Nonlinear Diffraction of Irregular Waves Around a Large Structure
Authors: Isaacson Michael , Cheung Kwok Fai 
Published: October 2008

ABSTRACT
The present paper describes a numerical method for simulating xansient, nonlinear interactions of an irregular wave train with a Largefried offshore structure of arbh.rary shape in three dimensions. rhe boundary conditions are satisfied to second order by a time- ;tepping procedure, and the tleld solution at each time-step is &gt;btained by an integral equation method based on Green's theorem. I'he second-order incident wave train can he developed from a specified wave spectrum or from a specified wave record. The method time-steps the development of the flow, and computes timehistories of the second-order wave forces and free surface elevation u-ound the structure. The force maxima and runup are thereby obtained deterministically. As an illustration of the method, the special case of a bottom-mounted surface-piercing circular cylinder subject to a specified wave record is examined. The effects of an k-regular wave profile are compared to those of an equivalent regukw wave profile, and the effects of large individual waves within an irregular wave record are thereby assessed. Second-order effects are shown to be significant, particularly with respect to wave runup predictions.

1. INTRODUCTION
Numerical modeling of nonlinear wave diffraction around large offshore structures has been the subject of investigation for a number of years. The motivation of such studies arises primarily because of the need to obtain more accurate wave force and runup predictions than those of linear diffraction theory, which is based on the assumption of infinitesimal wave heights. With the advancement of theories on nonlinear wave diffraction, an increasing number of practical problems inherent in the design of ships and large offshore structures can now be investigated numerically.
When irregular wave effects at second order are considered, there exist two second-order components acting at the differences and sums of the individual first-order wave frequencies. Although the amplitudes of these second-order components are generally small, they act at frequencies which are significantly different from those of the incident wave spectrum, and may be critical when such excitations are near the natural frequencies of structure motions or when damping forces are small. Typical examples are low frequency drift motions of moored offshore structures or tankers (for example, Pinkster and Withers [1], and Matsui [2]), and the high frequency excitation of tension-leg platforms (for example, Kim and Yue, [3]).
Traditionally, two approaches to the nonlinear interactions of waves with a large offshore structure have been developed. One is based on a second-order solution for regular or dichromatic waves using a perturbation method in the frequency domain (for example, Eatock Taylor and Hung [4], and Kim and Yue [5, 6]), while the other approach is based on a full nonlinear solution using a timestepping procedure (for example, Isaacson [7], and Dommetmuth andYue [8]). Recently,. an alternative approach developed by Isaacson and Cheung [9] for the two-dimensional, vertical plane case, and subsequently extended by Isaacson and Cheung [10] to the three-dimensional case, applies a perturbation method to the time-stepping procedure in order to provide a time-domain solution for second-order wave diffraction.