Transport in time-dependent dynamical systems: Finite-time coherent sets

TL;DR

This paper introduces a new probabilistic method using transfer operators to identify regions in nonautonomous chaotic systems that remain coherent over finite times, demonstrated on atmospheric flow data.

Contribution

A novel, simple transfer operator-based approach for detecting finite-time coherent sets in nonautonomous chaotic dynamical systems.

Findings

Successfully applied to idealized stratospheric flow

Analyzed European ECMWF reanalysis data in 2D and 3D

Method effectively identifies coherent regions despite chaos

Abstract

We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time, despite the chaotic nature of the system. We develop a novel probabilistic methodology based upon transfer operators that automatically detects maximally coherent sets. The approach is very simple to implement, requiring only singular vector computations of a matrix of transitions induced by the dynamics. We illustrate our new methodology on an idealized stratospheric flow and in two and three dimensional analyses of European Centre for Medium Range Weather Forecasting (ECMWF) reanalysis data.