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Open AccessArticle

Analytical Study of the Head-On Collision Process between Hydroelastic Solitary Waves in the Presence of a Uniform Current

1
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Yanchang Road, Shanghai 200072, China
2
Shanghai Key Laboratory of Mechanics in Energy Engineering, Yanchang Road, Shanghai 200072, China
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(3), 333; https://doi.org/10.3390/sym11030333
Received: 7 January 2019 / Revised: 24 February 2019 / Accepted: 1 March 2019 / Published: 6 March 2019
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
The present study discusses an analytical simulation of the head-on collision between a pair of hydroelastic solitary waves propagating in the opposite directions in the presence of a uniform current. An infinite thin elastic plate is floating on the surface of water. The mathematical modeling of the thin elastic plate is based on the Euler–Bernoulli beam model. The resulting kinematic and dynamic boundary conditions are highly nonlinear, which are solved analytically with the help of a singular perturbation method. The Poincaré–Lighthill–Kuo method is applied to obtain the solution of the nonlinear partial differential equations. The resulting solutions are presented separately for the left- and right-going waves. The behavior of all the emerging parameters are presented mathematically and discussed graphically for the phase shift, maximum run-up amplitude, distortion profile, wave speed, and solitary wave profile. It is found that the presence of a current strongly affects the wavelength and wave speed of both solitary waves. A graphical comparison with pure-gravity waves is also presented as a particular case of our study. View Full-Text
Keywords: nonlinear hydroelastic waves; uniform current; thin elastic plate; solitary waves; PLK method nonlinear hydroelastic waves; uniform current; thin elastic plate; solitary waves; PLK method
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MDPI and ACS Style

Bhatti, M.M.; Lu, D.Q. Analytical Study of the Head-On Collision Process between Hydroelastic Solitary Waves in the Presence of a Uniform Current. Symmetry 2019, 11, 333.

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