Material Barriers to Diffusive and Stochastic Transport

TL;DR

This paper introduces a method to identify material surfaces acting as transport barriers or enhancers in unsteady flows, applicable even under stochastic conditions, by analyzing extremizers of a universal transport functional.

Contribution

It develops a new framework for detecting transport barriers and enhancers as extremizers of a universal functional, extending to stochastic flows and differing from previous purely advective structures.

Findings

Explicit computation of transport extremizers as null-surfaces of an objective tensor

Identification of observable, uniform transport extremizers in unsteady flows

Extension of the method to stochastic velocity fields

Abstract

We seek transport barriers and transport enhancers as material surfaces across which the transport of diffusive tracers is minimal or maximal in a general, unsteady flow. We find that such surfaces are extremizers of a universal, non-dimensional transport functional whose leading-order term in the diffusivity can be computed directly from the flow velocity. The most observable (uniform) transport extremizers are explicitly computable as null-surfaces of an objective transport tensor. Even in the limit of vanishing diffusivity, these surfaces differ from all previously identified coherent structures for purely advective fluid transport. Our results extend directly to stochastic velocity fields and hence enable transport barrier and enhancer detection under uncertainties.