2010年7月
Unified Theory Based on Parameter Scaling for Derivation of Nonlinear Wave Equations in Bubbly Liquids
Journal of Fluid Science and Technology
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回数 : 96
- ,
- ,
- ,
- 巻
- 5
- 号
- 3
- 開始ページ
- 351
- 終了ページ
- 369
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1299/jfst.5.351
- 出版者・発行元
- 社団法人 日本機械学会
We propose a systematic derivation method of the Korteweg-de Vries-Burgers (KdVB) equation and nonlinear Schrödinger (NLS) equation for nonlinear waves in bubbly liquids on the basis of appropriate choices of scaling relations of physical parameters. The basic equations are composed of a set of conservation equations for mass and momentum and the equation of bubble dynamics in a two-fluid model. The scaling of parameters is related to the wavelength, frequency, propagation speed, and amplitude of waves concerned. With the help of the method of multiple scales, appropriate choices of the parameter scaling allow us to derive various nonlinear wave equations systematically from a set of basic equations. The result shows that the one-dimensional nonlinear propagation of a long wave with a low frequency is described by the KdVB equation, and that of an envelope of a carrier wave with a high frequency by the NLS equation. Thus, we establish a unified theory of derivation of nonlinear wave equations in bubbly liquids.
- リンク情報
- ID情報
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- DOI : 10.1299/jfst.5.351
- ISSN : 1880-5558
- CiNii Articles ID : 130000303623