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.
| Language | English |
|---|---|
| Pages | 290-299 |
| Number of pages | 10 |
| Journal | Ocean Engineering |
| Volume | 91 |
| DOIs | |
| Publication status | Published - 15 Nov 2014 |
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Keywords
- bi-chromatic wave
- fully nonlinear
- homotopy analysis
- series approximation
- deep-water
- velocity potential
- fast fourier transform analysis
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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 journal › Article
TY - JOUR
T1 - Fully nonlinear solution of bi-chromatic deep-water waves
AU - Lin, Zhiliang
AU - Tao, Longbin
AU - Pu, Yongchang
AU - Murphy, Alan J.
PY - 2014/11/15
Y1 - 2014/11/15
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.
KW - bi-chromatic wave
KW - fully nonlinear
KW - homotopy analysis
KW - series approximation
KW - deep-water
KW - velocity potential
KW - fast fourier transform analysis
UR - http://www.scopus.com/inward/record.url?scp=84907989582&partnerID=8YFLogxK
U2 - 10.1016/j.oceaneng.2014.09.015
DO - 10.1016/j.oceaneng.2014.09.015
M3 - Article
VL - 91
SP - 290
EP - 299
JO - Ocean Engineering
T2 - Ocean Engineering
JF - Ocean Engineering
SN - 0029-8018
ER -