Developments in Theory of Bulbous Ships 

 P 



Q tan 



f(k a) 



which are functions of only k^a. The amplitude of the total wave ^, 



= /q'^ + p2 + 2 Op cos /3 sin ( •<o'' ^ T ^ ' ) 



and the phase difference i between the total wave i^ and the first order wave ij 

 are shown in Figs. 11 and 12. p and ^ are shown in radian, considering that 

 one wave length (277, k ) is just 27^. 



8 

 f(koa) 



Fig. 10 - Phase difference between the 

 first and the higher order -waves s, and 

 the amplitude ratio/half entrance angle, 



These show that the total wave phase is indeed advanced considerably com- 

 pared with the first order wave, while the amplitude of the total wave height 

 does not differ too much from that of the first order wave. Namely the second 

 order effect is quite large. It is proportional to the slope of the entrance on the 

 free surface, for a given run, a. Therefore, the smaller the entrance slope 

 near the free surface is, the less the second order effect to be expected. As we 

 see in the integrand of the line integral (50), this effect mainly depends on the 

 potential and the wave on the free surface waterline where the waterline slope 

 is large. Since the local effect is usually big near the bow and the shoulder, the 

 influence of the local effect on the second order wave may be quite important. 



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