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Low-order model for successive bifurcations of the fluidic pinball

  • Nan Deng (a1) (a2), Bernd R. Noack (a2) (a3) (a4), Marek Morzyński (a5) and Luc R. Pastur (a1)

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 five-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 bifurcation on the way to chaos. The generalized mean-field Galerkin methodology may be employed to describe other transition scenarios.

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Corresponding author

Email address for correspondence: nan.deng@ensta-paris.fr

References

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Low-order model for successive bifurcations of the fluidic pinball

  • Nan Deng (a1) (a2), Bernd R. Noack (a2) (a3) (a4), Marek Morzyński (a5) and Luc R. Pastur (a1)

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