ambient waves. Cross products between the fluid velocity of incident waves 

 and that due to the steady forward motion appear in the same order of 

 magnitude as that of the fluid motion due to the oscillation, making the 



free surface condition much more complicated. In this respect, the 



25 

 application of the slender body theory looks more profitable than the 



thin ship assumption. The assumption of the slender body increases the 



order of magnitude of the forward motion so that it is higher than that of 



lateral or vertical motions. Therefore, the effect of the steady forward 



motion does not appear at the lowest order in the far field expansion with 



respect to the hull shape parameter. Though the effect of the steady 



motion may appear in the lowest order in the expansion of the boundary 



condition in the near field, the first order solution may take a neat form 



if the wave amplitude and the slenderness ratio of the ship are taken as 



two independent parameters of the perturbation. However, some numerical 



computations have revealed another difficulty. This is that the first 



order theory gives only an unrealistic result. On the other hand, it is 



widely accepted that the strip theory has been able to present a reasonable 



27 

 agreement with measurement. The strip theory is regarded in one sense 



as another slender body theory, although it is originally derived by a 

 somewhat intuitive method. In a rigorous sense, it is a rational approxi- 

 mation for a slender ship in oscillations with high frequency without 

 forward speed. Thus, it is eventually known that results may become 



different if the different choice of magnitude of frequency and forward 



28 

 velocity is taken. Discussions in this connection will be given in the 



next section. 



Once the slender body theory is employed, the boundary conditions are 



expanded by the slenderness ratio. Terms of the lowest order are taken 



first. One of the features of the slender body theory is the singular 



perturbation. It makes a difference in the expansion at near field and 



at far field, and a matching procedure is applied between them. The 



problem which we are going to discuss is a slender body floating on regular 



waves and moving with a uniform average speed U in the mean direction of 



its longitudinal axis. In the most general case, the direction of the 



37 



