A Green function approach is utilized to investigate wave interaction with a rectangular pit of finite dimensions in water of otherwise constant depth. The fluid domain is divided into two regions: an interior region which is finite in extent and represents the pit itself, and an exterior region consisting of the remainder of the fluid domain. An integral equation solution utilizing an appropriate Green function in the exterior region is linked to an interior solution in the form of a Fourier expansion containing unknown potential coefficients through matching conditions at the imaginary interface between the two regions. Discretizing the integral equation leads to a matrix system for these potential coefficients which may be solved using standard matrix techniques. Numerical results are presented for several example geometries which illustrate the effect of pit characteristics and incident wave direction on the water surface elevation.

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A complete second-order solution is presented for the hydrodynamic forces due to the action of bichromatic, bidirectional waves on an array of bottom-mounted, surface-piercing cylinders of arbitrary cross section in water of uniform finite depth. Based on the constant structural cross section, the first-order problem is solved utilizing a two-dimensional Green function approach, while an assisting radiation potential approach is used to obtain the hydrodynamic loads due to the second-order potential. Results are presented which illustrate the influence of wave directionality on the second-order sum and difference frequency hydrodynamic forces on a two-cylinder array. It is found that wave directionality may have a significant influence on the second-order hydrodynamic forces on these arrays and that the assumption of unidirectional waves does not always lead to conservative estimates of the second-order loading.

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An integral equation approach is utilized to investigate the influence of tank walls on the hydrodynamic forces experienced by an arbitrary three-dimensional body situated in a narrow wave tank. An appropriate three-dimensional Green function which satisfies the tank-wall boundary conditions is developed to facilitate the solution. Numerical results are presented for truncated cylinders of circular and elliptic cross section which illustrate the effect of the tank walls on the wave-induced forces. The numerical results indicate that the hydrodynamic loads on a three-dimensional body in a narrow tank may be quite different from those on the same body in the open sea.