Vortex boundaries as barriers to diffusive vorticity transport in two-dimensional flows

TL;DR

This paper introduces a method to identify vortex boundaries in two-dimensional flows as material barriers to vorticity diffusion, using an algorithm that detects these structures in both laminar and turbulent flows.

Contribution

It proposes a novel definition of vortex boundaries as diffusive barriers and develops an automated algorithm for their detection in unsteady flow data.

Findings

Successfully identified vortex boundaries in laminar flow.

Detected vortex boundaries in turbulent Navier-Stokes flow.

Demonstrated the method's applicability to different flow regimes.

Abstract

We put forward the idea of defining vortex boundaries in planar flows as closed material barriers to the diffusive transport of vorticity. Such diffusive vortex boundaries minimize the leakage of vorticity from the fluid mass they enclose when compared to other nearby material curves. Building on recent results on passive diffusion barriers, we develop an algorithm for the automated identification of such structures from general, two-dimensional unsteady flow data. As examples, we identify vortex boundaries as vorticity diffusion barriers in two flows: an explicitly known laminar flow and a numerically generated turbulent Navier--Stokes flow.