extreme conditions. Since little is known of how a ship reacts even to non- 

 breaking waves, it would be extremely valuable to have a method available 

 for predicting ship motions in the presence of large-amplitude nonbreaking 

 waves. The method would be of practical value in a systematic study of how 

 ship design changes would add stability in rough seas. 



Researchers have spent much effort in devising methods for computing 

 large-amplitude ship motions. Their work is usually based on the assumptions 

 that the fluid is incompressible and the fluid motion is Irrotational . The 

 assumptions lead to the existence of a velocity potential, which simplifies 

 the problem formulation. But, since the equations describing the free surface 

 are nonlinear and cannot be linearized for large-amplitude waves, great 

 difficulties arise in the computation of solutions to free-surface potential 

 flow problems. When a body is present in the free surface, additional 

 difficulties related to the intersection of the free surface and the body 

 occur. For instance, the potential flow in the region is known to be 

 singular. Lin et al. [1]* have recently described some aspects of the 

 singularity. Dagan and Tulin [2] and Fernandez [3] discuss nonllnearl ties in 

 fluid flow about blunt bodies. Because of the formidable difficulties, most 

 of the work on nonlinear free surface flows has been for two-dimensional 

 (2-D) flows. 



Many authors have formulated the 2-D problem as an initial-boundary value 

 problem whose solution is obtained from an integral equation for functions 

 defined along the boundaries of the fluid. Longuet-Higgins and Cokelet [4] 

 used such a method combined with a time-stepping procedure to calculate free- 

 surface heights with no body present. Faltinsen [5] and Vinje and Brevig [6-8] 



*A complete listing of references Is given on pages 39 and 40. 



2 



