Comptes Rendus
no. 10
The two-dimensional problem of steady waves on water of finite depth: regimes without waves of small amplitude
[Le problème bidimensionelle d'ondes de surface stationnaires en profondeur finie : le régime sans ondes de petite amplitude]

Présenté par : Évariste Sanchez-Palencia

Vladimir Kozlov1  ; Nikolay Kuznetsov2
1 Department of Mathematics, Linköping University, 581 83 Linköping, Sweden
2 Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol'shoy pr. 61, St. Petersburg 199178, Russia
Comptes Rendus. Mécanique, Volume 333 (2005) no. 10, pp. 733-738.

Nous étudions le problème bidimensionnel d'ondes stationnaires sur la surface des eaux de profondeur finie sans hypothèse préalable concernant leur symétrie ou périodicité. Une nouvelle forme d'équations de Bernoulli est dérivée avec l'introduction d'un nouveau paramètre de bifurcation qui est le produit du nombre de Froude μ et le débit fluide ω. Il résulte de cette équation que les ondes de petite amplitude n'existent pas pour |μω|>1.

The two-dimensional problem of steady waves on water of finite depth is considered without assumptions about periodicity and symmetry of waves. A new form of Bernoulli's equation is derived, and it involves a new bifurcation parameter which is the product of the Froude number μ and the rate of flow ω. The main result obtained from this equation is the absence of waves, having sufficiently small amplitude, provided |μω|>1.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2005.09.001
Keywords: Fluid mechanics, Steady water waves, Bernoulli's equation, Small amplitude, Froude number, Rate of flow
Mot clés : Mécanique des fluides, Ondes de surface stationnaires, Équation de Bernoulli, Petite amplitude, Nombre de Froude, Débit fluide
Vladimir Kozlov 1 ; Nikolay Kuznetsov 2

1 Department of Mathematics, Linköping University, 581 83 Linköping, Sweden
2 Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol'shoy pr. 61, St. Petersburg 199178, Russia 
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Vladimir Kozlov; Nikolay Kuznetsov. The two-dimensional problem of steady waves on water of finite depth: regimes without waves of small amplitude. Comptes Rendus. Mécanique, Volume 333 (2005) no. 10, pp. 733-738. doi : 10.1016/j.crme.2005.09.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.09.001/

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[4] B. Buffoni; E.N. Dancer; J.F. Toland The regularity and local bifurcation of steady periodic waves, Arch. Ration. Mech. Anal., Volume 152 (2000), pp. 207-240

[5] B. Buffoni; E.N. Dancer; J.F. Toland The sub-harmonic bifurcation of Stokes waves, Arch. Ration. Mech. Anal., Volume 152 (2000), pp. 241-271

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