Anomalous Hydrodynamics of Two-Dimensional Vortex Fluids

A dense system of vortices can be treated as a fluid and itself could be described in terms of hydrodynamics. We develop the hydrodynamics of the vortex fluid. This hydrodynamics captures characteristics of fluid flows averaged over fast circulations in the intervortex space. The hydrodynamics of the vortex fluid features the anomalous stress absent in Euler's hydrodynamics. The anomalous stress yields a number of interesting effects. Some of them are a deflection of streamlines, a correction to the Bernoulli law, and an accumulation of vortices in regions with high curvature in the curved space. The origin of the anomalous stresses is a divergence of intervortex interactions at the microscale which manifest at the macroscale. We obtain the hydrodynamics of the vortex fluid from the Kirchhoff equations for dynamics of pointlike vortices.