Radiation and scattering of flexural-gravity waves by a submerged porous disc

The radiation and scattering of flexural gravity waves by a porous disc submerged in a deep ocean with an ice cover is investigated here assuming linear theory. The problem is reduced to solving a hypersingular boundary integral equation which can be reduced further to a system of one-dimensional Fredholm integral equations of the second kind by introducing a new function and using two-dimensional Fourier series expansion. The solution of each integral equation is associated with a radial component of the difference in potential function. The total scattering cross-section and hydrodynamic force for the scattering problem and added mass and damping coefficient for the radiation problem have been determined in terms of this newly defined function and computed numerically. Also, the effect of different parameters like the porosity of the disc, depth of submergence, flexural rigidity on these physical quantities has been investigated.