Wave Pressure in Short Waves 



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When the order of magnitude of the frequency parameter U)/£/g is e , 



the variation of the diffraction potential along the x-axis is no longer 

 small. Therefore, the slender body assumption, in which the flow field 

 varies slowly along the axis of the body, does not hold, and the strip 

 theory is by no means applicable. We need not worry about this fact, as 

 far as the total force or moment is concerned, because the total force be- 

 comes very small and unimportant in short waves. However, we need another 

 theory if we intend to discuss more local phenomena such as pressure on the 

 surface of the body. 



In the case of a long ship in a heading with the propagation of short 

 waves, one may think of an infinitely long cylinder placed in waves with 



its axis parallel to the propagation of the wave. However, it has been 



32 

 shown by Ursell that there is no steady state solution in this case. 



The fluid motion is highly three-dimensional and cannot be replaced by the 



two-dimensional solution. However, there is an acceptable assumption which 



can reduce the boundary value problem to a much more simplified form. 



That is, the variation of the diffraction potential in the longitudinal 



axis of the ship deviates from the sinusoidal variation very slightly. 



-1/2 

 Here, we consider the case of to = 0(e ). 



As mentioned before, it is not easy to formulate the linearized so- 



-1/2 

 lution of the boundary value problem in the case of 0) = 0(e ) and 



1/2 

 U = 0(1). If U = 0(e ), the effect of the forward speed appears only in 



the higher order term. Therefore, we will confine our discussion in the 



case without forward speed. The velocity potential of the incident wave 



which propagates in the positive x-direction can be expressed by 



<j> = c h exp(Kz-iKx+iwt) (212) 



where c = g/co is the phase velocity of the wave. Now let us express the 

 diffraction potential in the form 



<J> = lp(x,y,z) exp(iU)t-iKx) (213) 



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