Wave forces acting on a semi-submerged porous circular cylinder

With potential applications in aquaculture as a sea cage or as floating breakwaters, a porous circular-cylinder semi-submerged in waves is investigated under the assumption of linear wave theory. To simplify the problem, the linear Darcy's law is applied to the porous boundary. The problem is solved by means of the eigenfunction expansion. The fluid domain is divided into two regions and different eigenfunctions are used. There are two horizontal porous plates in the inner region, i.e. the cover and bottom of the cylinder. This leads to a complicated ‘dispersion’ relation to determine the eigenvalues, the solutions of which are complex numbers. To solve the radiation problem, some particular solutions are sought to take account of the normal velocity of the body. The hydrodynamic forces are evaluated by integrating the pressure difference on the two sides of body surface. Computed examples are presented to observe the effects of porosity. The Haskind relations are examined for the porous body. It is found that the damping coefficient consists of two parts. In addition to the component of conventional wave-radiating damping, there exists a second component caused by the porous effects.