Unified Theory Based on Parameter Scaling for Derivation of Nonlinear Wave Equations in Bubbly Liquids

DOI Web Site 被引用文献33件 参考文献19件
  • KANAGAWA Tetsuya
    Division of Mechanical and Space Engineering, Hokkaido University, Research Fellow of the Japan Society for the Promotion of Science
  • 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

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.

収録刊行物

被引用文献 (33)*注記

もっと見る

参考文献 (19)*注記

もっと見る

関連プロジェクト

もっと見る

キーワード

詳細情報 詳細情報について

問題の指摘

ページトップへ