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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Vydané v:	IEEE transactions on visualization and computer graphics Ročník 22; číslo 6; s. 1672 - 1682
Hlavní autori:	Hanqi Guo, Wenbin He, Peterka, Tom, Han-Wei Shen, Collis, Scott M., Helmus, Jonathan J.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States IEEE 01.06.2016 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	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
Author_xml	– sequence: 1 surname: Hanqi Guo fullname: Hanqi Guo email: hguo@anl.gov organization: Math. & Comput. Sci. Div., Argonne Nat. Lab., Lemont, IL, USA – sequence: 2 surname: Wenbin He fullname: Wenbin He email: he.495@buckeyemail.osu.edu organization: Dept. of Comput. Sci. & Eng., Ohio State Univ., Columbus, OH, USA – sequence: 3 givenname: Tom surname: Peterka fullname: Peterka, Tom email: tpeterka@mcs.anl.gov organization: Math. & Comput. Sci. Div., Argonne Nat. Lab., Lemont, IL, USA – sequence: 4 surname: Han-Wei Shen fullname: Han-Wei Shen email: shen.94@osu.edu organization: Dept. of Comput. Sci. & Eng., Ohio State Univ., Columbus, OH, USA – sequence: 5 givenname: Scott M. surname: Collis fullname: Collis, Scott M. email: scollis@anl.gov organization: Environ. Sci. Div., Argonne Nat. Lab., Lemont, IL, USA – sequence: 6 givenname: Jonathan J. surname: Helmus fullname: Helmus, Jonathan J. email: jhelmus@anl.gov organization: Environ. Sci. Div., Argonne Nat. Lab., Lemont, IL, USA
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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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