The integral-equation method is applied to calculate the effects of tank-wall reflections upon the hydrodynamic forces acting on a model of offshore structure. The Green function satisfying the tank-wall boundary condition is provided by first considering an infinite number of mirror images and then seeking a closed-form analytical expression for the resultant infinite series. By the analysis of energy and momentum conservation, the formulae are derived, giving damping coefficient, wave-exciting force, and drift force in terms only with the Kochin function. Numerical computations are performed for a structure, composed of four vertical circular cylinders with horizontal base, both in the open sea and in a towing tank. It is shown that the tank-wall effects on the second-order drift force is greater than those on the linear forces and resultant motions.
Measurements of the hydrodynamic forces on models of offshore structures such as semi-submersibles and tension-leg platforms are usually carried out in a towing tank with parallel side walls. If the tank width is not large enough, we must expect some degree of tank-wall effects to be included in the results of experiments. In order to clarify the degree and nature of the effects of tank-wall interference, a number of theoretical studies have been made so far. Ohkusu (1975) considered first-order wave forces and second-order drift force on vertical circular cylinders which are arranged in multiple rows and an infinite number of piles. Since Ohkusu" s theory was confined only to the case where each cylinder extends to the sea bottom, there exist no evanescent-wave components. These two works were not done for the problem of tank-wall effects, but mathematical formulation is equivalent to that of tandem cylinders placed on the centerline of the wave tank.