Comptes Rendus
Instabilities, patterns
The Kelvin–Helmholtz instability, a useful model for wind-wave generation?
Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 489-500.

The Kelvin–Helmholtz instability, one of the most classical instabilities in fluid mechanics, was initially introduced to describe the generation of waves by wind. This instability is relevant to several natural and engineering flow configurations, and has led to many experimental variants, in tilted channel with stratified fluids, in circular cells or quasi-2D Hele-Shaw cells. As many physicists, Yves Couder, who passed away in 2019, was fascinated by the problem of wind-wave generation, but also frustrated by the fact that, despite considerable studies over the years, it was still poorly understood. Yves was always eager for simple explanations about physics phenomena, with qualitative arguments rather than equations, and this problem was for him and his collaborators a recurrent source of inspiration. Sharing views about physics with him, making experiments, or even contemplating natural phenomena, was always highly stimulating. In the spirit of these discussions with Yves, we recall here the basics of the Kelvin–Helmholtz instability, and discuss to what extent it may be relevant to the problem of wind-wave generation — not in the air–water case but, rather surprisingly, for very viscous liquids.

L’instabilité de Kelvin–Helmholtz, l’une des instabilités les plus classiques de la mécanique des fluides, a été introduite initialement afin de décrire la génération des vagues par le vent. Cette instabilité est présente dans un certain nombre d’écoulements naturels ou industriels, et a donné lieu à de nombreuses variantes expérimentales, en canal incliné avec des fluides stratifiés, en cellules circulaires ou en cellules de Hele-Shaw quasi 2D. Comme beaucoup de physiciens, Yves Couder, disparu en 2019, était fasciné par ce problème de la génération des vagues par le vent, mais également frustré par le fait que, malgré un nombre considérable d’études, ce problème restait très mal compris. Yves avait toujours une préférence pour les explications simples sur les phénomènes physiques, avec des arguments qualitatifs plutôt que des équations, et cette instabilité a été pour lui et ses collaborateurs une source d’inspiration récurrente. Partager avec lui des points de vue sur la physique, faire des expériences, ou même contempler des phénomènes naturels, a toujours été très stimulant. Dans l’esprit de ces discussions avec Yves, nous rappelons ici les fondements de l’instabilité de Kelvin–Helmholtz, et discutons dans quelle mesure elle peut être pertinente pour le problème de la génération de vagues par le vent — non pas dans le cas de l’air et de l’eau mais, de façon plus surprenante, pour les liquides très visqueux.

Published online:
DOI: 10.5802/crmeca.31
Keywords: Kelvin–Helmholtz instability, Wind-waves

Marc Rabaud 1; Frédéric Moisy 1

1 Université Paris-Saclay, CNRS, FAST, 91405, Orsay, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Marc Rabaud; Frédéric Moisy. The Kelvin–Helmholtz instability, a useful model for wind-wave generation?. Comptes Rendus. Mécanique, Volume 348 (2020) no. 6-7, pp. 489-500. doi : 10.5802/crmeca.31. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.31/

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