Studies on the Motion of Viscous Flows — III 



DISCUSSION 



Dr. I. M. Schmiechen 

 Versuchsanstalt fur Schiffbau ' 



Hamburg, Germany 



The approach of Prof. Lieber will undoubtedly be of great importance in the 

 theory of viscous flows, and I congratulate him on the numerical results he has 

 obtained so far. Actually, I tried to follow the same line on a smaller scale 

 years ago. Coming from the thermodynamics of irreversible processes, I was 

 wondering whether the principle of minimum entropy production might have any 

 bearing in hydrodynamics. At that time I was involved in basic research on vor- 

 tex streets in connection with the general theory of propulsion. The stability 

 problem appeared to be most fundamental and at the same time most tractable. 

 In fact, I derived a criterion of minimum instability for Karman vortex streets, 

 which is in better agreement with experiments than those derived in the cus- 

 tomary fashion. 



DISCUSSION 



Dr. K. Wieghardt 



Institut fur Schiffbau der Universitdt Hamburg 



Hamburg, Germany 



A variational principle equivalent to the Navier-Stokes equations can be 

 formulated when Lagrange's coordinates are used. Yet, the principle of mini- 

 mum dissipation expressed in Eulerian coordinates corresponds to the Navier- 

 Stokes equations only in some restricted cases. Why should it be correct in 



general ? 



, .. ... '. -.* * + .- .- 



REPLY TO DISCUSSION 



Paul Lieber 



I will first respond to Dr. M. Schmiechen' s written discussion and refer to 

 the materials presented therein in subsequently responding to the written com- 

 ments of Professor K. Wieghardt. A self-contained bibliography is attached to 

 facilitate the examination of the references cited in my response to the comments 

 of the two discussants. 



665 



