Hydroelastic solitary wave during the head-on collision process in a stratified fluid

Abstract

In this study, head-on collision between hydroelastic solitary waves propagating in a two-layer fluid beneath a thin elastic plate is analytically investigated. The plate structure is modeled using the Euler–Bernoulli beam theory with the effect of compressive stress. We consider that the lower- and upper-layer fluids having different constant densities are incompressible, and the motion is irrotational. The asymptotic series solutions of the resulting highly nonlinear coupled differential equations are deduced with the combination of a method of strained coordinates and the Poincaré–Lighthill–Kuo method. The series solutions obtained are presented up to the third-order approximation. The inclusion of all the emerging parameters is discussed graphically and mathematically against interfacial waves, plate deflection, wave speed, phase shift, maximum run-up amplitude, and the velocity functions. The presence of the elastic plate reveals a decreasing impact on the wave profiles in the upper- and lower-layer fluid. However, the distortion profile shows converse behavior in the upper-layer fluid as compared with the lower-layer fluid. Interfacial wave speed also tends to diminish due to the elastic plate parameter and the density ratio as the wave amplitude is high.