Crossover from interaction to driven regimes in quantum vortex reconnections

Reconnections of coherent filamentary structures play a key role in the dynamics of fluids, redistributing energy and helicity among the length scales, triggering dissipative effects and inducing fine-scale mixing. Unlike ordinary (classical) fluids where vorticity is a continuous field, in superfluid helium and in atomic Bose-Einstein condensates (BECs) vorticity takes the form of isolated quantised vortex lines, which are conceptually easier to study. New experimental techniques now allow visualisation of individual vortex reconnections in helium and condensates. It has long being suspected that reconnections obey universal laws, particularly a universal scaling with time of the minimum distance between vortices $\delta$. Here we perform a comprehensive analysis of this scaling across a range of scenarios relevant to superfluid helium and trapped condensates, combining our own numerical simulations with the previous results in the literature. We reveal that the scaling exhibit two distinct fundamental regimes: a $\delta \sim t^{1/2}$ scaling arising from the mutual interaction of the reconnecting strands and a $\delta \sim t$ scaling when extrinsic factors drive the individual vortices.