Scaling Laws of Vortex Reconnections

The vortex reconnection rate f plays an important role in the dynamics of a tangle of quantised vortices in superfluid turbulence. The question which we address is how f depends on the vortex line density L. In the case of a homogeneous isotropic tangle of vortices we show that, besides the known regime which scales as f ～ L^5/2, another regime exists which scales as f ～ L². In the case of a polarised vortex confguration, we argue that the scaling law changes and show numerical evidence for it. Finally we construct an idealised model of turbulence decay based on vortex reconnections and discuss its implications. PACS numbers: 67.40.Vs, 67.57.Fg.