Scattering of Flexural Gravity Waves by a Pair of Submerged Vertical Porous Barriers Located Above a Porous Sea-Bed

An analytical study is presented here 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 by following Euler-Bernoulli beam equation. The complete analytical solution, under the assumption of small-amplitude theory and structural response, is acquired by employing eigenfunction expansion and least square method for the problem of flexural gravity waves interacting with the submerged porous barriers. Subsequently, computation for the reflection and transmission coefficients, energy loss and wave forces are 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. It further shows that when the inertial effect of the porous-effect parameter of the barriers is increased, the minima in wave reflection occur. 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 is affected. The hydrodynamic force on the barriers also follows an oscillatory pattern, and it increases when the length of the barrier is increased. Furthermore, wave transmission decreases significantly due to the energy dissipation by the porous sea-bed. 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. The effect of the ice-sheet on the propagation of the flexural waves is also examined by obtaining a number of results for variation of various parameters. 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.

Automated summary

This study presents an analytical investigation on the scattering of oblique flexural gravity waves by a pair of vertically placed porous barriers submerged in a homogeneous fluid with a porous sea-bed. The analysis takes into account a thin ice-sheet as the upper surface, treated as a thin elastic plate, and examines the reflection and transmission coefficients, energy loss, and wave forces for different parameter values. The study shows the significant influence of the barriers' inertial effect on wave reflection and dissipation of wave energy, as well as the impact of the length of the barriers on hydrodynamic forces. It further demonstrates the obstructive effect of the porous sea-bed on wave transmission and the effect of the ice-sheet on the propagation of flexural waves.