Different approaches in scattering of water waves by two submerged porous plates over an elastic sea-floor

Abstract

A hydroelastic model is presented here to look into the scattering of oblique water waves by two totally submerged vertical porous plates, placed at some distance from each other, in a homogeneous fluid flowing over an elastic sea-floor. Consideration of Euler–Bernoulli beam equation allows the elastic sea-floor to be approximated as a thin elastic plate whereas the porous plates follow the porous wave-maker theory. The complete analytical solution, under the assumption of small-amplitude theory and structural response, is obtained by employing eigenfunction expansion and least square method. Subsequently, numerical computation for the reflection and transmission coefficients and energy loss are carried out and discussed for different values of the elasticity of the sea-floor, porosity of the porous plates and other structural parameters. The present study establishes that reflection of the waves exhibits an oscillatory behaviour. It further shows that, due to an increase in the inertial effect of the porous plate, the minima in wave reflection occurs. The vertical porous plates are found to dissipate a significant portion of the wave energy when an increase in the inertial effect of the porous plates takes place. Furthermore, wave transmission decreases significantly due to the energy dissipation by the elastic sea-floor. Significant variation in the elastic specification of the sea-floor commands considerable influence when the propagating wave impinges upon the submerged vertical porous plates. In order to validate the present model, the obtained results are compared with available results which points towards a good agreement.