Figures 5, 6 and 7 give this information for plane channel, boundary layer and 

 wake: 



(4) 



It seems noteworthy that the magnitudes of principal stress and strain-rate 

 tend to vary together, loosely speaking. However, the directions of the corresponding 

 principal axes are quite different in the two bounded flows, and this should recall 

 the well known fact that assumptions of simple gradient transport of momentum in 

 these flows have been rather unsuccessful. 



In contrast, the wake shows a wide zone of rough coincidence of principal 

 directions, a result consistent with the fact that its velocity profile is close to that 

 obtained with the assumption of simple gradient transport with constant exchange 

 coefficient. Some consequences of this directional coincidence are explored by Town- 

 send ([1], pp. 1 17 et seq.). 



Local Isotropy 



Recent measurements on the anisotropy produced by irrotational, homogeneous 

 strain-rate on the (roughly) isotropic turbulence downstream of grids [10, 11] (Fig- 

 ure 8) suggest re-examination of Kolmogoroff's postulate of local isotropy in shear 

 flow [12]. The ubiquitous strain-rate of shear flow acts upon "eddies" of all sizes, 

 tending to make the turbulence anisotropic at all wave numbers. 



In shear flow the situation is complicated by the fact that energy is received 

 by the turbulence from the mean flow in a highly anisotropic condition, as can be seen 

 from component energy equations. In plane turbulent channel flow, for example, 



_dU p d dp 



puv 1 (mi 2 ) -f- u \- (viscous terms) = 0, (5) 



dy 2 dy dx 



p d _ dp 



(v 3 ) + v y (viscous terms) = 0, (6) 



2dy dy 



p d dp 



(vw 2 ) + w y (viscous terms) = 0, (7) 



2 dy dz 



which shows that all turbulent energy appears first as u 2 . This is very nearly true for 

 all flows in which the boundary layer approximation is valid. 



379 



