28 



which do not show such clear definition as is evident in Figure 25, the re- 

 sultant pattern appears to be a more complicated function of the surface 

 roughness and of the flow conditions than would follow from the simplified 

 assumption of cavitation formation about nuclei. 



It is proposed to outline here a hypothesis which explains somewhat 

 more satisfactorily the formation of the strlations. It is known, see Refer- 

 ence (7), that conditions in the boundary layer near the point of separation 

 of flow are such that a strong vortex is formed. If the vortex formation is 

 a stable one, the flow should separate in a smooth sheet. For a flat plate, 

 the conditions at separation can be considered as giving rise to a line vor- 

 tex; while for the sphere or a body of revolution, such as the balsa-wood 

 displacement float shown In Figure 32, the vortex can be considered as a ring. 

 In order that strlations may be formed at the point of separation, the vortex 

 pattern must be altered so that a number of strlations are formed depending 

 on speed and on the strength of the vortex. That such conditions may arise 

 can be seen by analogy with a free vortex ring generated in a fluid at rest. 



An excellent series of experimental observations on the stability 

 of vortex rings has been reported in Reference (8). In these experiments, 

 vortex rings were generated in water at rest and were observed by means of 

 dye filaments. Observations were made of the vortex ring shape both in cross 

 section and plan on rings generated at various speeds of translation. The 

 result of most interest to this discussion is the change In shape of the vor- 

 tex ring shortly after its generation. It was shown that for a definite 

 range of speeds of propagation, the circular ring is unstable. In cross 

 section, the vortex core changes from a circular to an elliptical section 

 and the entire ring assumes a polygonal shape with a number of evenly spaced 

 deformations or waves. Photographs of two rings taken from Reference (8) 

 are shown in Figure 24. The observations showed that the maximum diameter of 

 the ring remains approximately constant but that the deformations form toward 

 the Inside of the ring. For very slow rings and for rings with a very high 

 speed of propagation, these deformations were not observed. However, the 

 number of discrete deformations in the ring increases with speed of propaga- 

 tion, the wave height decreasing as the number of deformations Increase. In 

 addition to these changes, the ring no longer remains plane but exhibits os- 

 cillations when viewed at right angles to the path of translation. The state- 

 ment is further made in Reference (8) that the pressure at the peaks on the 

 outside of the ring Is lower than that at the Inward peaks. 



If, then, it can be assumed that a region of high vortlclty exists 

 near the point of separation, and, In the case of actual separation, a vortex 

 does exist, the instability of the vortex can be expected to give rise to the 

 type of deformation shown by the vortex ring with the resultant configuration 



