Gradient enhancement and filament ejection for a non-uniform elliptic vortex in two-dimensional turbulence

The axisymmetrization of a two-dimensional non-uniform elliptic vortex is s tudied in terms of the growth of palinstrophy, the squared vorticity gradie nt. 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 e nstrophy growth in three-dimensions-the vortex-stretching equation. Then pa linstrophy production is analysed, particularly for non-uniform elliptic vo rtices. It is shown analytically and verified numerically that a non-unifor m elliptic vortex in general has a quadrupole structure for palinstrophy pr oduction, and that in the positive production regions, vortex filaments are ejected following the gradient enhancement process for vorticity. Numerica l simulations are conducted for two different initial conditions, compact s upport and Gaussian vorticity distributions. These are characterized by dis tinctly different features of filament ejection and energy spectra. For bot h cases, the total palinstrophy production is a good indicator of the devel opment of small-scale vorticity, In particular for the compact support case , a possible intermittency mechanism in the filament ejection process is pr oposed.