12 



x|0 



Shear Spectrum in Turbulent Boundary Layer 

 ( from Klebanoff , ref . 7 ) 



JL . 1.5 cm. 



I ave. 



S = 0.74 



cm. 



r-n- 



=*a= 



'Vove. 



wave number k. (cm."') 



Fig. 4 



zone width. Since the shear stress is carried principally by the large eddies, and these 

 may be influenced by the boundaries, there exists a question of whether a turbulent 

 shear theory postulating homogeneity can be expected to give quantitative results 

 for momentum transfer. 



Figure 4 demonstrates the momentum transfer burden carried by the large 

 structure, and shows that the average wave number for transfer Mt ,(&i) ave , corre- 

 sponds to a length greater than the displacement thickness of the boundary layer. The 



result would look even more emphatic in terms of wavelength . 



uv\^l) ave 



It seems likely, however, that homogeneous shear flow theories could give semi- 

 quantitative explanation of the momentum transfer, and should certainly be quantita- 

 tively applicable to the large wave number region, including that in which the shear 

 correlation coefficient spectrum n R uv is small but not zero. 



Mean Stress and Strain-Rate 



The early theories of turbulent shear flow focussed attention upon the mean 

 momentum equations (the Reynolds equations), seeking to render them determinate 

 by various postulates expressing the turbulent shear stress ( — puv) in terms of the local 



du \ 



-> I or its derivatives. Reserving criticism of the local feature 



By ) 



for later, it is instructive to look at the magnitudes and directions of the mean principal 

 stresses and strain-rates in some turbulent flows. 



mean strain rate 



377 



