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Motivated by recent experiments, we theoretically analyze the flow past anobstacle of a one-dimensional "quantum fluid of light" which is resonantlydriven, and exhibits bistability. The flow is found to abruptly change severaltimes when the fluid velocity or the obstacle potential strength are increased.In contrast to the cases of usual fluids and superfluids, the transitions takeplace between stationary states. They involve the fluid bistability in anessential way. Remarkably, at the transitions points, the fluid in the obstaclewake lies in the unstable intermediate density state.

Metamorphoses of the flow past an obstacle of a resonantly-driven bistable polariton fluid