Please wait a minute...
Chin. Phys. B, 2009, Vol. 18(7): 3090-3098    DOI: 10.1088/1674-1056/18/7/080
GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS Prev  

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.
Keywords:  sea surface      nonliear interaction      numerical method  
Received:  14 December 2008      Revised:  30 December 2008      Accepted manuscript online: 
PACS:  93.85.-q (Instruments and techniques for geophysical research: Exploration geophysics)  
  92.10.Hm (Ocean waves and oscillations)  
  92.10.Dh (Deep ocean processes)  
  02.60.-x (Numerical approximation and analysis)  
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

[1] Numerical simulations of strong-field processes in momentum space
Yan Xu(徐彦), Xue-Bin Bian(卞学滨). Chin. Phys. B, 2020, 29(2): 023202.
[2] Effective dielectric constant model of electromagnetic backscattering from stratified air-sea surface film-sea water medium
Tao Xie(谢涛), William Perrie, He Fang(方贺), Li Zhao(赵立), Wen-Jin Yu(于文金), Yi-Jun He(何宜军). Chin. Phys. B, 2017, 26(5): 054102.
[3] Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients
Dong Hao (董灏), Nie Yu-Feng (聂玉峰), Cui Jun-Zhi (崔俊芝), Wu Ya-Tao (武亚涛). Chin. Phys. B, 2015, 24(9): 090204.
[4] A study of the early warning signals of abrupt change in the Pacific decadal oscillation
Wu Hao (吴浩), Hou Wei (侯威), Yan Peng-Cheng (颜鹏程), Zhang Zhi-Sen (张志森), Wang Kuo (王阔). Chin. Phys. B, 2015, 24(8): 089201.
[5] Three-dimensional simulation method of multipactor in microwave components for high-power space application
Li Yun (李韵), Cui Wan-Zhao (崔万照), Zhang Na (张娜), Wang Xin-Bo (王新波), Wang Hong-Guang (王洪广), Li Yong-Dong (李永东), Zhang Jian-Feng (张剑锋). Chin. Phys. B, 2014, 23(4): 048402.
[6] Effects of clouds, sea surface temperature, and its diurnal variation on precipitation efficiency
Shen Xin-Yong (沈新勇), Qing Tao (庆涛), Li Xiao-Fan (李小凡). Chin. Phys. B, 2013, 22(9): 094213.
[7] Effects of sea surface temperature, cloud radiative and microphysical processes, and diurnal variations on rainfall in equilibrium cloud-resolving model simulations
Jiang Zhe(蒋哲), Li Xiao-Fan(李小凡), Zhou Yu-Shu(周玉淑), and Gao Shou-Ting(高守亭) . Chin. Phys. B, 2012, 21(5): 054215.
[8] Analysis of multiple scattering from two-dimensional dielectric sea surface with iterative Kirchhoff approximation
Luo Wei(罗伟), Zhang Min(张民), Zhou Ping(周平), and Yin Hong-Cheng(殷红成). Chin. Phys. B, 2010, 19(8): 084102.
[9] Microwave Doppler spectra of sea return at small incidence angles: specular point scattering contribution
Zhang Yan-Min(张彦敏), Wang Yun-Hua(王运华), and Zhao Chao-Fang(赵朝方). Chin. Phys. B, 2010, 19(8): 084103.
[10] An angular cutoff composite model for investigation on electromagnetic scattering from two-dimensional rough sea surfaces
Nie Ding(聂丁) and Zhang Min(张民). Chin. Phys. B, 2010, 19(7): 074101.
[11] Investigation on the Doppler shifts induced by 1-D ocean surface wave displacements by the first order small slope approximation theory: comparison of hydrodynamic models
Wang Yun-Hua(王运华), Zhang Yan-Min(张彦敏), and Guo Li-Xin(郭立新). Chin. Phys. B, 2010, 19(7): 074103.
[12] A two scale nonlinear fractal sea surface model in a one dimensional deep sea
Xie Tao(谢涛),Zou Guang-Hui(邹光辉), William Perrie, Kuang Hai-Lan(旷海兰), and Chen Wei(陈伟). Chin. Phys. B, 2010, 19(5): 059201.
[13] Investigation on global positioning system signal scattering and propagation over the rough sea surface
Yang Chao(杨超), Guo Li-Xin(郭立新), and Wu Zhen-Sen(吴振森). Chin. Phys. B, 2010, 19(5): 054101.
[14] Electromagnetic backscattering from freak waves in (1+1)-dimensional deep-water
Xie Tao(谢涛), Shen Tao(沈涛), William Perrie, Chen Wei(陈伟), and Kuang Hai-Lan(旷海兰). Chin. Phys. B, 2010, 19(5): 054102.
[15] Study of scattering from time-varying Gerstners sea surface using second-order small slope approximation
Zhang Yan-Min(张彦敏), Wang Yun-Hua(王运华), and Guo Li-Xin(郭立新). Chin. Phys. B, 2010, 19(5): 054103.
No Suggested Reading articles found!