  Spatially resolved transport in two-dimensional quantum materials can reveal
dynamics which is invisible in conventional bulk transport measurements. We
predict striking patterns in spatially inhomogeneous transport just above the
critical temperature in two-dimensional superconducting thin films, where
electrical current will appear to flow as if it were a viscous fluid obeying
the Navier-Stokes equations. Compared to viscous electron fluids in ultrapure
metals such as graphene, this analogue viscous vortex fluid can exhibit a far
more tunable crossover, as a function of temperature, from Ohmic to non-Ohmic
transport, with the latter arising on increasingly large length scales close to
the critical temperature. Experiments using nitrogen vacancy center
magnetometry, or transport through patterned thin films, could reveal this
analogue viscous flow in a wide variety of materials.
