Scattering of water waves by thick rectangular barriers in presence of ice cover

Abstract

Assuming linear theory, the two dimensional problem of water wave scattering past thick rectangular barrier in presence of thin ice cover, is investigated here. Mainly four types of thick barriers are considered here and also the ice cover is taken as a thin elastic plate. May be the barrier is partially immersed or bottom standing or fully submerged in water or in the form of thick rectangular wall with a submerged gap presence in water. The problem is formulated in terms of a first kind integral equation by considering the symmetric and antisymmetric parts of velocity potential function. The integral equation is solved by using multi term Galerkin approximation method involving ultraspherical Gegenbauer polynomials as its basis function. The numerical solutions of reflection and transmission coefficients are obtained for different parametric values and these are seen to satisfy the energy identity. These coefficients are depicted graphically against the wave number in a number of figures. Some figures available in the literature drawn by using different mathematical methods as well as laboratory experiments are also recovered following the present analysis without the presence of ice cover, thereby confirming the correctness of the results presented here. It is also observed that the reflection and transmission coefficients depend significantly on the width of the barriers.