From large deviations to semidistances of transport and mixing: coherence analysis for finite Lagrangian data

Abstract

One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time and space semidistance that comes from the "best" approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, hence they occur as extremal regions on a spanning structure of the state space under this semidistance---in fact, under any distance measure arising from the physical notion of transport. Based on this notion we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases.

J Nonlinear Sci, 2018

References in corpus (10)

• A Spectral Clustering Approach to Lagrangian Vortex Detection
• Vortex flow generated by a magnetic stirrer
• On the Lagrangian Dynamics of Atmospheric Zonal Jets and the Permeability of the Stratospheric Polar Vortex
• Geometry of the ergodic quotient reveals coherent structures in flows
• Understanding the geometry of transport: diffusion maps for Lagrangian trajectory data unravel coherent sets
• Coherent structure coloring: identification of coherent structures from sparse data using graph theory
• A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds
• Estimating long-term behavior of periodically driven flows without trajectory integration
• Lagrangian transport through surfaces in volume-preserving flows
• Finite-time Partitions for Lagrangian Structure Identification in Gulf Stream Eddy Transport

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