Numerical method of studying nonlinear interactions between long waves and multiple short waves
Xie Tao(谢涛)a)†, Kuang Hai-Lan(旷海兰)a), William Perrieb), Zou Guang-Hui(邹光辉)a), Nan Cheng-Feng(南撑峰)a), He Chao(何超)a), Shen Tao(沈涛)a), and Chen Wei(陈伟)a)
a School of Information Engineering, Wuhan University of Technology, Wuhan 430070, China; b Bedford Institute of Oceanography, B2Y 4A2, Dartmouth, NS, Canada
Abstract Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water. Specifically, this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves. Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train. From simulation results, we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train (expressed as wave train 2) leads to the energy focusing of the other short wave train (expressed as wave train 3). This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3.
Received: 14 December 2008
Revised: 30 December 2008
Accepted manuscript online:
PACS:
93.85.-q
(Instruments and techniques for geophysical research: Exploration geophysics)
Fund: Project supported by the National
High Technology Research and Development Program of China (Grant No
2007AA12Z170), the Major Research Plan of the National Natural
Science Foundation of China (Grant No 40706058) , the
Science-Technology Chenguang foundation for Young Scientist of
Wuhan, China (Grant No 200850731388), and the Canadian Space Agency
Government Related Initiatives Program (GRIP) entitled Building
Satellite Data into Fisheries and Oceans
Operational Systems.
Cite this article:
Xie Tao(谢涛), Kuang Hai-Lan(旷海兰), William Perrie, Zou Guang-Hui(邹光辉), Nan Cheng-Feng(南撑峰), He Chao(何超), Shen Tao(沈涛), and Chen Wei(陈伟) Numerical method of studying nonlinear interactions between long waves and multiple short waves 2009 Chin. Phys. B 18 3090
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
