Fully nonlinear solution of bi-chromatic deep-water waves
Fully nonlinear solution of bi-chromatic deep-water waves
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.
Bi-chromatic wave, Fully nonlinear, Homotopy analysis, Series approximation
290-299
Lin, Zhiliang
77e465d9-569b-47c8-9c24-710abf94c225
Tao, Longbin
d2cd2478-aa50-45ff-b24f-f9f2063db024
Pu, Yongchang
c792021e-f917-4c9b-9a67-254005bb9d6d
Murphy, Alan J.
8e021dad-0c60-446b-a14e-cddd09d44626
Lin, Zhiliang
77e465d9-569b-47c8-9c24-710abf94c225
Tao, Longbin
d2cd2478-aa50-45ff-b24f-f9f2063db024
Pu, Yongchang
c792021e-f917-4c9b-9a67-254005bb9d6d
Murphy, Alan J.
8e021dad-0c60-446b-a14e-cddd09d44626
Lin, Zhiliang, Tao, Longbin, Pu, Yongchang and Murphy, Alan J.
(2014)
Fully nonlinear solution of bi-chromatic deep-water waves.
Ocean Engineering, 91, .
(doi:10.1016/j.oceaneng.2014.09.015).
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.
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Accepted/In Press date: 10 September 2014
e-pub ahead of print date: 3 October 2014
Additional Information:
Funding Information:
The presented study was undertaken with the support from the GLOBAL SECURE (Sustainable Energy through China–UK Research Engagement) project funded by EPSRC , EP/K004689/1 . The authors would also like to acknowledge the support of British Council and Chinese Scholarship Commission through the Sino-UK Higher Education Research partnership for Ph.D. Studies (Newcastle University – Shanghai Jiao Tong University). The first author would like to express his thanks to the National Natural Science Foundation of China (no. 51209136 ) and the National Key Basic Research Program of China (Approval no. 2014CB046801 ) for the support on this work.
Keywords:
Bi-chromatic wave, Fully nonlinear, Homotopy analysis, Series approximation
Identifiers
Local EPrints ID: 483828
URI: http://eprints.soton.ac.uk/id/eprint/483828
ISSN: 0029-8018
PURE UUID: ac48f08d-182e-46bb-a39d-ad5b4435016f
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Date deposited: 06 Nov 2023 18:19
Last modified: 17 Mar 2024 13:35
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Contributors
Author:
Zhiliang Lin
Author:
Longbin Tao
Author:
Yongchang Pu
Author:
Alan J. Murphy
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