Water wave scattering by a bottom-standing thick rectangular barrier in the presence of an ice cover

The problem of scattering of a normally incident surface wave train by an obstacle in the form of a thick rectangular vertical bottom-standing barrier submerged in finite-depth water with a free surface is extended here with an ice cover modelled as a thin uniform elastic plate. The problem is reduced to a set of singular integral equations of the first kind. The Galerkin approximation in terms of simple polynomials multiplied by appropriate weight functions whose form is dictated by the behavior of the fluid velocity near the barrier edges is used for solving the integral equations. The reflection and transmission coefficients are obtained numerically, and they are depicted graphically against the wavenumber for various ice cover parameters. It is observed that the barrier thickness plays a significant role in modelling of efficient breakwaters.