Simulation of the initial three-dimensional instability of a vortex ring

Computational simulations of a perturbed vortex ring are performed to recreate and understand the instability seen in impacting water droplet experiments. Three initial conditions are tried to respectively trigger a Widnall instability, a Rayleigh centrifugal instability, and a vortex breakdown instability. Simulations with a perturbed solitary ring result in an instability similar to that seen experimentally. Waviness of the core which would be expected from a Widnall instability is not visible. Adding an opposite-signed secondary vortex ring or an image vortex ring to the initial conditions does not appear to significantly change the instability from what is seen with a solitary ring. This suggests that a Rayleigh centrifugal instability or a vortex breakdown instability are not likely at work, though tests are not conclusive. Elliptical streamlines are visible in the core of the solitary ring at early times, suggesting that an elliptic instability may be the source of the experimental instability.