Nonlinear Wave Equation for Ultrasound Beam in Nonuniform Bubbly Liquids

• KANAGAWA Tetsuya

  Division of Mechanical and Space Engineering, Hokkaido University

• YANO Takeru

  Department of Mechanical Engineering, Osaka University

• WATANABE Masao

  Division of Mechanical and Space Engineering, Hokkaido University

• FUJIKAWA Shigeo

  Division of Mechanical and Space Engineering, Hokkaido University

抄録

In our previous paper (Kanagawa et al., J. Fluid Sci. Tech., 5, 2010), we have proposed a systematic method for derivation of various types of nonlinear wave equations for plane waves in bubbly liquids. The method makes use of an asymptotic expansion with multiple scales in terms of a small wave amplitude as an expansion parameter and a set of scaling relations of physical parameters, based on basic equations of two-fluid model of bubbly flows. In this paper, we extend the method so as to handle a weakly diffracted ultrasound beam in a quiescent liquid containing a number of spherical gas bubbles distributed with a weak nonuniformity. Because of the high expandability of the original method, the extension can be accomplished by adding a scaling relation of the diameter of the beam to the original set of scaling relations. As a result, we derive a generalized Khokhlov—Zabolotskaya—Kuznetsov (KZK) equation [or a generalized Kadomtsev—Petviashvili (KP) equation] for a long wave and low frequency case.

収録刊行物

• Journal of Fluid Science and Technology

  Journal of Fluid Science and Technology 6 (2), 279-290, 2011

  一般社団法人 日本機械学会

キーワード

• Bubbly Liquid
• Pressure Wave
• Ultrasound
• Beam
• Diffraction
• Nonuniformity
• Nonlinear Wave Equation
• KZK Equation
• KP Equation
• Multiple Scales

詳細情報

• CRID: 1390001205246505216
• NII論文ID: 130000664748
• DOI: 10.1299/jfst.6.279
• ISSN: 18805558
• Web Site: http://www.jstage.jst.go.jp/article/jfst/6/2/6_2_279/_pdf
• 本文言語コード: en
• データソース種別:
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