Universal expansion of vortex clusters in a dissipative two-dimensional superfluid

At finite temperatures the dynamics of superfluids become dissipative due to the presence of thermal friction. Here we apply a recently developed dissipative hydrodynamical vortex fluid theory [X. Yu and A. S. Bradley, Phys. Rev. Lett. 119, 185301 (2017)] to describe the expansion dynamics of collections of quantum vortices in two-dimensional superfluids. We find that the long-time dynamics of the vorticity distribution is universal, leading to an expanding Rankine (top-hat) vortex distribution that is independent of the initial conditions. This is in stark contrast to viscous diffusion of vorticity in classical fluids, highlighting the fundamentally different dissipation mechanism. We perform numerical simulations of large ensembles of chiral point vortices that confirm the universal expansion dynamics, and further reveal the emergence of a frustrated lattice structure marked by strong correlations. We present results from experiments in a quasi-two-dimensional Bose-Einstein condensate that demonstrate the universal dynamics.