2024/03/11 by Yves-Marie Ducimetière, Ducimetière, Yves-Marie, Édouard Boujo +3 · 1 citation
Environmental Science · Physics and Astronomy · #Ecosystem dynamics and resilience #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Statistical Mechanics (cond-mat.stat-mech) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2403.06824
openalex publication_date 2024/03/11 · openalex created_date 2024/03/13 · openalex updated_date 2026/07/28
We consider fluid flows, governed by the Navier-Stokes equations, subject to a steady symmetry-breaking bifurcation and forced by a weak noise acting on a slow time scale. By generalizing the multiple-scale weakly nonlinear expansion technique employed in the literature for the response of the Duffing oscillator, we rigorously 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. The validity of this reduced order model is tested on the flow past a sudden expansion, for a given Reynolds number and different noise amplitudes. At a very low numerical cost, the statistics obtained from the amplitude equation accurately reproduce those of long-time direct numerical simulations.