期刊
JOURNAL OF FLUID MECHANICS
卷 884, 期 -, 页码 -出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2019.959
关键词
bifurcation; low-dimensional models; wakes
资金
- French National Research Agency (ANR) as part of the 'Investissement d'Avenir' programme, through the 'iCODE Institute project' - IDEX Paris-Saclay [ANR-11-IDEX-0003-02]
- ANR grant 'ACTIV_ROAD' [ANR-17-ASTR-0022]
- ANR grant 'FlowCon' [ANR-17-ASTR-0022]
- Polish Ministry of Science and Higher Education (MNiSW) [05/54/DSPB/6492]
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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