A numerical method for calculating the nonlinear interaction of steep ocean waves with large floating structures of arbitrary shape is described. The method is an extension to one used recently for fixed offshore structures (Isaacson2, 3), with the development of the flow and associated fluid forces and structural motions being obtained by a time stepping procedure in which the flow at each time step is calculated by an integral equation method. As an example of the method, an application to the case of a simple moored structure is presented.
Linear wave diffraction theory is generally used in the motion response analysis of large floating offshore structures. (See the text by Sarpkaya and Isaacson8 for a summary of the methods used.) This is based on a small wave height assumption, which becomes somewhat questionable under more extreme (design) sea states.
A new numerical method has recently been developed (Isaacson 2, 3) in order to account for the nonlinearities associated with large wave heights. This method attempts to provide a numerical solution to the complete boundary value problem in three dimensions, without applying any wave height perturbation procedure and is applicable to the general case of a body of arbitrary shape. The method was initially developed for the case of a fixed body, and the extension to treat the case of a compliant (moored and floating) body is summarized in the present paper.
Considerable progress has now been made on the related case of two-dimensional (vertical plane) flows describing the behavior of steep or breaking waves (Longuet-Higgins and Cokelet 7, Srokosz 9), even in the presence of a fixed obstacle (Vinje and Brevig 10). However, these methods rely critically on the assumption of a two-dimensional flow, and may not be extended directly to three-dimensional problems.
In the approach adopted here the wave diffraction is treated as a transient problem with known initial conditions corresponding to still water in the vicinity of the structure and a prescribed incident wave form approaching the structure. The development of the flow is obtained by a time stepping procedure, in which the velocity potential of the flow at anyone instant is obtained by an integral equation method based on Green's theorem. An example application of the method to the case of a simple floating dock restrained by linear moorings is described, and the influence of the nonlinearities in the incident waves is illustrated.
The theoretical basis of the method applied to the case of a freely floating body has been presented in detail in a recent paper (Isaacson 5) and only a summary is given here.
Since the body motions are not linearized in the usual way, it is convenient to employ two coordinate systems as indicated in Fig. 1. Gx'y'z' forms a right-handed Cartesian coordinate system fixed in space, with x measured in the direction of incident wave propagation and z measured upwards from the still water level.