An application of Nwogu’s Boussinesq model to analyze the head-on collision process between hydroelastic solitary waves

Abstract

This article deals with the nonlinear head-on collision between two hydroelastic solitary waves in plate–covered water with Nwogou’s Boussinesq model for the nonlinear fluid motion. This model contains a parameter α that is associated with horizontal velocities according to the chosen level of horizontal velocity variables. A thin elastic cover is considered as the Euler–Bernoulli beam model. To derive the series solution, we apply the Poincaré–Lighthill–Kuo (PLK) method to solve analytically the highly nonlinear coupled partial differential equations. The impact of all the physical parameters is discussed with the help of the asymptotic solutions and graphic representations. In particular, the authors address the behavior of plate deflection, maximum run-up during a collision, phase shift, distortion profile, and wave speed. It is found that the variation of the free parameter α and plate terms dramatically change the amplitude of a solitary wave. It is noticed that a very small tilting occurs due to the distortion in wave profile. The maximum run-up amplitude and the wave speed rise due to a greater influence of the free parameter. The phase shift tends to diminish due to an increment in the free parameter and plate terms. The novelty of the present methodology is compared with previously published results.

Keywords

• head-on collision
• nwogu’s boussinesq model
• perturbation method
• solitary waves
• thin elastic plate
• 47.35.fg
• 47.35.lf
• 52.65.vv