Comptes Rendus
Influence of high-frequency vibrations on the onset of convection in a two-layer system
Comptes Rendus. Mécanique, Volume 336 (2008) no. 3, pp. 269-274.

This Note deals with the influence of high-frequency translational oscillations on the onset of convection in a two-layer system of weakly heterogeneous immiscible fluids with deformable interface. The averaging method is applied to the generalized Oberbeck–Boussinesq equations. Vibration-generated forces and tensions appear as the result. A transition to the Oberbeck–Boussinesq approximation is made in the averaged equations. Analysis of averaged equations leads to the following conclusions. Horizontal vibrations are obtained not influencing the onset of convection, and in the cases of other directions the influence of vibration is determined by a single parameter, depending on velocity amplitude and direction. Vibration is shown to generate effective surface tension, smoothing the interface. Critical parameters are calculated for the case of homogeneous fluids.

Le but de ce travail est d'analyser l'influence des vibrations translationnelles haute fréquence sur le dèclenchement de la convection, dans un système à deux couches de fluides non miscibles faiblement inhomogènes, oú l'interface est déformable. On applique une méthode de moyennisation sur le système des équations d'Oberbeck–Boussinesq généralisé. Il en résulte l'apparition d'une densité supplémentaire de forces extérieures et une nouvelle tension à l'interface. On étudie le seuil d'instabilité de la solution de conduction stationnaire, sur le système moyenné. Un premier résultat est que les vibrations en translation horizontale n'influencent pas le seuil d'instabilité. Un seul paramètre, fonction de l'amplitude et de la direction, intervient pour les autres directions de vibrations. On montre alors que les vibrations engendrent une tension de surface effective qui aplanit l'interface. On calcule les paramètres critiques dans le cas de fluides homogènes (cas sans pesanteur).

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DOI: 10.1016/j.crme.2007.10.009
Keywords: Vibrations, Convection, Averaging
Mot clés : Vibrations, Convection, Moyennisation

Svetlana M. Zenkovskaya 1; Vasili A. Novosiadliy 1

1 Milchakova 8a, South Federal University, Rostov-on-Don 344019, Russia
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Svetlana M. Zenkovskaya; Vasili A. Novosiadliy. Influence of high-frequency vibrations on the onset of convection in a two-layer system. Comptes Rendus. Mécanique, Volume 336 (2008) no. 3, pp. 269-274. doi : 10.1016/j.crme.2007.10.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.10.009/

[1] S.M. Zenkovskaya; I.B. Simonenko The effect of high-frequency vibrations on the onset of convection, Izv. Akad. Nauk SSSR, MZhG, Volume 5 (1966), pp. 51-55

[2] S.M. Zenkovskaya, On the influence of vibration on convective instability, in: Numerical Methods in Viscous Fluid Dynamics, Novosibirsk, ITPM SO Akad. Nauk SSSR, 1979, Proc. of VII All Union Seminar on Numerical Methods in Viscous Fluids Dynamics, pp. 116–122

[3] I.B. Simonenko Substantiation of the method of averaging for the problem of convection in a field of rapidly oscillating forces and for other parabolic equations, Mat. Sbornik, Volume 87 (1972) no. 2, pp. 236-253

[4] V.B. Levenshtam Substantiation of the method of averaging for the problem of convection for high-frequency vibrations, Sib. Mat. Zh., Volume 2 (1993), pp. 92-109

[5] V.I. Yudovich The vibrodynamics of systems with constraints, Dokl. Ross. Akad. Nauk, Volume 354 (1997) no. 5, pp. 622-624

[6] S.M. Zenkovskaya; A.L. Shleykel Influence of high-frequency vibration on the onset of Marangoni convection in horizontal fluid layer, Appl. Math. Mech., Volume 66 (2002), pp. 573-583

[7] D.V. Lyubimov Thermovibrational flows in a fluid with a free surface, Microgravity Quart., Volume 4 (1994), pp. 117-122

[8] R.W. Zeren; W.C. Reynolds Thermal instabilities in two-fluid horizontal layers, J. Fluid Mech., Volume 53 (1972), pp. 305-327

[9] A. Juel; J.M. Burgess; W.D. McCormick; J.B. Swift; H. Swinney Surface tension-driven convection patterns in two liquid layers, Physica D: Nonlinear Phenomena, Volume 143 (2000), pp. 169-186

[10] B. Zhou; Q. Liu; Z. Tang Rayleigh–Marangoni–Benard instability in two-layer fluid system, Acta Mech. Sinica, Volume 20 (2004) no. 4, pp. 366-373

[11] V.I. Yudovich; S.M. Zenkovskaya; V.A. Novosiadliy; A.L. Shleykel Parametric excitation of waves on a free boundary of a horizontal fluid layer, C. R. Mecanique, Volume 332 (2004), pp. 257-262

[12] S.M. Zenkovskaya, V.A. Novosiadliy, Influence of high-frequency vibration on the onset of convection in two-layer system with deformable interface, Preprint 2007, Dep. in VINITI, 29.06.2007 N 683-B 2007, 60 p

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