B,3 • DIFFUSIVENESS OF TURBULENCE 



larger sizes. The turbulent velocities which contain the bulk of the turbu- 

 lent energy likewise tend to maintain a constant ratio to the mean local 

 velocity. This general condition is termed "Reynolds number similarity." 

 This and the related property of preservation of form from section to 

 section, commonly called "self preservation," are very important features 

 of turbulent flow. They give to the flow a permanence of form and a 

 continuity of behavior that simplify description and make possible cer- 

 tain general laws. 



B,3. Diffusiveness of Turbulence. It is a well-known fact that 

 frictional effects, mean velocity distributions, rate of spreading, and other 

 features of turbulent flow bear little resemblance to those found in lami- 

 nar flow. These differences can be attributed to a diffusiveness of turbu- 

 lence that far exceeds molecular diffusion and has a more intimate con- 

 nection with the mean flow. The mechanism of turbulent diffusion is 

 commonly compared to that of molecular diffusion wherein a molecule 

 moves and collides with another and so by a process of random walk 

 migrates farther and farther from some initial point. Turbulent move- 

 ments may also be hkened to a random walk, and now bulk currents 

 wander randomly in generally curved paths producing a cumulative in- 

 crease in the distance from an initial point. 



Except for the region near a wall where turbulent movements are 

 inhibited, the bulk-lot transfers by turbulent motions so surpass trans- 

 fer by molecular motions that the latter has little effect other than to 

 smooth out the spotty condition of properties in their new neighborhood. 

 Thus, molecular diffusion may often be neglected as far as the rate of 

 transport is concerned. Where it cannot be neglected, molecular and 

 turbulent diffusion are assumed to be additive. 



When we concern ourselves with mean flow, we intentionally ignore 

 the turbulent motions themselves and deal in effect with a fictitious 

 "laminar flow" of a fluid behaving as though it had special properties. 

 The analogy to laminar flow involves endowing the fluid with properties 

 called "eddy viscosity" and "eddy heat conductivity," or more gener- 

 ally, "eddy diffusion coefficient." If we attempt to account for behavior 

 in terms of an eddy viscosity, our fluid appears to be a very peculiar one. 

 It might be described as non-Newtonian because of the dependence of 

 the viscosity on rate of shear. We find further that the viscosity varies 

 from point to point in one part of the flow and remains practically con- 

 stant in other parts. Moreover, the numerical value is often hundreds of 

 times larger than that of ordinary viscosity and bears no definite rela- 

 tion to it. What is even more unconventional is the fact that eddy vis- 

 cosity increases with the size of the flow field and increases with over-all 

 velocity. The fluid flow in a large pipe, for example, behaves as though 



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