  A review of analyses based upon anti-parallel vortex structures suggests that
structurally stable vortex structures with eroding circulation may offer a path
to the study of rapid vorticity growth in solutions of Euler's equations in $
\scriptstyle{\mathbb{R}}^3$. We examine here the possible formation of such a
structure in axisymmetric flow without swirl, leading to maximal growth of
vorticity as $t^{4/3}$. Our study suggests that the optimizing flow giving the
$t^{4/3}$ growth mimics an exact solution of Euler's equations representing an
eroding toroidal vortex dipole which locally conserves kinetic energy. The
dipole cross-section is a perturbation of the classical Sadovskii dipole having
piecewise constant vorticity, which breaks the symmetry of closed streamlines.
The structure of this perturbed Sadovskii dipole is analyzed asymptotically at
large times, and its predicted properties are verified numerically.
