The Mixing efficiency of open flows

TL;DR

This paper investigates the efficiency of mixing in open incompressible flows with inhomogeneous scalar injection, providing bounds on scalar concentration variance and discussing their sharpness and potential saturation at different Peclet numbers.

Contribution

It introduces bounds on mixing efficiency in open flows and analyzes their sharpness, connecting them to flow chaoticity at high Peclet numbers.

Findings

Bound on scalar concentration variance is sharp at low Peclet number.

Estimate likely approached by flows with sustained chaotic regions at high Peclet number.

Provides theoretical insights into mixing efficiency in open flows.

Abstract

Mixing in open incompressible flows is studied in a model problem with inhomogeneous passive scalar injection on an inlet boundary. As a measure of the efficiency of stirring, the bulk scalar concentration variance is bounded and the bound is shown to be sharp at low Peclet number. Although no specific flow saturating the bound at high Peclet number is produced here, the estimate is conjectured to be approached for flows possessing sufficiently sustained chaotic regions.