Scattering of flexural gravity waves by a pair of submerged vertical porous barriers located above a porous sea-bed

Abstract

Abstract An analytical study is presented to investigate the scattering of oblique flexural gravity waves by a pair of totally submerged vertically placed porous barriers, located at some distance from each other, for a homogenous fluid flowing over a porous sea-bed. A thin ice-sheet, replacing the usual free surface, is considered as the upper surface where it is treated as a thin elastic plate. The complete analytical solution, under the assumption of small-amplitude theory and structural response, is acquired by employing eigenfunction expansion and least square method. Subsequently, computation for the reflection and transmission coefficients, energy loss and wave forces is carried out and discussed for different parameter values corresponding to the ice-sheet, porous sea-bed and porous barriers. This study establishes that the oscillatory behavior exhibited by the reflection of the waves. The vertical porous barriers are found to dissipate a significant portion of the wave energy when an increase in the inertial effect of the porous barriers takes place. The hydrodynamic force on the barriers also follows an oscillatory pattern and it increases when the length of the barrier is increased. It is demonstrated that, corresponding to various structural parameters, almost no reflection and full transmission take place for an impermeable sea-bed and also when only real porosity parameter of the porous sea-bed is considered. Further, variation in the elastic parameter of the floating ice-sheet is observed to command a considerable influence when the wave impinges upon the submerged vertical porous barriers.