Formation of a wave on an ice-sheet above the dipole, moving in a fluid

Theory of wave motions of a fluid with an ice-sheet was developed due to the necessity of solving of a number of problems of marine and land physics. The main attention in these investigations was focused on propagation and interaction of free waves, and also on appearance of waves under action of different loadings on the ice-sheet. From the other side, the problems dealing with waves on the fluid surface, free from the ice due to motion in the mass of the fluid of rigid bodies, has the known solutions. In this connection, it seems natural to disserminate the formulation and methods of such problems to the case of the fluid with the ice-sheet. In the present note we describe the character of formation of waves from the singularity, localized in the fluid of infinite depth beneath the ice-sheet. We use the example of the dipole, which models a cylinder in the infinite mass of the fluid. The character of the formation does not depend on the type of singularity. The ice-sheet is considered as a thin elastic plate of a constant width, floating on the water surface.