|Title||Finite-Time Lyapunov Exponents and Lagrangian Coherent Structures in Uncertain Unsteady Flows |
|Publication Type||Journal Article |
|Year of Publication||2015 |
|Authors||Guo, H, He, W, Peterka, T, Shen, H |
|Journal||IEEE Transactions of Visualization and Computer Graphics |
|Date Published||2016 |
|Other Numbers||ANL/MCS-P5414-1015 |
|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.