Vortex Flows on Surfaces and Their Anomalous Hydrodynamics

Aleksandr Bogatskii
Hydrodynamic flows with large numbers of vortices have been a staple of theoretical hydrodynamics since Onsager and Feynman. Treating such vortices as constituents of a new fluid of their own leads to an interesting anomalous hydrodynamics that exhibits curious phenomena such as odd viscosity. Starting with the incompressible Euler equation, we rigorously derive the entire coarse-grained hydrodynamics of the "vortex matter" consisting of many identical discrete point vortices on an arbitrary closed 2D surface. The...
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