Comptes Rendus
Parametric excitation of waves on a free boundary of a horizontal fluid layer
Comptes Rendus. Mécanique, Volume 332 (2004) no. 4, pp. 257-262.

We consider the dynamical stability of horizontal fluid layer, performing harmonic oscillations in vertical direction. The continued fractions approach allowed us to avoid the conventional restriction to the case of small viscosity and almost-resonant frequencies. Our numerical results cover a wide range of the parameters (viscosity, amplitude and frequency of the oscillation, and depth of the layer).

Nous examinons l'instabilité dynamique d'une couche horizontale d'un liquide faisant des oscillations harmoniques verticales. L'utilisation des fractions continues nous a permis déviter les restrictions habituelles de petite viscosité et de fréquences presque résonnantes. Nous obtenons des résultats numériques pour un large domaine des paramètres (la viscosité, l'amplitude et la fréquence des oscillations, la profondeur de la couche).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2004.01.010
Keywords: Fluid mechanics, Vibration, Waves, Parametric resonance, Averaging, Continuous fractions
Mot clés : Méchanique des fluides, Vibration, Ondes, Résonnance paramètrique, Moyennisation, Fractions continues

V.I. Yudovich 1; S.M. Zenkovskaya 1; V.A. Novossiadliy 1; A.L. Shleykel 1

1 Department of Numerical Methods and Mathematical Physics, Rostov State University, 5 Zorge, Rostov-on-Don, 344090, Russia
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V.I. Yudovich; S.M. Zenkovskaya; V.A. Novossiadliy; A.L. Shleykel. Parametric excitation of waves on a free boundary of a horizontal fluid layer. Comptes Rendus. Mécanique, Volume 332 (2004) no. 4, pp. 257-262. doi : 10.1016/j.crme.2004.01.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.01.010/

[1] S.M. Zenkovskaya, V.I. Yudovich, Method of integro-differential equations in the free boundary problems and parametric wave exitation, Preprint, Part I, Dep. in VINITI 2587-B, 2001, p. 33

[2] S.M. Zenkovskaya, V.I. Yudovich, Method of integro-differential equations and continued fractions in the problem of parametric wave exitation, submitted for publication

[3] A.A. Cherepanov, Influence of variable fields on Rayleigh–Taylor instability, Preprint. Some of the problems of liquid boundary instability, Uralsk. Scientific center AN SSSR, Sverdlovsk, 1984, pp. 29–53

[4] G.S. Markman; V.I. Yudovich Numerical study of the onset of convection in fluid layer under influence of periodic in time external forces, Izv. Akad. Nauk SSSR Ser. Mech. Fluid and Gas, Volume 3 (1972), pp. 81-86

[5] V.I. Yudovich Continued Fractions Method in Spectral Theory of Linear Differential Operators with Periodical Coefficients, Novgorodskiy Universitet, 2001, pp. 20-24

[6] M.J.O. Strett Lame, ONTI, Moscow, 1935

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This research was supported by the Russian Foundation for Basic Research (02-01-00337 and 01-01-22002) and the program “Universities of Russia – fundamental research” (project UR.04.01.063).

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