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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Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics Vol. 22; no. 6; pp. 1672 - 1682
Main Authors: Hanqi Guo, Wenbin He, Peterka, Tom, Han-Wei Shen, Collis, Scott M., Helmus, Jonathan J.
Format: Journal Article
Language:English
Published: United States IEEE 01.06.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1077-2626
1941-0506
1941-0506
DOI:10.1109/TVCG.2016.2534560