Water-wave Scattering by an Ice-strip

The problem of water-wave scattering by a strip of ice-cover floating on the surface of deep water is investigated here. The ice-cover is modelled as a thin elastic plate of very small thickness. The problem is reduced to that of solving two singular integral equations of Carleman type over a semi-infinite range and are solved approximately by casting them into two separate Riemann-Hilbert problems by assuming the strip width to be large. The reflection and transmission coefficients are derived approximately. Numerical results for the reflection coefficient are presented graphically against the wave number and also against the ice-cover parameter. The oscillatory nature of the reflection coefficient against the wave number as well as the ice-cover parameter is found to be one of the main features of the curves. It is also seen that, in the limiting case when the ice-cover parameter tends to zero (i.e.,the ice-cover is almost absent), the amount of reflection is negligible