Water-Wave Scattering by a Sphere in a Two-Layer Fluid with an Ice-Cover

Using linearwater-wave theory, wave scattering (both heave and sway) by a sphere submerged in a two-layer ocean consisting of a layer of fresh water of finite depth with an ice-cover and an infinite layer of salt water. The sphere is submerged in the lower layer of the two layers. Employing the method of multipoles, the problem is reduced to an infinite system of linear equations which are solved numerically by standard technique after truncation. The vertical and horizontal exciting forces on the sphere are obtained and depicted graphically against the wave number for various values of the submersion depths of the sphere in the lower layer in a number of figures to show the effect of the presence of ice-cover.