Water wave scattering by a finite dock over a step-type bottom topography

The two-dimensional problem of water wave scattering by a dock of finite width present in water with a step-type bottom topography is investigated assuming linear theory. Two cases are considered. In the first case water wave is incident on the dock from the lower depth region and in the second case the wave is incident on the dock from the higher depth region. By applying Havelock׳s expansion formula for water wave potential along with the matching conditions, the boundary value problem in each case is reduced to a linear system of algebraic equations. The system of equations are then solved numerically after truncation and numerical estimates of the reflection and transmission coefficients and motion characteristics such as the force and the moment on the dock, for different values of various parameters and the wavenumber are obtained. These are depicted graphically against the wavenumber in a number of figures. Energy relation is also derived and used to check the accuracy of the computational results.