The short-wave stability properties of a Batchelor vortex are used to explain the intrinsic resistance of vortices to turbulent diffusion. We show that turbulence produced
within the vortex core has to overcome a stabilizing ‘dispersion buffer’, where energy
of the perturbations is dispersed by inertial waves without interfering with the mean
flow, before they can reach the periphery of the vortex. While angular momentum
is maintained by this mechanism, the difference in energy extraction by turbulence
from the axial and tangential velocity fields due to a lack of alignment between the
mean and turbulent strain tensors, a typical effect of flow rotation or curvature, leads
to stabilization through a progressive damping of the axial shear in the vortex core.
We show that the efficiency of these stabilizing mechanisms depends on the swirl
number, the ratio between the maximum tangential velocity and the axial velocity
difference. If the swirl parameter is low enough, turbulence is able to reach the vortex
periphery and a small circulation overshoot develops, leading to weak diffusion of
angular momentum outward.
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