Based on experimental evidence that vortex reconnection commences with the approach of nearly antiparallel segments of vorticity, a linearised model is developed in which two Burgers-type vortices are driven together and stretched by an ambient irrotational strain field induced by more remote vorticity. When these Burgers vortices are exactly antiparallel, they are annihilated on the strain time-scale, independent of kinematic viscosity ν in the limit ν → 0. When the vortices are skew to each other, they are annihilated under this action over a local extent that increases exponentially in the stretching direction, with clear evidence of reconnection on the same strain time-scale. The initial helicity associated with the skewed geometry is eliminated during the process of reconnection. The model applies equally to the reconnection of weak magnetic flux tubes under the action of a strain field, when Lorentz forces are negligible.

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.

Motions of fluid particles advected by a vortex soliton are studied. In the moving frame which makes the vortex soliton steady in space, particle motions are confined in a torus near the loop for a wide range of three parameters that characterize the shape and strength of the vortex soliton. To extract the essential mechanism of the transport properties, an ODE model is proposed, which is named the chopsticks model.

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