Barriers to the Transport of Diffusive Scalars in Compressible Flows

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.

arXiv comment33 pages, 6 figures, submitted

References in corpus (11)

• A Critical Comparison of Lagrangian Methods for Coherent Structure Detection
• Coherent Lagrangian vortices: The black holes of turbulence
• Material Barriers to Diffusive and Stochastic Transport
• Zonal Jets as Transport Barriers in Planetary Atmospheres
• Automated detection of coherent Lagrangian vortices in two-dimensional unsteady flows
• Uncovering the Edge of the Polar Vortex
• Advection-Diffusion in Lagrangian Coordinates
• A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds
• Geodesic Transport Barriers in Jupiter's Atmosphere: A Video-Based Analysis
• Efficient Computation of Null-Geodesic with Applications to Coherent Vortex Detection
• Level set formulation of two-dimensional Lagrangian vortex detection methods

Cited by in corpus (7)

• Confronting Grand Challenges in Environmental Fluid Mechanics
• Objective barriers to the transport of dynamically active vector fields
• A Geometric Heat-Flow Theory of Lagrangian Coherent Structures
• Vortex boundaries as barriers to diffusive vorticity transport in two-dimensional flows
• A Lagrangian perspective on nonautonomous advection-diffusion processes in the low-diffusivity limit
• Heat-content and diffusive leakage from material sets in the low-diffusivity limit
• An Objective Measure of Unsteadiness