B,29 ■ TRAXSPORT PROCESSES IX FREE TURBULEXT FLOW 



cation "\;dll depend mainly on their past enTironment and will reflect the 

 character of the flow as a whole rather than that of any particular locality. 

 The large-eddy part of the structure helps greatly to promote this general 

 averaging. The central idea here is that the lengths and velocities enter- 

 ing into a turbulent transport coefficient are not primarily determined by 

 local conditions. What has been stated here is true to a degree of aU 

 turbulent flow, but the greater preponderance of large eddies and the 

 exposure to mixing from the beginning enhance the enects in jets and 

 wakes. 



We have the picture, then, that any property that has been in the 

 flow for a considerable length of time should be mixed to a fair degree of 

 uniformity when it has arrived at a particular cross section. Dilution 

 occurs at the sharp boundaries, and also new fluid has recently become 

 turbulent there. Therefore we would not expect complete uniformity 

 everywhere within the sharp boundaries. Experiments show that turbu- 

 lent energy, temperature in the case of a heated jet or wake, and concen- 

 tration of a tracer gas in a jet are nearly uniform over the fully turbulent 

 core and decrease gradually in the turbulent bulges as the boundary is 

 approached. The over-all average decrease toward the boundaries is faster 

 than that in the turbulent parts alone due to the absence of any contribu- 

 tion from the nonturbulent parts. 



The foregoing behavior does not apply in the same degree to the axial 

 momentum. The mean velocity difference decreases considerably across 

 the core and continues to decrease in the protruding turbulent bulges. 

 This is ob-'.i.ously why the mean velocity distribution is less broad than 

 the mean-temperature distribution, but it is only a superficial explanation 

 since it leaves unexplained why the momentum should have been given 

 preferential treatment in the mixing process. 



We must now be concerned with the question of how to express the 

 transfer processes. ^lixuig length theory and Eq. 29-1 both assume a 

 gradient type of transfer in which the rate can be expressed in terms of 

 the local gradient. This requires that the diffusing movements shall be 

 small compared to the distance over which the gradient changes. This 

 condition may be satisfied as far as the smaller eddies are concerned, but 

 it is obviously not satisfied for eddies comparable in size to the width of 

 the jet or wake. Townsend proposes that the total rate of transport is a 

 combination gradient diffusion by the smaller eddies, which contain most 

 of the turbulent energy*, and bulk convection by the larger eddies. Since 

 the gradients in scalar quantities, like heat, matter, and turbulent energy 

 have been reduced due to the long continued mixing, it would appear 

 that these quantities have been transported laterally more by the bulk 

 convection than by gradient diffusion. On the other hand, since mo- 

 mentum has not been so thoroughly mixed, the prospects for gradient 

 diffusion are better. 



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