SECTION G 



m I m 



STATISTICAL THEORIES 

 OF TURBULENCE 



C. C. LIN 



CHAPTER 7. BASIC CONCEPTS 



C,l. Introduction. The general concepts of turbulent motion have 

 been discussed in the previous section. It is recognized that the details 

 of turbulent flow are so complicated that statistical description must be 

 used. Indeed, only statistical properties of turbulent motion are experi- 

 mentally reproducible. The purpose of the present section is to give a 

 more comprehensive treatment of the statistical theory. 



Current literature on the statistical theory of turbulence is mainly 

 limited to the treatment of the case of homogeneous turbulence^ without 

 any essential mean motion. Superficially, one might think that there is 

 little to be known about such fluid motions. Actually, the very absence 

 of mean motion allows one to go more deeply into the inherent nature 

 of the turbulent flow itself. Many basic concepts have been developed in 

 the study of homogeneous turbulence, and these concepts now gradually 

 find their way into the study of shear flow. 



Since there is available an account of the theory of homogeneous tur- 

 bulence [1] with a complete discussion of the mathematical background, 

 a somewhat different presentation is adopted in the present section. 

 Following the historical order, the isotropic case is taken up first. It is 

 hoped that this will be helpful to those readers who wish to get an idea 

 of the essentials without going through all the preliminaries required in a 

 complete mathematical treatment. 



In the later parts of this section, other aspects of the statistical theory 

 and their applications will be treated.^ We have, however, omitted several 

 other approaches to the problem of turbulence. Among these, the work of 

 Burgers [3,4] and Hopf [5] should especially be mentioned; nor is any 

 attempt made to include a discussion of related mathematical studies, 

 such as that of Hopf [6] and Kampe de Feriet [7]. 



^ These concepts are explained more precisely in the following pages. 



^ For a brief survey of some aspects of the problem of turbulent motion, see [2]. 



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