  We study the two dimensional (2D) stochastic Navier Stokes (SNS) equations in
the inertial limit of weak forcing and dissipation. The stationary measure is
concentrated close to steady solutions of the 2D Euler equation. For such
inertial flows, we prove that bifurcations in the flow topology occur either by
changing the domain shape, the nonlinearity of the vorticity-stream function
relation, or the energy. Associated to this, we observe in SNS bistable
behavior with random changes from dipoles to unidirectional flows. The
theoretical explanation being very general, we infer the existence of similar
phenomena in experiments and in models of geophysical flows.
