Noise-induced transitions past the onset of a steady symmetry-breaking bifurcation: the case of the sudden expansion
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| Format: | Preprint |
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2024
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| _version_ | 1866914709474639872 |
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| author | Ducimetière, Yves-Marie Boujo, Edouard Gallaire, François |
| author_facet | Ducimetière, Yves-Marie Boujo, Edouard Gallaire, François |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_06824 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noise-induced transitions past the onset of a steady symmetry-breaking bifurcation: the case of the sudden expansion Ducimetière, Yves-Marie Boujo, Edouard Gallaire, François Fluid Dynamics Statistical Mechanics 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. |
| title | Noise-induced transitions past the onset of a steady symmetry-breaking bifurcation: the case of the sudden expansion |
| topic | Fluid Dynamics Statistical Mechanics |
| url | https://arxiv.org/abs/2403.06824 |