Investigation of Oblique Flexural Gravity Wave Scattering by Two Submerged Thin Vertical Porous Barriers with Different Porosities

Abstract

A hydroelastic model is developed here for studying the interaction of oblique water waves by two fully submerged thin vertical porous barriers placed some distance apart in a homogeneous fluid. The upper surface is a thin ice-sheet covering the standard free surface, and it is treated as a thin elastic plate by following the Euler–Bernoulli beam equation. The roots of the complex dispersion relation are studied with the help of a suitable contour plot. Assuming small-amplitude theory and structural response, the analytical solution is developed. In order to achieve the result, eigenfunction expansion and the least square method are employed to discuss the flexural gravity waves interaction with the submerged porous barriers. One of the current results is validated against two available results, and subsequent to the successful validation, the reflection and transmission coefficients, energy loss, and wave forces are computed and a parametric study is carried out involving different parameter values of the ice-sheet, porous barriers and angle of incidence. It points to an oscillatory behavior of the wave reflection. It further shows that due to an increase in the inertial effect of the porous barrier, the minima for reflection occur. It is observed that the vertical porous barriers succeed in dissipating a substantial amount of the wave energy when the inertial effect of the porous barriers is increased. Similar to the reflection coefficients, the hydrodynamic forces acting on the barriers also exhibit an oscillatory nature, and they can be observed to increase when the height of the barriers is increased. The effects of the floating ice-sheet on flexural waves are examined by obtaining and studying various results on the hydrodynamic forces. An important observation is that variation in the values of the elasticity of the floating ice-sheet has a significant impact on the wave forces acting on the submerged vertical porous barriers.