Radiation of Water Waves by a Sphere in an Ice-Covered Two-Layer Fluid of Finite Depth

Interaction of water waves with a sphere in a two-layer fluid, where the upper layer has an ice-cover being modelled as an elastic plate of very small thickness, while the lower one has a rigid horizontal bottom surface, is investigated within the framework of linearized water wave theory. The effects of surface tension at the surface of separation is neglected. There exist two modes of time-harmonic waves - the one with lower wave number propagating along the ice-cover and the one with higher wave number along the interface. Method of multipole expansions is used to find the particular solution for the problem of wave radiation by a submerged sphere placed in either of the upper or lower layers. The added-mass and damping coefficients for heave and sway motions are derived and plotted against different values of the wave number for different submersion depths of the sphere and flexural rigidity of the ice-cover. When the flexural rigidity and the density of the ice-cover are taken to be zero (thus making it equivalent to free surface), the numerical results for the added-mass and damping coefficient for the problem with free surface are recovered as particular cases.