Noise-induced transitions past the onset of a steady symmetry-breaking bifurcation: The case of the sudden expansion

We consider flows subject to a steady symmetry-breaking bifurcation and forced by a weak noise acting on a slow timescale. By employing a multiple-scale weakly nonlinear expansion technique, we derive a stochastically forced Stuart-Landau equation for the dominant symmetry-breaking mode. The probability density function of the solution, and of the escape time from one attractor to the other, are then determined by solving the associated Fokker-Planck equation, which is made possible by the extremely low dimensionality of the amplitude equation. The validity of this reduced order model is then tested on the flow past a planar sudden expansion.