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Saddle-node and subcritical bifurcations in fluid mechanics
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DOI：10.1140/epjs/s11734-025-01897-1.png)
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Abstract
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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.
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