Transport in Transitory Dynamical Systems

Abstract

We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case. This requires knowing only the "action" of relevant heteroclinic orbits at the intersection of invariant manifolds of "forward" and "backward" hyperbolic orbits. These manifolds can be easily computed by leveraging the autonomous nature of the vector fields on either side of the time-dependent transition. As illustrative examples we consider a two-dimensional fluid flow in a rotating double-gyre configuration and a simple one-and-a-half degree of freedom model of a resonant particle accelerator. We compare our results to those obtained using finite-time Lyapunov exponents and to adiabatic theory, discussing the benefits and limitations of each method.

Updated and corrected version. LaTeX, 29 pages, 21 figures

References in corpus (3)

• Finite-time Lagrangian transport analysis: Stable and unstable manifolds of hyperbolic trajectories and finite-time Lyapunov exponents
• The turnstile mechanism across the Kuroshio current: analysis of dynamics in altimeter velocity fields
• Evolutionary phase space in driven elliptical billiards

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• The Lagrangian description of aperiodic flows: a case study of the Kuroshio Current
• A Geometric Heat-Flow Theory of Lagrangian Coherent Structures
• A Study in Three-Dimensional Chaotic Dynamics: Granular Flow and Transport in a Bi-Axial Spherical Tumbler
• From large deviations to semidistances of transport and mixing: coherence analysis for finite Lagrangian data
• Local stable and unstable manifolds and their control in nonautonomous finite-time flows
• Transport in Transitory, Three-Dimensional, Liouville Flows
• Quantifying the role of folding in nonautonomous flows: the unsteady Double-Gyre
• Mesochronic classification of trajectories in incompressible 3D vector fields over finite times
• Analysis of adiabatic trapping phenomena for quasi-integrable area-preserving maps in the presence of time-dependent exciters