Internal waves in a two-layer liquid filling a wedge-shaped region

An analysis is presented for diffraction of an internal small amplitude surface wave traveling along the interface between two homogeneous layers of an ideal compressible fluid. Diffraction occurs at a solid wall bounding the fluid and forming a wedge. The Mellin integral transform is used to reduce the transform of the unknown stream potentials of the fluid to linear first-order finite difference equations. Explicit expressions for the velocity field potentials of wave motion are then derived for the wedge angle by means of the Mellin inversion formula. If the wedge angle is less than 90 deg, there is no reflected wave and Stroker solutions are required. For angles over 90 deg, the velocity potentials are obtained in terms of superpositions of the incident and reflected waves at a distance from the wedge.