The notion of a Lagrangian Coherent Structure (LCS) is by now well established as a way to
capture transient coherent transport dynamics in unsteady and aperiodic fluid flows that are …

High-resolution ocean velocity data has become readily available since the introduction of
very high frequency (VHF) radar technology. The vast amount of data generated so far …

The method of invariant manifolds was originally developed for hyperbolic rest points of
autonomous equations. It was then extended from fixed points to arbitrary solutions and from …

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 …

Transitionally turbulent flows frequently exhibit spatiotemporal intermittency, reflecting a
complex interplay between driving forces, dissipation, and transport present in these …

Over the past several years, there has been an explosion of interest in analyzing flow
barriers in fluids. This has been driven by a variety of reasons. One is a concern for our …

Transport in laminar flows is governed by chaotic stirring and striation in long thin filaments.
In turbulent flows, isotropic mixing dominates and tracers behave like stochastic variables. In …

The issue of determining the best perturbation which results in optimal chaotic flux across a
separatrix is addressed, using the Melnikov function and lobe dynamics. This theoretical …

The stable and unstable manifolds associated with a saddle point in two-dimensional non–
area-preserving flows under general time-aperiodic perturbations are examined. An …

Nonautonomous differential equations on finite-time intervals play an increasingly important
role in applications that incorporate time-varying vector fields, eg observed or forecasted …