Comptes Rendus
Instabilities, patterns
The Kelvin–Helmholtz instability, a useful model for wind-wave generation?
Comptes Rendus. Mécanique, Tribute to an exemplary man: Yves Couder, 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, Tribute to an exemplary man: Yves Couder, 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/

[1] W. Thomson XLVI. Hydrokinetic solutions and observations, Lond. Edinburgh Dublin Phil. Mag. J. Sci., Volume 42 (1871) no. 281, pp. 362-377 | DOI

[2] H. Squire Investigation of the instability of a moving liquid film, Br. J. Appl. Phys., Volume 4 (1953) no. 6, p. 167 | DOI

[3] N. Bremond; C. Clanet; E. Villermaux Atomization of undulating liquid sheets, J. Fluid Mech., Volume 585 (2007), pp. 421-456 | DOI | MR | Zbl

[4] N. Andritsos; L. Williams; T. J. Hanratty Effect of liquid viscosity on the stratified-slug transition in horizontal pipe flow, Int. J. Multiph. Flow, Volume 15 (1989) no. 6, pp. 877-892 | DOI

[5] O. Darrigol Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl, Oxford University, 2005 | Zbl

[6] W. Thomson On ship waves, Lecture delivered at the “Conversazione” in the Science and Art Museum, Edinburgh, on 3 Aug 1887. Institution of Mechanical Engineers, Minutes of Proceedings, 1887, pp. 409-434

[7] H. L. von Helmholtz On discontinuous movements of fluids, Phil. Mag., Volume 36 (1868), p. 337 | DOI

[8] O. Cadot; T. Glomeron; A. Khémili (Vent et vagues, Rapport de licence, 1990)

[9] J. W. Miles On the generation of surface waves by shear flows. Part 3. Kelvin-Helmholtz Instability, J. Fluid Mech., Volume 6 (1959) no. 04, pp. 583-598 | DOI | Zbl

[10] P. Drazin Kelvin–Helmholtz instability of finite amplitude, J. Fluid Mech., Volume 42 (1970) no. 02, pp. 321-335 | DOI | Zbl

[11] P. Huerre; M. Rossi Hydrodynamic Instabilities in Open Flows, Vol. 1, Cambridge University Press, 1998, pp. 81-294 | Zbl

[12] F. Charru Hydrodynamic Instabilities, Cambridge University Press, 2011 | MR

[13] O. M. Phillips On the generation of waves by turbulent wind, J. Fluid Mech., Volume 2 (1957) no. 05, pp. 417-445 | DOI | MR | Zbl

[14] J. W. Miles On the generation of surface waves by shear flows, J. Fluid Mech., Volume 3 (1957), pp. 185-204 | DOI | MR | Zbl

[15] L. Rayleigh On the stability, or instability, of certain fluid motions, Proc. Lond. Math. Soc., Volume 9 (1880), pp. 57-70 | MR | Zbl

[16] D. Acheson Elementary Fluid Dynamics, 1990 | MR | Zbl

[17] S. H. Lamb Hydrodynamics, Cambridge University Press, 1995. | Zbl

[18] G. I. Taylor Generation of ripples by wind blowing over a viscous fluid, The Scientific Papers of G. I. Taylor, Volume 3 (1940), pp. 244-254

[19] J. R. D. Francis Wave motions and the aerodynamic drag on a free oil surface, Phil. Mag., Volume 45 (1954), pp. 695-702 | DOI

[20] J. R. D. Francis LXIX. Correspondence. Wave motions on a free oil surface, Phil. Mag., Volume 1 (1956) no. 7, pp. 685-688 | DOI

[21] E. J. Hinch A note on the mechanism of the instability at the interface between two shearing fluids, J. Fluid Mech., Volume 144 (1984), pp. 463-465 | DOI

[22] S. Thorpe Experiments on the instability of stratified shear flows: miscible fluids, J. Fluid Mech., Volume 46 (1971) no. 02, pp. 299-319 | DOI

[23] O. Pouliquen; J.-M. Chomaz; P. Huerre Propagative Holmboe waves at the interface between two immiscible fluids, J. Fluid Mech., Volume 266 (1994), pp. 277-302 | DOI

[24] Y. Couder The observation of a shear-flow instability in a rotating system with a soap membrane, J. Phys. Lett., Volume 42 (1981), pp. 429-431 | DOI

[25] M. Rabaud; Y. Couder A shear-flow instability in a circular geometry, J. Fluid Mech., Volume 136 (1983), pp. 291-319 | DOI

[26] Y. Couder Two-dimensional grid turbulence in a thin liquid film, J. Phys. Lett., Volume 45 (1984), pp. 353-360 | DOI

[27] Y. Couder; C. Basdevant Experimental and numerical study of vortex couples in two-dimensional flows, J. Fluid Mech., Volume 173 (1986), pp. 225-251 | DOI

[28] Y. Couder; J. Chomaz; M. Rabaud On the hydrodynamics of soap films, Physica D, Volume 37 (1989), pp. 384-405 | DOI

[29] E. Villermaux On the role of viscosity in shear instabilities, Phys. Fluids (1994-present), Volume 10 (1998) no. 2, pp. 368-373 | DOI | MR | Zbl

[30] P. Gondret; M. Rabaud Shear instability of two-fluid parallel flow in a Hele-Shaw cell, Phys. Fluids, Volume 9 (1997), pp. 3267-3274 | DOI

[31] L. Meignin (Formation et dynamique de vagues en cellule de Hele-Shaw, PhD Thesis, Universite Paris-Sud, 2001)

[32] A. Paquier; F. Moisy; M. Rabaud Surface deformations and wave generation by wind blowing over a viscous liquid, Phys. Fluids, Volume 27 (2015) (122103) | DOI

[33] A. Paquier; F. Moisy; M. Rabaud Viscosity effects in wind wave generation, Phys. Rev. Fluids, Volume 1 (2016) (083901) | DOI

[34] F. Moisy; M. Rabaud; K. Salsac A synthetic Schlieren method for the measurement of the topography of a liquid interface, Exp. Fluids, Volume 46 (2009), pp. 1021-1036 | DOI

[35] M. Aulnette; M. Rabaud; F. Moisy Wind-sustained viscous solitons, Phys. Rev. Fluids, Volume 4 (2019) (084003) | DOI

[36] S. Perrard; A. Lozano-Durán; M. Rabaud; M. Benzaquen; F. Moisy Turbulent windprint on a liquid surface, J. Fluid Mech., Volume 873 (2019), pp. 1020-1054 | DOI | MR | Zbl

[37] M.-Y. Lin; C.-H. Moeng; W.-T. Tsai; P. P. Sullivan; S. E. Belcher Direct numerical simulation of wind-wave generation processes, J. Fluid Mech., Volume 616 (2008), pp. 1-30 | DOI | Zbl

[38] F. Zonta; A. Soldati; M. Onorato Growth and spectra of gravity–capillary waves in countercurrent air/water turbulent flow, J. Fluid Mech., Volume 777 (2015), pp. 245-259 | DOI

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