The axisymmetrization of a two-dimensional non-uniform elliptic vortex is studied in
terms of the growth of palinstrophy, the squared vorticity gradient. First, it is pointed
out that the equation for palinstrophy growth, if written in terms of the strain rate
tensor, has a similar form to that of enstrophy growth in three-dimensions – the
vortex-stretching equation. Then palinstrophy production is analysed, particularly for
non-uniform elliptic vortices. It is shown analytically and verified numerically that
a non-uniform elliptic vortex in general has a quadrupole structure for palinstrophy
production, and that in the positive production regions, vortex filaments are ejected
following the gradient enhancement process for vorticity. Numerical simulations are
conducted for two different initial conditions, compact support and Gaussian vorticity
distributions. These are characterized by distinctly different features of filament ejection
and energy spectra. For both cases, the total palinstrophy production is a good
indicator of the development of small-scale vorticity. In particular for the compact
support case, a possible intermittency mechanism in the filament ejection process is
proposed.