Ogilvie 



Some of this controversy has been stimulated by the observations, largely 

 in Japan and Germany, that if a centerplane source distribution for a thin body 

 in an infinite fluid is determined by the recipe of thin ship theory, and if the 

 streamlines which result from this source distribution are actually traced, it is 

 found that the body which is generated is quite different from that which was 

 originally prescribed. This observation certainly suggests that one should be 

 more careful than heretofore about satisfying the body boundary condition. 



However, I can only assume that the investigators who discovered this fact 

 have never tried to trace streamlines in a linearized free surface problem. 

 Figure 6 shows the results of tracing streamlines in a very simple linearized 

 free surface problem. A dipole is located at (0,0) in the figure, and there is a 

 steady superimposed flow from left to right. Of course, a dipole exactly gener- 

 ates a circle in the flow of an infinite fluid (in two dimensions). For the flow 

 depicted, the dipole potential has been modified to satisfy the linearized free 

 surface condition on y = 2 . We would expect that under these conditions, the 

 "free surface dipole" might generate a somewhat distorted circle. However, we 

 note first of all that it does not even generate a closed body; the forward and 

 after stagnation points lie on different streamlines! The streamline containing 

 the after stagnation point passes right out of the lower half-space, as if it were 

 part of a vertical jet flow. This is immediately followed by a downward jet, as 

 the same streamline re-enters the lower half- space. The double -jet pattern 

 repeats every cycle of the wave behind the "body." On the other hand, the or- 

 dinary linearized-theory free surface condition gives the broken line as the free 

 surface shape — a not unreasonable looking wave, although its amplitude is 

 rather extraordinary. 



This figure was prepared by Dr. E. O. Tuck, to whom I am indebted for al- 

 lowing its use here. He will be publishing a paper soon which will include a dis- 

 cussion of the problems pointed up by this calculation. Here it must sviffice to 

 say that, although the case depicted is so severe that one would be suspicious of 

 linearized theory, one would not expect the streamlines to do such ridiculous 



10 II 12 13 14 15 



Fig. 6 - Streamlines around a dipole under a free surface 

 (linearized problem) (by courtesy of Dr. E. O. Tuck) 



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