DISCUSSION 



K. Wieghardt 



The following remark refers to a complication which might occur in the boundary 

 layer along a three-dimensional body without incidence. A study of the flow around 

 the run of double-models of simplified ships in a wind tunnel has shown a longitudinal 

 vortex-pair near the keel plane produced by the flow around the sharp bilges (see Fig. 1). 



v e 



Figure I. 



The strength of the vortices was so that they induced a downward velocity of almost 

 half the main speed in the center line of the wake. This might be of practical interest 

 for double screw ships. In most cases outward turning propellers are best, i.e. screws 

 running in the opposite sense to these vortices. This would seem plausible since in this 

 case the residual vorticity is as small as possible. Of course, on a real ship, the influence 

 of bossings and the interference with the wave drag will also be of great importance. 

 Further on, this effect will certainly be much smaller with bilges well rounded off. E.g. 

 with a second extreme model, a circular cylinder and a run with elliptical sections lead- 

 ing to the same vertical edge, no such vortices were observed. However, since some 

 ships are more similar to the first model such a vortex-pair might play a certain role 

 with real ships. 



L. Landweber 



First I would like to ask Professor Corrsin's opinion of the relative importance 

 in the boundary-layer momentum equation of the term 



d f8 



— (u 2 - v 2 ) dij. (71) 



dx Jo 



It was shown in several papers, in about 1950, that this term could become large in 

 adverse pressure gradients, but recently it has been indicated that the term is negligible. 

 This apparent contradiction should be clarified. 



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