American Journal of Modern Physics
Volume 6, Issue 5, September 2017, Pages: 91-95
Received: Jul. 12, 2017;
Accepted: Jul. 19, 2017;
Published: Aug. 15, 2017
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Zuwen Qian, Institute of Acoustics, Chinese Academy of Sciences, Beijing, China
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.
Bifurcation of Sound Waves in a Disturbed Fluid, American Journal of Modern Physics.
Vol. 6, No. 5,
2017, pp. 91-95.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
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M. J. Feigenbaum, “Quantitative universality for a class of nonlinear transformations”, J. Stat. Phys. 19, 25-52 (1978).
W. Lauterborn and E. Cramer, “Subharmonic route to chaos observed in acoustics”, Phys, Rev. Lett. 47, 1445-1448 (1981).
Song-Yoon Kim and Bambi Hu，“Bifurcations and transitions to chaos in an inverted Pendulum”, Phys. Rev. E. 58, 3028 (1998).
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).
Ruby Lawrence, “Applications of the Mathieu equation”, Am. J. Phys. 64, 39-44 (1996).
D. Shao, Z. W. Qian, “First subharmonic sound in disturbed water”, Chinese Physical Letters 4, 133-135 (1987).
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.
M J. Lighthill. “On sound generated aerodynamically”, Proc Roy Soc (London) A 211, 564-587 (1952).
N W. McLachlan, Theory and application of Mathieu functions. (Dover, New York, Publications, 1964), pp, 1-401.
Zu-Wen Qian, “Cumulative solutions of nonlinear longitudinal vibration in isotropic solid Bars”, Chin. Phys. B, 23, 064301 (2014).