'.- i Yajnik and Lieber 



ACKNOWLEDGMENTS 



This investigation was carried out mostly at the University of California, 

 Berkeley, for the Ph.D. dissertation of the first coauthor of this paper, under 

 the supervision of the second (Yajnik, 1964) (17,23). The financial support pro- 

 vided by the Office of Naval Research is deeply appreciated. The experimental 

 facilities provided by the Hydraulics Laboratory are also acknowledged. The 

 authors would like to thank Professors John Wehausen and Hans Einstein, and 

 Doctors Lyle Macros and Shrikant Desai for their assistance and discussions. 

 The expression of swirl in Eq. (23) was constructed as an extension of a simpler 

 one constructed by Lyle Macros in 1962 (24). 



REFERENCES 



1. von Karman, T., Nachr. Akad. Wiss. Goettingen, Math. Physik. Kl., 509-517, 

 547-556 (1911, 1912); also, collected Werke 1, 324-330, 331-338 



2. Taylor, G., Rept. Mem. Adv. Com. Aeron., No. 598 (1918); also Scientific 

 Papers 2, 96-101, Cambridge, 1958 



3. Oseen, C, Arkiv Math. Astron. Cch. Fysik 7 (1911) 



4. Hamel, G., Jahrber. Deut. Math. Verein. 34 (1916) 



5. Rott, N., ZAMP 9b, 543-553 (1958) 



6. Kuchman, D., J. Fluid Mech. 21, 1-20 (1965) 



7. Moffatt, J. Fluid Mech. 18, 1-18 (1964) 



8. Wille, R., Advan. Appl. Mech. 6 (No. 11), 273-287 (1960) 



9. Michalke, A., J. Fluid Mech. 19, 543-556 (1964) 



10. Hung, T.K. and Macagno, E., La Houille Blanche, 391-402 (1966) 



11. Macagno, E. and Hung, T.K., J. Fluid Mech. 28, 43-64 (1967) 



12. Cauchy, A.L., Ex. d'Abal. Phys. Math. 2, 302-330 (1841); also, Oeuvres 12 

 (2), 343-377 



13. Truesdell, C, "The Kinematics of Vorticity," Indiana University Press, 

 1954 



14. Thomson, W. and Tait, P., "Treatise on Natural Philosophy," Cambridge, 

 1867 



15. Bertrand, J., C.R. Acad. Sci. 67, 1227-1230, Paris, 1868 



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