A second order analytical solution for nonlinear wave diffraction due to multiple cylinders has been derived. Laboratory experiments have been conducted to investigate the validity of the obtained solution. By examining theoretical and experimental results of the water surface profiles, it has been confirmed that the attained solution is good enough to simulate the water surface profile although it cannot satisfy the equation of continuity exactly because of an approximation.
A second order solution for nonlinear wave diffraction caused by an isolated surface piercing cylinder was obtained by Kriebel (1990) and Chau and Taylor (1992) in an analytical form. Kim and Tue (1989) also derived the solution for axisymmetric body. The corresponding solution in the case of multiple cylinders has not derived yet, although some researchers have calculated the wave forces on them with use of the radiation potential (Ghalayini and Williams, 1991). The wave profile, in particular run-up height on the cylinder surface, may be enlarged due to the nonlinear interaction of the diffracted waves generated by each cylinder. Thus, a theory which can evaluate the nonlinear behavior of diffracted waves is necessary indeed. The present authors have derived a second order analytical solution of the velocity potential for the diffracted wave from an isolated cylinder without using Green function (Sanada et al, submitted). In this study, the solution for the isolated cylinder has been modified to include the case of multiple cylinders, applying the same method developed by Linton and Evans (1990). The accuracy of the proposed theory has been validated by laboratory experiments.
In this study, we have considered the case of N bottom-seated vertical surface piercing cylinders which are located at (Xj, Yj) (j = 1 ∼ N) in the sea area at constant water depth (d). (Equations are shown in the paper)