Scattering ofWaterWave by a Surface Discontinuity over a Single Step at the Bottom

The present study is concerned with the scattering of an incoming water wave over a single step below the upper surface where the height of the step may be finite or very large(infinite) in presence of a surface discontinuity. Using linear theory, the problem is formulated mathematically as a boundary value problem in two separate regions of the ocean corresponding to two different depths. By utilising the eigenfunction expansion of the velocity potentials in conjunction with the impendence conditions along the common vertical boundary of the two regions, the mathematical problem is reduced to a system of linear equations which are solved numerically to obtain the hydrodynamic coefficients. If the surface discontinuity is due to a semi-infinite floating dock over an infinite step at the bottom, use of Havelock expansion of the velocity potentials and impendence conditions, the boundary value problem leads to another system of linear equation involving integral equations. The explicit form of the reflection coefficient is computed numerically in terms of wave number of the incoming wave and a number of graphical representations is given.