Wave radiation by a sphere submerged in a two-layer ocean with an ice-cover

Using linear water-wave theory, we consider wave radiation (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 either of the two layers. Employing the method of multipoles each problem is reduced to an infinite system of linear equations which are solved numerically by standard techniques after truncation. The added-mass and damping coefficients for a heaving and a swaying sphere are obtained and depicted graphically against the wave number for various values of depth of the submerged sphere and flexural rigidity of the ice-cover to demonstrate the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be very small, the numerical results for these quantities almost coincide with those for a two-layer ocean with a free-surface.