Fission law of solitary waves propagating over sharply variable topography
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Available online at https://link.springer.com/journal/42241 http://www.jhydrodynamics.com Journal of Hydrodynamics, 2020, 32(4): 727-734 https://doi.org/10.1007/s42241-020-0049-6
Fission law of solitary waves propagating over sharply variable topography * Da-lin Tan1, 2, Ji-fu Zhou1, 2, Xu Wang1 1. Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China 2. School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China (Received February 1, 2019, Revised May 7, 2019, Accepted May 13, 2019, Published online August 26, 2020) ©China Ship Scientific Research Center 2020 Abstract: The fission of solitary waves propagating over variable topography is investigated. In previous theories, to predict the number and the amplitudes of disintegrated solitons in the wave packet generated from a solitary wave, the parameters of the water environment and the incident solitary wave are required. However, it is difficult to measure these parameters in the ocean because of their temporal and spatial variations. In this paper, a fission law, in the form of the expressions of the number and the amplitudes of the disintegrated solitons, is derived from the partial information available on the wave packet. Theoretical analysis shows that the law is suitable for describing the fission of both surface and internal solitary waves and is also applicable to the cases of wave damping and wave breaking. Comparisons between the model output and the results from laboratory experiments, numerical simulations and field observations available in the literature demonstrate that the fission law can efficiently estimate the number and the amplitudes of solitons in the wave packet generated by a solitary wave. Key words: Fission law, solitary wave packet, wave breaking
Introduction The solitary wave packets are ubiquitous in the ocean and play a significant role in the biological processes[1-2], the sediment transport[3-4] and the offshore engineering[5-10]. In examining the satellite images of 116 internal wave packets from 1995 to 2001 in the South China Sea (SCS), Zhao et al.[11] found that all internal wave packets on the continental shelf of the SCS are composed of rank-ordered internal solitary waves. Near the continental shelf break in the SCS, Ramp et al.[12] observed that highly nonlinear internal soliton packets were responsible for the most energetic motions recorded by moored and shipboard observations. More recently, seven packets of internal solitary waves were observed near the Dongsha Plateau from the synchronized satellite and
* Project supported by the National Key Research and Development Program of China (Grant No. 2017YFC1404202), the National Natural Science Foundation of China (Grant Nos. 11572332, 11602274) and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDB22040203, XDA22000000). Biography: Da-lin Tan (1992-), Male, Ph. D., E-mail: [email protected] Corresponding auth
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