Volume 135, Number 2, July 2021
|Number of page(s)||5|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||20 September 2021|
Coinciding local bifurcations in the Navier-Stokes equations
1 Institute of Mechanical Sciences and Industrial Applications (IMSIA), ENSTA- Paris, Institut Polytechnique de Paris 828 Bd des Maréchaux, F-91120 Palaiseau, France
2 Laboratoire de Physique de Mécanique des Milieux Hétéerogènes (PMMH), CNRS, ESPCI Paris, PSL Research University; Sorbonne Université, Université de Paris - F-75005, Paris, France
3 School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen) Shenzhen 518058, China
Received: 7 June 2021
Accepted: 27 July 2021
Generically, a local bifurcation only affects a single solution branch. However, branches that are quite different may nonetheless share certain eigenvectors and eigenvalues, leading to coincident bifurcations. For the fluidic pinball, two supercritical pitchfork bifurcations, of the equilibrium and the periodic solutions, occur at nearly the same Reynolds number. The mechanism of this kind of non-generic coincidence is modelled and explained.
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