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Waves on the Liquids-Gas Free Surface in the Presence of the Acoustic Field in Gas

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Book cover Free Boundary Problems in Continuum Mechanics

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Abstract

We investigate the low-gravity problem on wave motions of the liquid (Q2) - gas (Q1) free surface Σ(ξ(x,y,Z,t) = 0), that is placed in a limited volume Q = Q 1 U Q2 (W(x,y, z) < 0). The high-frequency vibrator is contained in gas on

$$ {{S}_{0}} \subset {{S}_{1}} = \partial {{Q}_{1}}\backslash \Sigma \subset \partial Q. $$

It creates the acoustic field. This problem is being studied in nonlinear hydrodynamics formulation under hypothesis about idealized and potential motions of mediums. Frequency range of acoustic field is in 1 ÷3 kHZ with Bond number 0 ÷30.

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References

  1. Lukowsky I.A., Timoha A.N. Nonlinear dynamics of liquid-gas free surface in the presence of acoustic field in gas. Stable regime of motion, Kiev, 1988, 39p. (Preprint/ Ac. of Sc. Ukr.SSR. In-t of mathematics: 88.9).

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  2. Lukowsky I.A., Timoha A.N. One class of the boundary problems in theory of surface waves// Ukr. mathem. journ, 1991, 43, N 3, pp. 359–364.

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  3. The zero-gravity hydromechanic/Edited by A.D.Myshkies, M.:Nauka, 1978, 504p.

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  4. Lukowsky I.A., Timoha A.N. On stabilization of liquid-gas freesurface when interacting with acoustic field in gas// News of Ac.of Sc. USSR. Mech. of fluid and gas, 1991, N 3, pp. 80–84.

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Authors and Affiliations

  1. Institute of Mathematics, Kiev, 252601, Ukraine

    I. A. Lukowsky & A. N. Timoha

Authors
  1. I. A. Lukowsky
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  2. A. N. Timoha
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Editor information

Editors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Novosibirsk, 630090, Russia

    S. N. Antontsev  & A. M. Khludnev  & 

  2. Institut für Angewandte Mathematik und Statistik, Dachauer Str. 9 a, München, D-W-8000, Germany

    K.-H. Hoffmann

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© 1992 Springer Basel AG

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Lukowsky, I.A., Timoha, A.N. (1992). Waves on the Liquids-Gas Free Surface in the Presence of the Acoustic Field in Gas. In: Antontsev, S.N., Khludnev, A.M., Hoffmann, KH. (eds) Free Boundary Problems in Continuum Mechanics. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 106. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8627-7_21

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  • DOI: https://doi.org/10.1007/978-3-0348-8627-7_21

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9705-1

  • Online ISBN: 978-3-0348-8627-7

  • eBook Packages: Springer Book Archive

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