Studies on the Motion of Viscous Flows — III 



7. The numerical calculations have served a twofold purpose; (a) to test 

 the theory, and (b) to give information that corresponds to observations but 

 extends significantly beyond available observed information and which bears 

 on the details concerning the evolution of flow fields with Reynolds number. 



8. The Symmetry Theorem is supported by the experimental evidence. It 

 predicts the asymptotic behavior which was looked for and found independently 

 by Grove et al., through experiments. .:. 



9. The results support the validity and the use of the idea of a physically 

 infinite distance. 



10. The presence and the behavior of a subdomain in which the viscous 

 effects are very significant is demonstrated by the results. 



ACKNOWLEDGMENTS 



The authors gratefully acknowledge the support of the Fluid Mechanics 

 branch of the Office of Naval Research, Washington, D.C. We thank the Com- 

 puter Center at the University of California, Berkeley, for providing almost un- 

 limited use of their facilities which has lead to the concrete numerical results 

 presented in this series of reports. Also, we thank warmly Mrs. Etha Webster 

 for her invaluable assistance in preparing this manuscript and Mrs. Dorathy 

 Brohl for printing the reports on which it is based. 



REFERENCES 



1. Desai, S., "On a Linear Substructure Underlying the Navier Stokes Equa- 

 tions as Applied to the Problem of Flow of a Viscous Incompressible fluid 

 Past a Circular Cylinder," Ph.D. thesis. University of California, Berkeley, 

 1965 



2. Desai, S., and Lieber, P., Reports AM-67-5, 9, 10, and 13, Parts I, II, III, 

 and IV, Office of Research Services, University of California, Berkeley, 

 1967 



3. Lieber, P., "A Dissipation Mechanism in Gas Flows and Similar Physical 

 Systems," Trans. N.Y. Acad., Sci., Vol. II (No. 5), 175-181 (1949) 



4. Lieber, P., Wan, K.S., and Anderson, O., "A Principle of Virtual Displace- 

 ments for Real Fluids," Int. Congr. Mech., Proc. IX, Belgium, 1957 (Also 

 issued as a Rensselaer Polytechnic Institute Research Division Report 

 AFOSR TN 57-476, AD 136 468, under Air Force Contract AF 18(600)- 

 1704, July 1957) 



589 



