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Nonlinear interaction of longitudinal—Transverse acoustic waves in a circular cylinder

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Abstract

The limiting amplitudes of acoustic oscillations in a cylindrical volume of a heat releasing medium in which one or several modes are unstable in the linear approximation are determined. One of the mechanisms limiting the amplitudes of unstable acoustic modes is the transfer of energy from them to damped modes by nonlinear interaction. The nonlinear interactions of plane acoustic waves in a long channel have been considered by Artamonov and Vorob'ev [1]; in the present paper, the interaction of mixed longitudinal—transverse acoustic modes in a closed cylindrical volume is considered. The equations describing the interaction of two and three longitudinal—transverse modes are derived and investigated in the quadratic approximation by the method of slowly varying amplitudes and phases of the oscillations [2]. The treatment is applicable to a high-temperature gas, for which general stability conditions in the linear approximation have been formulated by Artamonov [3].

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Literature cited

  1. V. I. Artamonov and A. P. Vorob'ev, “Nonlinear stabilization of unstable acoustic oscillations in a bounded heat releasing medium,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 34 (1978).

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  2. Ali-Hasan Nayfeh, Perturbation Methods, Wiley, New York (1973).

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  3. K. I. Artamonov, “Thermoacoustic stability of a high-temperature heat releasing gas,” Dokl. Akad. Nauk SSSR,231, 563 (1976).

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  4. O. V. Rudenko and S. I. Soluyan, Theoretical Foundations of Nonlinear Acoustics [in Russian], Nauka, Moscow (1975), p. 288.

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  5. Yu. V. Firsov, “Nonlinear interaction of waves in an active medium,” in: Proc. 23rd Scientific Conference of the Moscow Physicotechnical Institute, 1977 [in Russian], Dolgoprudnyi (1978), pp. 6–11.

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Authors and Affiliations

  1. Moscow

    Yu. V. Firsov

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  1. Yu. V. Firsov
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–9, September–October, 1982.

I should like to express my thanks to K. I. Artamonov (deceased) for suggesting the problem and for scientific supervision and A. P. Vorob'ev for constant interest in the work and helpful advice.

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Firsov, Y.V. Nonlinear interaction of longitudinal—Transverse acoustic waves in a circular cylinder. Fluid Dyn 17, 657–662 (1982). https://doi.org/10.1007/BF01090141

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  • DOI: https://doi.org/10.1007/BF01090141

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