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Projecting technique is used for a system of coupled nonlinear equations for interacting modes derivation. Three independent modes of the viscous flow: leftwards, rightwards propagating (acoustic) and the stationary one (heat) are specified by a set of orthogonal projectors. The final system of coupled equations is equivalent to the basic one with the accuracy up to the third-order nonlinear terms and its form allows to apply nonsingular perturbations method for an approximate solution in the case when one mode is dominant compared with other iterated modes. Caloric and thermal equations of state are taken in the general form. Thermoviscous media are treated, that leads to a system of coupled equations of the Burgers type. The modified Burgers equation for rightwards mode affected by other ones is obtained as well as its stationary solutions.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
121--131
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
Bibliografia
- 1. O.V. Rudenko and S.I. Soluyan, Theoretical foundations of nonlinear acoustics, Plenum, Consultant Bureau, New York 1977.
- 2. N.S. Bakhvalov, Ya.M. Zhileikin and E.A. Zabolotskaya, Nonlinear theory of sound beams, American Institute of Physics, New York 1987.
- 3. V.I. Kuznetsov, Equations of nonlinear acoustics, Sov. Phys.-Acoust, 16, 467-470 (1971).
- 4. A.A. Perelomova, Nonlinear dynamics of vertically propagating acoustic waves in a stratified atmosphere, Acta Acustica, 84, 6, 1002-1006 (1998).
- 5. A.A. Perelomova, Projectors in nonlinear evolution problem: acoustic solitons of bubbly liquid, Applied Mathematical Letters, 13, 93-98 (2000).
- 6. A.A. Novikov, On application of coupled waves method to non-resonance interactions analysis, Izv. Vuzov, Radiofizika, 19, 2, 321-328 (1976).
- 7. L.S.G. Kovasznay, Turbulence in supersonic flow, J.Aero. Sci., 20, 657-682 (1953).
- 8. S. Makarov and M. Ochmann, Nonlinear and thermoviscous phenomena in acoustics, Acta Acustica, 82, 579-606 (1996).
- 9. J.N. Tjøtta and S. Tjøtta, Finite amplitude ultrasound beams, Proceedings of 1994 IFFE International Ultrasonics Symposium, Cannes 1994.
- 10. A.M. Berg, A theoretical investigation of some nonlinear propagation modes in ultrasound, Thesis, Dept. Mathematics, University of Bergen, Bergen 1996.
- 11. S.B. Leble, Nonlinear waves in waveguides with strati cation, Springer-Verlag, Berlin 1990.
- 12. S.A. Gabov, Introduction to the theory of nonlinear waves [in Russian], Moscow State University, Moscow 1988.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT3-0005-0013
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