%0 Journal Article %T Low-order model for successive bifurcations of the fluidic pinball %+ Institut des Sciences de la mécanique et Applications industrielles (IMSIA - UMR 9219) %+ Laboratoire Interdisciplinaire des Sciences du Numérique (LISN) %+ Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI) %+ Harbin Institute of Technology (HIT) %+ Institut für Strömungsmechanik und Technische Akustik %+ Poznan University of Technology (PUT) %A Nan, Deng %A Noack, Bernd, R. %A Morzyński, Marek %A Pastur, Luc, R. %< avec comité de lecture %@ 0022-1120 %J Journal of Fluid Mechanics %I Cambridge University Press (CUP) %V 884 %8 2020-02-10 %D 2020 %R 10.1017/jfm.2019.959 %Z Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn] %Z Nonlinear Sciences [physics] %Z Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]Journal articles %X 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. %G English %2 https://ensta-paris.hal.science/hal-03195631/document %2 https://ensta-paris.hal.science/hal-03195631/file/JFM1.pdf %L hal-03195631 %U https://ensta-paris.hal.science/hal-03195631 %~ CEA %~ ENSTA %~ CNRS %~ INRIA %~ LIMSI %~ ENSTA_UME %~ CENTRALESUPELEC %~ DSV %~ CEA-UPSAY %~ UNIV-PARIS-SACLAY %~ EDF %~ CEA-DRF %~ INRIA-AUT %~ IP_PARIS %~ IP_PARIS_COPIE %~ TEST-HALCNRS %~ UNIVERSITE-PARIS-SACLAY %~ LISN %~ GS-ENGINEERING %~ GS-COMPUTER-SCIENCE