Nonlinear propagation of weakly diffracted sound beams in a weakly nonuniform bubbly liquid is analytically studied based on the method of multiple scales and scaling relations of some physical parameters. The system of basic equations consists of the conservation equations of mass and momentum for gas and liquid in a two-flui model, the Keller equation for bubble wall, the state equations for gas and liquid, and so on. The compressibility of liquid is taken into account and this leads to the wave attenuation due to bubble oscillations. It is assumed that the spatial distribution of the number density of bubbles in an initial state at rest is a slowly varying function of space coordinates and the amplitude of its variation is small compared with a mean number density. As a result, a Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation with dispersion and nonuniform effects for a low frequency and long wavelength case and a nonlinear Schro¨dinger (NLS) equation with dissipation, diffraction, and nonuniform effects are derived from the basic equations.
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ASME-JSME-KSME 2011 Joint Fluids Engineering Conference
July 24–29, 2011
Hamamatsu, Japan
Conference Sponsors:
- Fluids Engineering Division
ISBN:
978-0-7918-4441-0
PROCEEDINGS PAPER
Nonlinear Propagation of Sound Beam in Nonuniform Bubbly Liquids
Tetsuya Kanagawa,
Tetsuya Kanagawa
Hokkaido University, Sapporo, Japan
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Junya Kawahara,
Junya Kawahara
Hokkaido University, Sapporo, Japan
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Kazumichi Kobayashi,
Kazumichi Kobayashi
Hokkaido University, Sapporo, Japan
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Masao Watanabe,
Masao Watanabe
Hokkaido University, Sapporo, Japan
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Shigeo Fujikawa
Shigeo Fujikawa
Hokkaido University, Sapporo, Japan
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Tetsuya Kanagawa
Hokkaido University, Sapporo, Japan
Takeru Yano
Osaka University, Suita, Japan
Junya Kawahara
Hokkaido University, Sapporo, Japan
Kazumichi Kobayashi
Hokkaido University, Sapporo, Japan
Masao Watanabe
Hokkaido University, Sapporo, Japan
Shigeo Fujikawa
Hokkaido University, Sapporo, Japan
Paper No:
AJK2011-33017, pp. 237-241; 5 pages
Published Online:
May 25, 2012
Citation
Kanagawa, T, Yano, T, Kawahara, J, Kobayashi, K, Watanabe, M, & Fujikawa, S. "Nonlinear Propagation of Sound Beam in Nonuniform Bubbly Liquids." Proceedings of the ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 2, Fora. Hamamatsu, Japan. July 24–29, 2011. pp. 237-241. ASME. https://doi.org/10.1115/AJK2011-33017
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