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Anomalous Hydrodynamics of Two-Dimensional Vortex Fluid

Turbulent flows of incompressible liquid in two dimensions are comprised of dense systems of vortices. Such 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 inter-vortex 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 stream lines, a correction to the Bernoulli law, accumulation of vortices in regions with high curvature in the curved space. The origin of the anomalous stresses is a divergence of inter-vortex interactions at the micro-scale which manifest at the macro-scale. We obtain the hydrodynamics of the vortex fluid from the Kirchhoff equations for dynamics of point-like vortices