A fully dispersive weakly nonlinear model for water waves

K. Nadaoka, S. Beji, Y. Nakagawa

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


A fully dispersive weakly nonlinear water wave model is developed via a new approach named the multiterm-coupling technique, in which the velocity field is represented by a few vertical-dependence functions having different wave-numbers. This expression of velocity, which is approximately irrotational for variable depth, is used to satisfy the continuity and momentum equations. The Galerkin method is invoked to obtain a solvable set of coupled equations for the horizontal velocity components and shown to provide an optimum combination of the prescribed depth-dependence functions to represent a random wave-field with diversely varying wave-numbers. The new wave equations are valid for arbitrary ratios of depth to wavelength and therefore it is possible to recover all the well-known linear and weakly nonlinear wave models as special cases. Numerical simulations are carried out to demonstrate that a wide spectrum of waves, such as random deep water waves and solitary waves over constant depth as well as nonlinear random waves over variable depth, is well reproduced at affordable computational cost.

Original languageEnglish
Pages (from-to)303-318
Number of pages16
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1957
Publication statusPublished - 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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