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2022-04-27T09:03:22Z
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3:62:5592:3116
Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density
金川, 哲也
Kanagawa, Tetsuya
Copyright 2015 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.
The following article appeared in J. Acoust. Soc. Am. 137, 2642 (2015) and may be found at http://dx.doi.org/10.1121/1.4916371
This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351–369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov–Zabolotskaya–Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.
Acoustical Society of America
2015-05
eng
journal article
http://hdl.handle.net/2241/00125510
https://tsukuba.repo.nii.ac.jp/records/34533
25994696
10.1121/1.4916371
0001-4966
AA00253792
The Journal of the Acoustical Society of America
137
5
2642
2654
https://tsukuba.repo.nii.ac.jp/record/34533/files/JASA_137-5.pdf
application/pdf
418.6 kB
2015-12-01