Impact of a porous structure placed at the sea-bed in wave scattering around ice floes

Abstract

The present work examines the two-dimensional wave scattering problem involving a pair of ice floes of finite length separated by a finite gap over a finite ocean depth with a thick porous structure lying on an impermeable sea-bed. The physical and mathematical considerations of wave propagation through thick porous structures are analysed by analysing the interaction between the wave and the porous medium. Following linear water wave theory, the boundary value problem (BVP) is solved using the matched eigenfunction expansion method. Numerical results on various hydrodynamic coefficients are presented by varying the parameters pertaining to the porous structure and the ice floe. The reflection coefficient oscillates with an increase in the length of the first floe in the direction of the incoming waves and settles down when the length of the second floe increases. Maximum transmission is experienced when the gap between the two floes is substantial, since a higher gap allows more waves to pass through, thereby increasing the rate of transmission. The present study shows that an increase in the porosity shifts the phase of the maximum reflection, whereas a thick porous structure diminishes the maximum reflection coefficient by absorbing wave energy. With an increase in rigidity, the reflection coefficient increases, and at higher compressive force, the energy absorption increases, and consequently, the reflection reduces.