Nonlinear shallow water wave analysis by concentrated mass model (1st report, suggestion and validity of analytic model)

Satoshi Ishikawa, Takahiro Kondou, Kenichiro Matsuzaki

Research output: Contribution to journalArticlepeer-review


A waveform of a water surface caused by water sloshing in a tank often changes because of nonlinear effect of fluid. In the case of a small water depth, shallow water wave theory can be applied to this phenomenon. When Tsunami propagates on a sloping beach, soliton wave is generated because of nonlinear effect of fluid. This Tsunami phenomenon also can be evaluated based on shallow water wave theory. The purpose of this study is to establish a practical analytical model to analyze these phenomena. This model consists of masses, connecting nonlinear springs, connecting dampers, base support dampers, and base support springs. The characteristic of connecting nonlinear spring is derived from the gravitational pressure, and the base support damper and the base support spring are derived from the shear stress on a bottom. Water waves generated in a rectangle tank, on a sloping beach are analyzed numerically by using the proposed model in order to confirm the validity of the model. All numerical computational results agree very well with the experimental results. Especially, the phenomena that the distorted waves are generated by the nonlinear effect of fluid are numerically reproduced. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear shallow water wave problem.

Original languageEnglish
Pages (from-to)1851-1862
Number of pages12
JournalNihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
Issue number790
Publication statusPublished - Jul 23 2012

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering


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