https://doi.org/10.1140/epjs/s11734-025-01897-1
Regular Article
Saddle-node and subcritical bifurcations in fluid mechanics
1
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR7342, 13384, Marseille, France
2
Laboratoire d’Hydrodynamique, LadhyX, CNRS UMR 7646, École Polytechnique, 91128, Palaiseau, France
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
25
August
2025
Accepted:
28
August
2025
Published online:
5
September
2025
Abstract
Dedicated to the memory of Etienne Guyon, this contribution introduces examples of macroscopic phenomena that are explained by subcritical bifurcations and not by linear stability analyses of a steady state against small disturbances. The first topic is the transition to turbulence of pipe flows studied long ago by Osborne Reynolds who suggested that the turbulence is not due to the instability of a steady flow against small disturbances. The first theoretical analysis of turbulence based on a subcritical bifurcation was proposed in 1984 and confirmed slightly later by experiments. Another topic is the sharp transition of flame to detonation, better known by the abbreviation DDT (deflagration-to-detonation transition) and recently explained by a subcritical bifurcation one century and a half after its first experimental observation. Our point, agreeing with what we believe was dear to the heart of Etienne, is to explain phenomena out of equilibrium by physical analyses faced with experiments.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
