The three-dimensional scattering of cnoidal waves by cylinder arrays are studied numerically by using the generalized Boussinesq equations. The boundary-fitted coordinate transformation and a dual-grid technique are used to simplify the finite-difference computation. Also, a set of open boundary conditions and an incident cnoidal wave are incorporated for time-domain simulation. The free-surface elevation and hydrodynamic forces on each cylinder are calculated to illustrate the evolution of nonlinear waves and their interactions wi til large cylinder arrays. Comparisons are made between the present nonlinear wave loads and those obtained from linear diffraction theory. The sheltering role played by the neighboring cylinders and the feature of wave interference are discussed.
The study of hydrodynamic interaction of nonlinear shallow water waves with large multi-component structures has important applications in many fields of ocean engineering. The interference between neighboring members may significantly affect the wave field and the wave loads on individual components. As the size of structures increases, the scattering of nonlinear waves becomes more critical to the determination of wave run up and wave forces on those structures. By using a series representation of the first-order cnoidal wave, Isaacson (1977) presented a linear diffraction solution for cnoidal waves propagating past a vertical cylinder. Later, Su and Pan (1987) utilized a transformation theorem of Bessel function to estimate the cnoidal wave forces on cylinder arrays. However, their study was also based on the linear diffraction approach and may not be valid for the computation of nonlinear shallow water waves and the associated wave-structure interaction. For the nonlinear wave interactions with structures in shallow water, Wang et al. (1992) developed a generalized Boussinesq numerical model in a curvilinear coordinate system to examine the scattering of solitary waves by an isolated vertical cylinder. Recently, Wang and Jiang (1994) extended this model to investigate solitary wave interactions with an array of two vertical cylinders.
