A review of analyses based upon anti-parallel vortex structures suggests that structurally stableuddipoles with eroding circulation may offer a path to the study of vorticity growth in solutions ofudEuler’s equations in R3ud. We examine here the possible formation of such a structure in axisymmetricudflow without swirl, leading to maximal growth of vorticity as tud4/3ud. Our study suggests that theudoptimizing flow giving the tud4/3 growth mimics an exact solution of Euler’s equations representingudan eroding toroidal vortex dipole which locally conserves kinetic energy. The dipole cross-sectionudis a perturbation of the classical Sadovskii dipole having piecewise constant vorticity, whichudbreaks the symmetry of closed streamlines. The structure of this perturbed Sadovskii dipole isudanalyzed asymptotically at large times, and its predicted properties are verified numerically. Weudalso show numerically that if mirror symmetry of the dipole is not imposed but axial symmetryudmaintained, an instability leads to breakup into smaller vortical structures.
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