  This paper is devoted to the stability analysis of the Lamb-Oseen vortex in
the regime of high circulation Reynolds numbers. When strongly localized
perturbations are applied, it is shown that the vortex relaxes to axisymmetry
in a time proportional to $Re^{2/3}$, which is substantially shorter than the
diffusion time scale given by the viscosity. This enhanced dissipation effect
is due to the differential rotation inside the vortex core. Our result relies
on a recent work by Li, Wei, and Zhang, where optimal resolvent estimates for
the linearized operator at Oseen's vortex are established. A comparison is made
with the predictions that can be found in the physical literature, and with the
rigorous results that were obtained for shear flows using different techniques.
