Critical velocity in resonantly driven polariton superfluids

We study the necessary condition under which a resonantly driven exciton polariton superfluid flowing against an obstacle can generate turbulence. The value of critical velocity is well estimated by transition from elliptic to hyperbolic operator following ideas developed Frisch, Pomeau, Rica for flow around obstacle, though nature equations governing quite different. find analytical estimates depending on pump amplitude and energy detuning, consistent with our numerical computations.