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We study the two dimensional (2D) stochastic Navier Stokes (SNS) equations inthe inertial limit of weak forcing and dissipation. The stationary measure isconcentrated close to steady solutions of the 2D Euler equation. For suchinertial flows, we prove that bifurcations in the flow topology occur either bychanging the domain shape, the nonlinearity of the vorticity-stream functionrelation, or the energy. Associated to this, we observe in SNS bistablebehavior with random changes from dipoles to unidirectional flows. Thetheoretical explanation being very general, we infer the existence of similarphenomena in experiments and in models of geophysical flows.

Random changes of flow topology in two dimensional and geophysical turbulence