  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.
