17 



It will be observed in Figure 4 that cavitation appears to be intermittent even though 

 this case is one in which the cavitation number is well below the values associated with the 

 shedding of well defined vortices (see Reference 3). This intermittency further suggests the 

 close connection with the turbulent wake flow mentioned previously. Furthermore, the 

 "billowing" nature of the surface resembles the descriptions of the turbulent wake as given 

 by Townsend. Nevertheless, the average envelopes of such regions evidently behave as 

 steady-state cavities. Thus, the problem of cavitation in such turbulent regions and adequate 

 descriptions of the processes remain to be investigated and reconciled with available theory. 

 Otherwise stated, the problem is one of describing the transition from a cavitating wake flow 

 to free streamline flow.* 



THE ANALYTICAL DESCRIPTION OF STEADY-STATE CAVITIES 



Some results of free streamline theory for two-dimensional flows were given in Refer- 

 ence 3. Further work continues on these flows based on the Riabouchinsky and the re-entrant 

 jet models but the results have not been applied in a sufficient number of technically impor- 

 tant cases. Discussions of these flows will be found in References 3, 29, 30, and 31 which 

 are cited here not only for their own content but also for the bibliographies and references 

 given therein. 



Theoretical work on three-dimensional cavities has been concerned almost exclusively 

 with existence and uniqueness of solutions for axially symmetric flows. Recent work in this 

 direction is given in References 32 and 33 which also summarize previous work on this prob- 

 lem. Various attempts to apply numerical procedures to the solution of specific problems 

 have been made but have evidently been unsuccessful in producing accurate or even physi- 

 cally realistic results and will not be discussed here (a brief account of some computations 

 will be found in Reference 29). 



In addition to the above attempts to develop exact solutions of free streamline flows, 

 a recent theory which avoids the necessity for artificial mathematical models deserves spe- 

 cial mention. M.F. Tulin, in a recent report,^"* has developed a linearized theory for two- 

 dimensional cavity flows about slender, symmetric bodies. An im.portant feature of the re- 

 sults is that the calculation of drag and cavity shapes of arbitrary slender bodies is reduced 

 to quadratures with the resultant attractiveness for use in actual applications. In this report, 

 only some comparisons between Tulin's results and the exact results for the Riabouchinsky 

 model will be presented to indicate the range of applicability of this theory. The method of 

 linearization is similar to that of the linearized airfoil theory. The results chosen for illus- 

 tration are from computations for wedge profiles. Tulin gives the following results for the 



*Froin another point of view, such cavitating turbulent wakes might be used in studying the pressure fluctua- 

 tions associated with turbulence, as has been pointed out by others, as welL 



