An analytical study of scattering of water waves by a surface-piercing bottom-mounted compound porous cylinder placed on a porous sea-bed

The scattering problem of a bottom-mounted surface-piercing compound porous cylinder located on a porous sea-bed is theoretically investigated under the assumption of small amplitude wave theory. The compound cylinder is comprised of an impermeable upper cylinder and a porous lower cylinder beneath it. The boundary conditions on the porous boundaries follow Darcy's law by assuming fine pores in the porous structure. The whole fluid region is split into three bounded and an unbounded sub-regions, within which the individual velocity potentials are found by using eigenfunction expansion technique. Further, utilization of the matching conditions along the boundaries of individual successive regions leads to a semi-analytical solution of the proposed problem. The impact of the non-dimensional porous-effect parameter of the cylindrical wall, the draft ratio, radius ratio and the sea-bed porosity on waveloads and wave run-ups are studied. The results show that suitable consideration of porosity and structure parameters enhance the efficiency of the proposed compound cylinder in mitigating wave impact. Furthermore, the hydrodynamic waveload acting on the lower as well as upper cylinder can be reduced by the suitable positioning of the annular spacing of the system, which will provide explicit information for the purpose of engineering design in the coastal area.