Water wave scattering by a sphere submerged in uniform finite depth water with an ice-cover

Abstract

Using the multipole method, we formulate the problem of water wave scattering by a submerged sphere in uniform finite water depth with an ice-cover, the ice-cover being modelled as an elastic plate of very small thickness. This leads to an infinite system of linear equations which are solved numerically by standard techniques. The vertical and horizontal forces on the sphere are obtained and depicted graphically against the wave number for various values of the depth of water and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover and also the effect of varying depth of water on these quantities. When the flexural rigidity is taken to be zero, the numerical results exactly coincide with the curves of the vertical and horizontal forces on the sphere for the cases of uniform finite depth water with a free surface.