Bubble Dynamics and Shock Waves pp 107-140

Part of the Shock Wave Science and Technology Reference Library book series (SHOCKWAVES, volume 8) | Cite as

Nonlinear Wave Propagation in Bubbly Liquids


Weakly nonlinear wave equations for pressure waves in bubbly liquids are derived in a general and systematic way based on the asymptotic expansion method of multiple scales. The derivation procedure is explained in detail with a special attention to scaling relations between physical parameters characterizing the wave motions concerned. In the framework of the present theory, one can systematically deal with various weakly nonlinear wave motions for various systems of governing equations of bubbly liquids, thereby deriving such as the Korteweg–de Vries–Burgers equation, the nonlinear Schrödinger equation, and the Khokhlov–Zabolotskaya–Kuznetsov equation. In this sense, the method may be called a unified theory of weakly nonlinear waves in bubbly liquids.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • T. Yano
    • 1
  • T. Kanagawa
    • 2
  • M. Watanabe
    • 3
  • S. Fujikawa
    • 1
  1. 1.Osaka UniversityOsakaJapan
  2. 2.University of TokyoTokyoJapan
  3. 3.Hokkaido UniversityHokkaidoJapan

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