On solitary wave in nonuniform shear currents
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Available online at https://link.springer.com/journal/42241 http://www.jhydrodynamics.com Journal of Hydrodynamics, 2020, 32(4): 800-805 https://doi.org/10.1007/s42241-020-0051-z
On solitary wave in nonuniform shear currents * Zhan Wang1, Bin-bin Zhao1, Wen-yang Duan1, R. Cengiz Ertekin1, 2, Masoud Hayatdavoodi1, 3, Tian-yu Zhang1 1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China 2. Department of Ocean and Resources Engineering, University of Hawaii, Honolulu, USA 3. Civil Engineering Department, School of Science and Engineering, University of Dundee, Dundee, UK (Received September 6, 2019, Revised January 19, 2020, Accepted February 5, 2020, Published online August 26, 2020) ©China Ship Scientific Research Center 2020 Abstract: In this paper, steady solutions of solitary waves in the presence of nonuniform shear currents are obtained by use of the high-level Green-Naghdi (HLGN) model. We focus on large-amplitude solitary waves in strong opposing shear currents. The linear-type currents, quadratic-type currents and cubic-type currents are considered. In particular, the wave speed, wave profile, velocity field, particle trajectories and vorticity distribution are studied. It is demonstrated that presence of the nonuniform shear current modifies the velocity field and vorticity field of the solitary wave. Key words: Solitary wave, nonuniform shear current, velocity field, particle trajectories, vorticity field
Solitary waves have been an important topic in nonlinear water wave field for many decades. Dutykh and Clamond[1] proposed an effective method to calculate the profile and the velocity field of the solitary waves ( H / d 0.79 , where H is the wave amplitude and d is the water depth) by solving Euler’s equations. Recently, Duan et al.[2] calculated steep solitary waves, and even a limiting-amplitude solitary wave with H / d = 0.833199 by using the high-level irrotational Green-Naghdi (HLIGN) model. Zhong and Wang[3] derived a strongly nonlinear weakly dispersive wave model to study some solitary wave transformation problems. Tong et al.[4] used a harmonic polynomial cell method to study the solitary wave collisions problems. Meanwhile, wave-current interaction is universal in coastal regions, and the wave profile, speed and particle trajectories are different when compared with wave field with no current. Thus, it is important to study the effect of wave-current interaction of the flow field. * Project supported by the National Natural Science Foundation of China (Nos. 11772099, 11972126, 11572093 and 51490671). Biography: Zhan Wang (1989-), Male, Ph. D. Candidate, E-mail: [email protected] Corresponding author: Bin-bin Zhao, E-mail: [email protected]
Steady solutions of solitary waves in the presence of linear shear currents have been studied by some researchers. Choi[5], Pak and Chow[6] used asymptotic method and third-order solution, respectively, to study the solitary-wave profile, wave speed and streamlines for a solitary wave in linear shear cur
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