stochasticity
Three-dimensional displays
Topology
Transport
Uncertain flow visualization
Uncertainty
Unsteady flow
Uncertain flow visualization
stochastic particle tracing
Lagrangian coherent structures
ISSN:1077-2626, 1941-0506, 1941-0506
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Abstract The objective of this paper is to understand transport behavior in uncertain time-varying flow fields by redefining the finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structure (LCS) as stochastic counterparts of their traditional deterministic definitions. Three new concepts are introduced: the distribution of the FTLE (D-FTLE), the FTLE of distributions (FTLE-D), and uncertain LCS (U-LCS). The D-FTLE is the probability density function of FTLE values for every spatiotemporal location, which can be visualized with different statistical measurements. The FTLE-D extends the deterministic FTLE by measuring the divergence of particle distributions. It gives a statistical overview of how transport behaviors vary in neighborhood locations. The U-LCS, the probabilities of finding LCSs over the domain, can be extracted with stochastic ridge finding and density estimation algorithms. We show that our approach produces better results than existing variance-based methods do. Our experiments also show that the combination of D-FTLE, FTLE-D, and U-LCS can help users understand transport behaviors and find separatrices in ensemble simulations of atmospheric processes.
AbstractList The objective of this paper is to understand transport behavior in uncertain time-varying flow fields by redefining the finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structure (LCS) as stochastic counterparts of their traditional deterministic definitions. Three new concepts are introduced: the distribution of the FTLE (D-FTLE), the FTLE of distributions (FTLE-D), and uncertain LCS (U-LCS). The D-FTLE is the probability density function of FTLE values for every spatiotemporal location, which can be visualized with different statistical measurements. The FTLE-D extends the deterministic FTLE by measuring the divergence of particle distributions. It gives a statistical overview of how transport behaviors vary in neighborhood locations. The U-LCS, the probabilities of finding LCSs over the domain, can be extracted with stochastic ridge finding and density estimation algorithms. We show that our approach produces better results than existing variance-based methods do. Our experiments also show that the combination of D-FTLE, FTLE-D, and U-LCS can help users understand transport behaviors and find separatrices in ensemble simulations of atmospheric processes.
The objective of this paper is to understand transport behavior in uncertain time-varying flow fields by redefining the finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structure (LCS) as stochastic counterparts of their traditional deterministic definitions. Three new concepts are introduced: the distribution of the FTLE (D-FTLE), the FTLE of distributions (FTLE-D), and uncertain LCS (U-LCS). The D-FTLE is the probability density function of FTLE values for every spatiotemporal location, which can be visualized with different statistical measurements. The FTLE-D extends the deterministic FTLE by measuring the divergence of particle distributions. It gives a statistical overview of how transport behaviors vary in neighborhood locations. The U-LCS, the probabilities of finding LCSs over the domain, can be extracted with stochastic ridge finding and density estimation algorithms. We show that our approach produces better results than existing variance-based methods do. Our experiments also show that the combination of D-FTLE, FTLE-D, and U-LCS can help users understand transport behaviors and find separatrices in ensemble simulations of atmospheric processes.The objective of this paper is to understand transport behavior in uncertain time-varying flow fields by redefining the finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structure (LCS) as stochastic counterparts of their traditional deterministic definitions. Three new concepts are introduced: the distribution of the FTLE (D-FTLE), the FTLE of distributions (FTLE-D), and uncertain LCS (U-LCS). The D-FTLE is the probability density function of FTLE values for every spatiotemporal location, which can be visualized with different statistical measurements. The FTLE-D extends the deterministic FTLE by measuring the divergence of particle distributions. It gives a statistical overview of how transport behaviors vary in neighborhood locations. The U-LCS, the probabilities of finding LCSs over the domain, can be extracted with stochastic ridge finding and density estimation algorithms. We show that our approach produces better results than existing variance-based methods do. Our experiments also show that the combination of D-FTLE, FTLE-D, and U-LCS can help users understand transport behaviors and find separatrices in ensemble simulations of atmospheric processes.
Author Helmus, Jonathan J.
Peterka, Tom
Wenbin He
Han-Wei Shen
Collis, Scott M.
Hanqi Guo
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  surname: Wenbin He
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  surname: Han-Wei Shen
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  email: shen.94@osu.edu
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SubjectTerms Algorithms
Atmospheric measurements
Behavior
Coherence
Computer simulation
Data visualization
Divergence
Lagrangian coherent structures
Liapunov exponents
Lyapunov exponents
Meteorology
Particle measurements
Probability density functions
Ridges
Statistical analysis
stochastic particle tracing
Stochasticity
Three-dimensional displays
Topology
Transport
Uncertain flow visualization
Uncertainty
Unsteady flow
Title Finite-Time Lyapunov Exponents and Lagrangian Coherent Structures in Uncertain Unsteady Flows
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