Diffraction of Long Waves by Rectangular Pit

Linearized shallow water wave theory is utilized to investigate the interaction of surface waves with a rectangular pit of finite dimensions in water of otherwise uniform depth. The fluid domain is divided into two regions: an interior region whose boundary consists of the projection of the outline of the pit and an exterior region consisting of the remainder of the fluid domain. Application of Green's second identity utilizing an appropriate Green's function in each region leads to a pair of simultaneous integral equations for the velocity potential and its normal derivative at the imaginary fluid interface between the two regions. These integral equations may then be discretized and the resulting systems of algebraic equations solved by standard matrix techniques. Utilizing the values of the velocity potential and its derivative on the imaginary fluid boundary, a reapplication of Green's identity allows the potential at any point in the fluid to be determined. Based on this solution technique, numerical results are presented that illustrate the influence of the various pit characteristics on the wave field for several example geometries.