Barriers to the Transport of Diffusive Scalars in Compressible Flows

TL;DR

This paper extends the identification of transport barriers and enhancers for diffusive scalars from incompressible to compressible flows, accounting for sources, sinks, and decay, with explicit equations for 2D flows and practical illustrations.

Contribution

It introduces a generalized framework for detecting diffusive transport extremizers in compressible flows, including effects of sources, sinks, and decay, with explicit 2D equations and diagnostics.

Findings

Explicit differential equations for 2D flows

Diagnostic scalar field for extremizers

Identification of diffusion barriers and enhancers

Abstract

Our recent work identifies material surfaces in incompressible flows that extremize the transport of an arbitrary, weakly diffusive scalar field relative to neighboring surfaces. Such barriers and enhancers of transport can be located directly from the deterministic component of the velocity field without diffusive or stochastic simulations. Here we extend these results to compressible flows and to diffusive concentration fields affected by sources or sinks, as well as by spontaneous decay. We construct diffusive transport extremizers with and without constraining them on a specific initial concentration distribution. For two-dimensional flows, we obtain explicit differential equations and a diagnostic scalar field that identify the most observable extremizers with pointwise uniform transport density. We illustrate our results by uncovering diffusion barriers and enhancers in analytic, numerical, and observational velocity fields.