title: Finite-Time Lyapunov Exponents and Lagrangian Coherent Structures in Uncertain Unsteady Flows.
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.
authors.forename: Hanqi
authors.initials: H
authors.lastname: Guo
authors.forename: Wenbin
authors.initials: W
authors.lastname: He
authors.forename: Tom
authors.initials: T
authors.lastname: Peterka
authors.forename: Han-Wei
authors.initials: HW
authors.lastname: Shen
authors.forename: Scott
authors.initials: S
authors.lastname: Collis
authors.forename: Jonathan
authors.initials: J
authors.lastname: Helmus