Simulation of the Initial 3-D Instability of an Impacting Drop Vortex Ring

Computational vortex particle method simulations of a perturbed vortex ring are performed to recreate and understand the instability seen in impacting water drop experiments. Three fundamentally different initial vorticity distributions are used to attempt to trigger a Widnall instability, a Rayleigh centrifugal instability, or a vortex breakdown-type instability. Simulations which simply have 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, to trigger a Rayleigh or breakdown respectively, does not appear to significantly change the instability from what is seen with a solitary ring. This suggests that a Rayleigh or vortex breakdown-type instability are not likely at work, though tests are not conclusive. Perhaps the opposite-signed secondary vortex was not strong enough or placed appropriately. Elliptical streamlines , as expected, are visible in the core of the solitary ring at early times. Support from the Canadian Natural Sciences and Engineering Research Council grant 41747 is gratefully acknowledged.