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arXiv · 1812.08529

Low-order model for successive bifurcations of the fluidic pinball

Nan Deng·Bernd R. Noack·Marek Morzynski·Luc R. Pastur
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Abstract

We propose the first least-order Galerkin model of an incompressible flow undergoing two successive supercritical bifurcations of Hopf and pitchfork type. A key enabler is a mean-field consideration exploiting the symmetry of the mean flow and the asymmetry of the fluctuation. These symmetries generalize mean-field theory, e.g. no assumption of slow growth-rate is needed. The resulting 5-dimensional Galerkin model successfully describes the phenomenogram of the fluidic pinball, a two-dimensional wake flow around a cluster of three equidistantly spaced cylinders. The corresponding transition scenario is shown to undergo two successive supercritical bifurcations, namely a Hopf and a pitchfork bifurcations on the way to chaos. The generalized mean-field Galerkin methodology may be employed to describe other transition scenarios.

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Nan Deng, Bernd R. Noack, Marek Morzynski, Luc R. Pastur. 2018-12-20. Low-order model for successive bifurcations of the fluidic pinball. https://doi.org/10.1017/jfm.2019.959

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