Effects of flexible bottom on radiation of water waves by a sphere submerged beneath an ice-cover

Abstract

A particular hydro-elastic model is considered to examine a radiation problem involving an immersed sphere in an infinitely extended ice-covered sea, where the lower surface is enveloped by a flexible base surface. Both the flexible base surface and floating ice-plate are modelled as thin elastic plates with different configurations and are based on the Euler–Bernoulli beam equation. The appearance of surface tension at the surface below the floating ice-plate is ignored. Under such circumstance, two different modes of propagating waves appear in the fluid for any particular frequency. One of the modes with lower wavenumber propagates along the surface beneath the ice-plate and the other with higher wavenumber propagates along the elastic base surface. The method of multipole expansions is used to calculate the solutions of the heave and sway radiation problems involving a submerged sphere in an ice-covered fluid. Furthermore, this procedure gives rise to an infinite system of linear equations, which can be solved computationally by any regular method. The added-mass as well as damping coefficients in case of heave as well as sway motions are calculated, and displayed graphically in various submergence depths of the oscillating sphere and elastic specifications of both the flexible base surface as well as the floating ice-plate.