Wave scattering by a thin vertical barrier in a two-layer fluid

The present paper is concerned with scattering of surface and interface waves by a vertical plate in a fluid consisting of a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of density greater than the upper layer. For such a situation time-harmonic waves can propagate with two different wavenumbers K   and v(>K) along the free surface and the interface respectively. The problems are formulated in terms of hypersingular integral equations by suitable applications of Green’s integral theorem in terms of difference of potential function across the barrier. These integral equations are solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients for incident waves of wavenumbers K and v are computed numerically and depicted graphically in a number of figures for various values of different parameters. The energy identities are used as a partial check on the correctness of the numerical results.