Fully nonlinear solution of bi-chromatic deep-water waves

Zhiliang Lin, Longbin Tao, Yongchang Pu, Alan J. Murphy

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Fully nonlinear bi-chromatic unidirectional waves propagating in deep-water are investigated using the homotopy analysis method. The velocity potential of the waves is expressed by Fourier series and the nonlinear free surface boundary conditions are satisfied by continuous mapping. The bi-chromatic wave elevation and velocity profiles underneath the wave crest and trough are presented and compared with the available perturbation results. Unlike the perturbation method, the present approach is not dependent on small parameters; therefore solutions are possible for steep waves. The Fast Fourier Transform analysis is then applied to study the effect of higher order wave components. The fully nonlinear dispersion relation is established. Comparisons of the wave characteristics demonstrate that the present method is effective to study the strongly nonlinear wave-wave interactions.

LanguageEnglish
Pages290-299
Number of pages10
JournalOcean Engineering
Volume91
DOIs
Publication statusPublished - 15 Nov 2014

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Water waves
Fourier series
Fast Fourier transforms
Boundary conditions

Keywords

  • bi-chromatic wave
  • fully nonlinear
  • homotopy analysis
  • series approximation
  • deep-water
  • velocity potential
  • fast fourier transform analysis

Cite this

Lin, Zhiliang ; Tao, Longbin ; Pu, Yongchang ; Murphy, Alan J. / Fully nonlinear solution of bi-chromatic deep-water waves. In: Ocean Engineering. 2014 ; Vol. 91. pp. 290-299.
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Fully nonlinear solution of bi-chromatic deep-water waves. / Lin, Zhiliang; Tao, Longbin; Pu, Yongchang; Murphy, Alan J.

In: Ocean Engineering, Vol. 91, 15.11.2014, p. 290-299.

Research output: Contribution to journalArticle

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N2 - Fully nonlinear bi-chromatic unidirectional waves propagating in deep-water are investigated using the homotopy analysis method. The velocity potential of the waves is expressed by Fourier series and the nonlinear free surface boundary conditions are satisfied by continuous mapping. The bi-chromatic wave elevation and velocity profiles underneath the wave crest and trough are presented and compared with the available perturbation results. Unlike the perturbation method, the present approach is not dependent on small parameters; therefore solutions are possible for steep waves. The Fast Fourier Transform analysis is then applied to study the effect of higher order wave components. The fully nonlinear dispersion relation is established. Comparisons of the wave characteristics demonstrate that the present method is effective to study the strongly nonlinear wave-wave interactions.

AB - Fully nonlinear bi-chromatic unidirectional waves propagating in deep-water are investigated using the homotopy analysis method. The velocity potential of the waves is expressed by Fourier series and the nonlinear free surface boundary conditions are satisfied by continuous mapping. The bi-chromatic wave elevation and velocity profiles underneath the wave crest and trough are presented and compared with the available perturbation results. Unlike the perturbation method, the present approach is not dependent on small parameters; therefore solutions are possible for steep waves. The Fast Fourier Transform analysis is then applied to study the effect of higher order wave components. The fully nonlinear dispersion relation is established. Comparisons of the wave characteristics demonstrate that the present method is effective to study the strongly nonlinear wave-wave interactions.

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