Nonlinear progressive waves in water of finite depth - an analytic approximation

Longbin Tao, Hao Song, Subrata Chakrabarti

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53 Citations (Scopus)


An analytical solution using homotopy analysis method is developed to describe the nonlinear progressive waves in water of finite depth. The velocity potential of the wave is expressed by Fourier series and the nonlinear free surface boundary conditions are satisfied by continuous mapping. Unlike the perturbation method, the present approach is not dependent on small parameters. Thus solutions are possible for steep waves. Furthermore, a significant improvement of the convergence rate and region is achieved by applying Homotopy-Padé Approximants. The calculated wave characteristics of the present solution agree well with previous numerical and experimental results.

Original languageEnglish
Pages (from-to)825-834
Number of pages10
JournalCoastal Engineering
Issue number11
Publication statusPublished - Nov 2007


  • finite water depth
  • homotopy analysis method
  • nonlinear
  • progressive waves
  • velocity potential
  • fourier series
  • continuous mapping
  • Homotopy-Padé approximants

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