Wave scattering by a coaxial pair of surface-piercing porous cylinder and bottomless thick annular cylinder

Abstract

In this work, we consider a mathematical model for wave scattering by two coaxial cylinders: a surface-piercing porous cylinder and a bottomless thick annular cylinder. Within the framework of linear water wave theory, the resulting boundary value problem is solved using the matched eigenfunction expansion method. Then, a numerical experiment is performed to examine the wave scattering of the porous hollow cylinder for two configurations: (i) the thick annular cylinder attached to the porous cylinder, with the gap between the porous and thick cylinder set to zero (Model-I), and (ii) the porous cylinder coupled with a bottom-mounted cylindrical trench, with the gap between the thick cylinder and the ocean floor set to zero (Model-II). A critical analysis of the numerical results reveals that, for Model-I, the width of the annular plate plays a more significant role in reducing wave impact on the porous cylinder than its thickness. Furthermore, for Model-II, it is observed that the thickness of the bottom trench significantly influences the vertical forces acting on the porous cylinder.