中国物理B ›› 2009, Vol. 18 ›› Issue (7): 3090-3098.doi: 10.1088/1674-1056/18/7/080

• • 上一篇    

Numerical method of studying nonlinear interactions between long waves and multiple short waves

WilliamPerrie1, 谢涛2, 旷海兰2, 邹光辉2, 南撑峰2, 何超2, 沈涛2, 陈伟2   

  1. (1)Bedford Institute of Oceanography, B2Y 4A2, Dartmouth, NS, Canada; (2)School of Information Engineering, Wuhan University of Technology, Wuhan 430070, China
  • 收稿日期:2008-12-14 修回日期:2008-12-30 出版日期:2009-07-20 发布日期:2009-07-20
  • 基金资助:
    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.

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)   

  1. a School of Information Engineering, Wuhan University of Technology, Wuhan 430070, China; b Bedford Institute of Oceanography, B2Y 4A2, Dartmouth, NS, Canada
  • Received:2008-12-14 Revised:2008-12-30 Online:2009-07-20 Published:2009-07-20
  • Supported by:
    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.

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摘要： 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.

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.

Key words: sea surface, nonliear interaction, numerical method

中图分类号:  (Instruments and techniques for geophysical research: Exploration geophysics)

  • 93.85.-q
92.10.Hm (Ocean waves and oscillations) 92.10.Dh (Deep ocean processes) 02.60.-x (Numerical approximation and analysis)