Studies on the Motion of Viscous Flows—Ill 



Although the theorem on the distribution of internal forces mentioned above 

 was first established in 1953 and subsequently presented on numerous occasions 

 in lectures, it was published in 1963 [3], and then, with modifications, in the 1968 

 issue of the Israel Journal of Science and Technology, with the title "A Principle 

 of Maximum Uniformity Obtained as a Theorem of the Distribution of Internal 

 Forces." The principle of minimum dissipation was conceived as a general re- 

 striction on the class of realizable flows, by identifying a relation between in- 

 ternal forces produced by binary collisions and a dissipation process according 

 to which the energy dissipation was found to be proportional to these forces when 

 the collisions are oblique. Consequently, for the class of oblique collisions that 

 are responsible for dissipation in gas flows, we found that the principle of mini- 

 mum dissipation may be used to give an approximate and indirect representation 

 to the information obtained from the theorem on the distribution of internal 

 forces cited above. The dissipation mechanism used for this purpose is pre- 

 sented in Ref. 5 and is further discussed and used in Ref . 6, 



As previously noted, the principle of minimum dissipation was originally 

 conjectured as a principle of realization from information we obtained by ap- 

 propriately using the Gauss-Hertz principles of mechanics, and by interpreting 

 this information as a particular and limited aspect of a general natural law, 

 called here the principle of maximum uniformity. This principle evidently in- 

 cludes the established laws of classical mechanics, as well as a realization 

 principle which is tantamount to a stability law. The evolutionary and historical 

 content of the information expressed by this principle of realization is absent in 

 the known laws of classical mechanics, and as far as I can see it is, in fact, not 

 included in any of the known propositions of physical theory as they are written 

 today. The principle of minimum dissipation is, in general, not implied by the 

 Navier-Stokes equations and can be deduced from them only for a highly re- 

 stricted class of viscous flows which are in fact endowed with unique solutions, 

 because of the linearity of the Navier-Stokes equations by which they are condi- 

 tioned and uniquely determined. Due to the linearity of the Navier-Stokes equa- 

 tions governing this restricted class of flows and the consequent uniqueness of 

 their solutions, a principle of realization that would in general select a realiz- 

 able member among multiple admissible solutions to the Navier-Stokes equa- 

 tions is redundant. For this very restricted class of flows the principle of 

 realization, which is the principle of minimum dissipation in the present dis- 

 cussion, and the laws of mechanics as expressed by the Navier-Stokes equations, 

 are equivalent. 



Stability criteria which are based on various definitions of stability are es- 

 sentially motivated by a search for realization criteria that augment and com- 

 plement the conditions of force equilibrium expressed by the principles of 

 mechanics. The laws of classical mechanics concern a particular aspect of 

 uniformity characterized and defined by the equilibrium of forces. They ac- 

 cordingly express and assert the proposition that this aspect of uniformity, as 

 characterized by the equilibrium of forces, is maintained for each and every 

 body in nature everywhere and always. The notion of force equilibrium to 

 which these laws refer is instantaneously associated with the states of the bodies 

 governed by the laws of mechanics, as are all the other parameters by which the 

 mechanical system is described in the statement of these laws. 



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