Wave scattering by a thin vertical barrier submerged beneath an ice-cover in deep water

The two-dimensional problem of water wave scattering by a thin inclined semi-infinite rigid barrier submerged in infinitely deep water covered by a thin uniform ice sheet modelled as an elastic plate, is investigated here. It is formulated in terms of a hypersingular integral equation for the discontinuity of the potential function across the barrier. The integral equation is solved numerically by approximating the discontinuity by a finite series involving Chebyshev polynomials of second kind multiplied by an appropriate weight function. The reflection and transmission coefficients are obtained approximately and their numerical estimates for the vertical barrier for different values of the ice-cover parameters and the wave number are found. In the absence of the ice-cover, known results for a free surface are recovered. The reflection and transmission coefficients for the vertical barrier are depicted graphically against the wave number for various values of the ice-cover parameters.