shallow Water Problems in Ship Eydrodynamias 



The results for zero clearance show pronounced wobbles as 

 a function of frequency. This is to be expected, and is due to inter- 

 ference between the waves diffracted around the two ends of the ship, 

 For non-zero P(x) there is a similar but much reduced effect, 

 since part of the wave energy is transmitted directly beneath the 

 ship, and a less strong diffraction pattern produced. 



The force decreases markedly as the clearance is increased 

 and the ship presents less of a barrier to passage of wave energy. 

 If in fact the clearance is la rge, P -* oo or C — ^ 0, it follows from 

 (5.7) that 4>(x,0+,-h) — - AVg/h C(x) and hence that 



r 



Fa -* ZipghkA \ C(x) dx, (7.2) 



The physical interpretation of this limit is that the effect of the free 

 surface on the disturbance flow field about the ship diminishes as the 

 clearance increases, until the flow is effectively the same as the low 

 frequency limit in which the force is in phase with the fluid particle 

 accelerations. This is in line with an interpretation (Newman [ 1969]) 

 of C(x) as related to the added mass of the section at x, with the 

 free surface replaced by a rigid wall. The resulting force Fg is of 

 course numerically small, if C(x) is itself small. 



On the other hand, the only cases shown in Fig. 4 correspond 

 to clearances small enough to give significant blockage C(x), and 

 hence a net force comparable with the standing-wave value 4pghiA. 

 It would appear that this limiting value is a useful, usually conserva- 

 tive, estimate for clearances of this order, but that it should be used 

 with caution for low frequencies (very long swell) or for non-small 

 clearances. In the latter case, e.g. with draft/water depth < 0,5, 

 the standing wave limit may be a substantial over-estimate of the 

 total force. 



The computations presented here are samples only. They 

 maybe considered extensions of similar computations given by Tuck 

 [ 1970] for a mathematically idealized ship with a blockage coefficient 



C(x) = cjl^ - x^ , (7.3) 







In fact the results for the Series 60 ship are not greatly different 

 fronn those given by Tuck [ 1970] , a reflection of the fact that (7,3) 

 Is not an unreasonable approximation to the shape of the curves in 

 Fig, 3. Further computations, including other ship geometries and 

 clearances, and treating the case of incident seas from directions 

 other than abeam, are given by Taylor [ 1971] , 



655 



