  We develop a coarse-grained description of the point-vortex model, finding
that a large number of planar vortices and antivortices behave as an inviscid
non-Eulerian fluid at large scales. The emergent binary vortex fluid is subject
to anomalous stresses absent from Euler's equation, caused by the singular
nature of quantum vortices. The binary vortex fluid is compressible, and has an
asymmetric Cauchy stress tensor allowing orbital angular momentum exchange with
the vorticity and vortex density. An analytic solution for vortex shear flow
driven by anomalous stresses is in excellent agreement with numerical
simulations of the point-vortex model.
