The University of Southampton
University of Southampton Institutional Repository

Fully nonlinear solution of bi-chromatic deep-water waves

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
0029-8018
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, 290-299. (doi:10.1016/j.oceaneng.2014.09.015).

Record type: Article

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.

This record has no associated files available for download.

More information

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

Catalogue record

Date deposited: 06 Nov 2023 18:19
Last modified: 10 May 2024 17:03

Export record

Altmetrics

Contributors

Author: Zhiliang Lin
Author: Longbin Tao
Author: Yongchang Pu
Author: Alan J. Murphy

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×