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

• 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
• DOI: 10.1109/TVCG.2016.2534560

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.