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), 2017. Published by Science Publishing Group |
Period-Doubling Bifurcation, Chaos, Subharmonics, Disturbed Media
| [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). |
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
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
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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Download@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}
}
TY - JOUR T1 - Bifurcation of Sound Waves in a Disturbed Fluid AU - Zuwen Qian Y1 - 2017/08/15 PY - 2017 N1 - https://doi.org/10.11648/j.ajmp.20170605.13 DO - 10.11648/j.ajmp.20170605.13 T2 - American Journal of Modern Physics JF - American Journal of Modern Physics JO - American Journal of Modern Physics SP - 91 EP - 95 PB - Science Publishing Group SN - 2326-8891 UR - https://doi.org/10.11648/j.ajmp.20170605.13 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. VL - 6 IS - 5 ER -
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