Linking Dispersion and Stirring in Randomly Braiding Flows

TL;DR

This paper establishes a universal link between dispersion and chaotic stirring in various random flows, showing that the Lyapunov exponent can be estimated from advective dispersivity, thus connecting transport and mixing.

Contribution

It introduces a universality class for pathline braiding that quantitatively relates dispersion and stirring in random flows, verified for 2D unsteady and 3D steady flows.

Findings

Lyapunov exponent can be estimated from dispersivity

Universal relation holds for 2D unsteady flows

Universal relation holds for 3D steady flows

Abstract

Many random flows, including 2D unsteady and stagnation-free 3D steady flows, exhibit non-trivial braiding of pathlines as they evolve in time or space. We show that these random flows belong to a pathline braiding \emph{universality class} that quantitatively links dispersion and chaotic stirring, meaning that the Lyapunov exponent can be estimated from the purely advective transverse dispersivity. We verify this quantitative link for both unsteady 2D and steady 3D random flows. This result uncovers a deep connection between transport and mixing over a broad class of random flows.