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Bifurcation of Sound Waves in a Disturbed Fluid

Received: 12 July 2017    Accepted: 19 July 2017    Published: 15 August 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.

Published in American Journal of Modern Physics (Volume 6, Issue 5)
DOI 10.11648/j.ajmp.20170605.13
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).
Cite This Article
  • 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://article.sciencepublishinggroup.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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    JO  - American Journal of Modern Physics
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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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