Vortex splitting in two-dimensional fluids and non-neutral electron plasmas with smooth vorticity profiles

Initially elliptical, quasi-two-dimensional (2D) fluid vortices can split into multiple pieces if the aspect ratio is sufficiently large, due to the growth and saturation of Love modes on the vortex edge. Presented here are experiments and numerical simulations showing that the aspect ratio threshold for vortex splitting is significantly higher for vortices with realistic, smooth edges than that predicted by a simple vortex patch model, where the vorticity is treated as piecewise constant [Hurst, et al., Phys. Plasmas 31, 052106 (2024)]. The experiments are conducted with non-neutral electron plasmas which closely model 2D vortex dynamics due to an isomorphism between the Drift-Poisson equations describing the plasma dynamics and the Euler equations describing ideal fluids. The simulations use a particle-in-cell method to model the evolution of a set of point vortices. The aspect ratio splitting threshold ranges up to about twice as large as the vortex patch prediction and depends on the edge vorticity gradient. This is thought to be due to spatial Landau or critical-layer damping, which decreases the vortex aspect ratio over time and thus stabilizes the Love modes. Near the threshold, asymmetric events are observed in which one of the split products contains much less circulation than the other.