RESULTS 



Several forced harmonic heave motions of the U-shaped body In the free 

 surface have been considered. The shape of the body has been fixed by setting 

 the parameter A In Equations (la,b) to 0.7407 In all cases. With A set to 

 this value, the half-beam of the body and the draft of the body are both 

 0.6667. Amplitudes considered were hg/b = 0.05, 0.3, and 0.4, in which hg is 

 the amplitude of the motion and b is the half-beam of the body. Most 

 researchers consider values of the frequency parameter ba^/g that lie between 

 0.0 and 2.0. In this study the frequency parameter is restricted to lie in 

 the interval from 1.5 to 2.0 since this interval contains the frequencies for 

 which nonlinear effects are greater. 



Linear theory for the problem of an oscillating body in a fluid of 



infinite depth and lateral extent predicts that the wavelength far from the 



body will approach 



X/L = 2Trg/La2 = 2TT(b/L)g/ba2 



asymptotically in time [17]. The dimensions of the rectangular tank are taken 

 to be about one such wavelength deep and four wavelengths in half-length. 

 Thus, if the frequency parameter bo^/g is no smaller than 1, the depth h 

 should be about 4 and the length should be about 16. This region is long 

 enough that no waves will reach the side boundary during the first few periods 

 of forced motion. Since the region is more than half a wavelength deep, the 

 effects of finite depth can be ignored. 



The fluid region has been divided into five time-dependent subregions. 

 Each subregion has been mapped onto a fixed rectangle of computational space 

 (Figs. 4, 5). The size of the mesh in each of these subregions has been 

 depicted in Figure 5. A total of 2916 grid points, counting twice those 



18 



