Decay of homogeneous two dimensional quantum turbulence

We numerically simulate the free decay of two-dimensional quantum turbulence in a large, homogeneous Bose-Einstein condensate. The large number of vortices, the uniformity of the density profile and the absence of boundaries (where vortices can drift out of the condensate) isolate the annihilation of vortex-antivortex pairs as the only mechanism which reduces the number of vortices, $\text{Nv}$, during the turbulence decay. The results clearly reveal that vortex annihilation is a four-vortex process, confirming the decay law $\Nv \sim t^{-1/3}$where$t$ is time, which was inferred from experiments with relatively few vortices in small harmonically trapped condensates.