been employed to predict the fully rolled up vortex sheet. However, 

 judgement must wait until some initial computational difficulties are 

 resolved. 



In summary, the most widely held theories for tip vortex rollup in- 

 volve the role of the wing-tip boundary layer and assume a laminar vortex 

 structure for simplicity. As a result of theoretical deficiencies, the 

 models fall short of predicting the turbulent tip vortex rollup and the 

 resulting vortex characteristics. The three-dimensional aspects of the 

 crossflows and the turbulent vortex are issues which remain unsolved and 

 await further study. 



Although the theoretical representations are still evolving, the 

 results of these analytical efforts, to date, in conjunction with the ex- 

 perimental observations, offer an insight to a general understanding of the 

 viscous rollup process. The two common parameters identified as governing 

 the formation of the tip vortex are: 



• the spanwise distribution of the lifting surface circulation, and 



• the detailed configuration of the lifting surface tip geometry. 

 Both the magnitude and distribution of the spanwise circulation 



directly control the basic shape and strength of the resulting tip vortex. 

 In addition, the wing tip geometry can be as equally significant in chang- 

 ing both the rollup process and the nature of the flow forming the vortex. 

 Experimental observations have indicated that the strength and stability 

 of the tip vortex is sensitive to changes in velocity due to the wing-tip 

 boundary layer and also to the turbulence level of the flow entering the 

 vortex core. 



The spanwise circulation distribution is fixed for a majority of the 

 lifting surface applications. Thus, a majority of the efforts to reduce the 

 tip vortex and the associated problems have involved modification of the 

 wing tip geometry. One exception is the marine propeller, where the cir- 

 culation or loading is decreased in the area of the tip for the purpose of 

 improving tip vortex cavitation performance. The intent of these various 

 modifications is to either delay or dissipate the tip vortex without an 

 unreasonable penalty in efficiency. The remainder of the present study 

 will involve a discussion of these various concepts and their potential 

 applicability to the marine propeller and tip vortex cavitation. 



