American Journal of Modern Physics

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Bifurcation of Sound Waves in a Disturbed Fluid

Received: Jul. 12, 2017    Accepted: Jul. 19, 2017    Published: Aug. 15, 2017
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Abstract

An equation that describes the wave propagation in the disturbed medium was deduced from the Lighthill’s equation. The so-called perturbation-cumulative approximation was suggested to solve this equation and the period-doubling bifurcation solutions were given. The results obtained in this paper helps to provide insights to the mechanism of the turbulence formation.

DOI 10.11648/j.ajmp.20170605.13
Published in American Journal of Modern Physics ( Volume 6, Issue 5, September 2017 )
Page(s) 91-95
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Period-Doubling Bifurcation, Chaos, Subharmonics, Disturbed Media

References
[1] M. J. Feigenbaum, “Quantitative universality for a class of nonlinear transformations”, J. Stat. Phys. 19, 25-52 (1978).
[2] W. Lauterborn and E. Cramer, “Subharmonic route to chaos observed in acoustics”, Phys, Rev. Lett. 47, 1445-1448 (1981).
[3] Song-Yoon Kim and Bambi Hu,“Bifurcations and transitions to chaos in an inverted Pendulum”, Phys. Rev. E. 58, 3028 (1998).
[4] T. B. Benjamin, F. Ursell, “The stability of the plane free surface of a liquid in vertical periodic motion”, Proc. Roy. Soc. A 225, 505-516 (1954).
[5] Ruby Lawrence, “Applications of the Mathieu equation”, Am. J. Phys. 64, 39-44 (1996).
[6] D. Shao, Z. W. Qian, “First subharmonic sound in disturbed water”, Chinese Physical Letters 4, 133-135 (1987).
[7] Z. W. Qian and D. Shao, “Some interesting phenomena of first subharmonic of sound in water”. In: Proc. IUPAP, IUTAM Symposium on Nonlinear Acoustics. V. K. Kidrinskii, editor. Vol. 2. Novosibirsh, Academy of Sciences USSR (1987), P. 245-248.
[8] M J. Lighthill. “On sound generated aerodynamically”, Proc Roy Soc (London) A 211, 564-587 (1952).
[9] N W. McLachlan, Theory and application of Mathieu functions. (Dover, New York, Publications, 1964), pp, 1-401.
[10] Zu-Wen Qian, “Cumulative solutions of nonlinear longitudinal vibration in isotropic solid Bars”, Chin. Phys. B, 23, 064301 (2014).
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  • APA Style

    Zuwen Qian. (2017). Bifurcation of Sound Waves in a Disturbed Fluid. American Journal of Modern Physics, 6(5), 91-95. https://doi.org/10.11648/j.ajmp.20170605.13

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    ACS Style

    Zuwen Qian. Bifurcation of Sound Waves in a Disturbed Fluid. Am. J. Mod. Phys. 2017, 6(5), 91-95. doi: 10.11648/j.ajmp.20170605.13

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    AMA Style

    Zuwen Qian. Bifurcation of Sound Waves in a Disturbed Fluid. Am J Mod Phys. 2017;6(5):91-95. doi: 10.11648/j.ajmp.20170605.13

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  • @article{10.11648/j.ajmp.20170605.13,
      author = {Zuwen Qian},
      title = {Bifurcation of Sound Waves in a Disturbed Fluid},
      journal = {American Journal of Modern Physics},
      volume = {6},
      number = {5},
      pages = {91-95},
      doi = {10.11648/j.ajmp.20170605.13},
      url = {https://doi.org/10.11648/j.ajmp.20170605.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajmp.20170605.13},
      abstract = {An equation that describes the wave propagation in the disturbed medium was deduced from the Lighthill’s equation. The so-called perturbation-cumulative approximation was suggested to solve this equation and the period-doubling bifurcation solutions were given. The results obtained in this paper helps to provide insights to the mechanism of the turbulence formation.},
     year = {2017}
    }
    

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    AB  - An equation that describes the wave propagation in the disturbed medium was deduced from the Lighthill’s equation. The so-called perturbation-cumulative approximation was suggested to solve this equation and the period-doubling bifurcation solutions were given. The results obtained in this paper helps to provide insights to the mechanism of the turbulence formation.
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Author Information
  • Institute of Acoustics, Chinese Academy of Sciences, Beijing, China

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