The minimum value of #; turns out to be 



#,•(0.40) = 1.8 ( - ) 



so that one necessary condition for local isotropy is 



4>V dU 



- ) »— • (15) 



v J dy 



Under still more simplifying assumptions (14), this can be translated into a Reynolds 



number inequality. 



k 

 Both inertial and viscous forces may be appreciable in the range 0.2 < — < 5 . 



(;)' 



Hence, rather severe conditions for local isotropy may exist since 



#,(0.2) pa 30 ( - ■ J , and ^(5.0) « 100 ( 



Turning to actual numbers, the homogeneous strain rate of Figure 8 has a maxi- 

 mum of 11 per second, and Uberoi's highest [11] (a 16-1 contraction) reached 63 per 

 second. Townsend's homogeneous plane strain-rate was 9.4 per second. These numbers 

 may be compared with principal strain rates varying from zero to 10 4 per second in 

 Laufer's plane channel [5] at a Reynolds number of 61,000. A general order of 



magnitude in this example is ^ 120 per sec. Klebanoff's boundary layer [7] 



2 d 



has strain-rates of the same order, while Townsend's wake strain-rates are appreciably 

 smaller [15], e.g. roughly 2.0 per second at 800 diameters behind a 0.159-inch cylinder 

 at Reynolds number 1360. Except near solid boundaries, these shear flow strain-rates 

 are comparable with the homogeneous ones imposed by Townsend and Uberoi, so it 

 is possible that the data of the latter may be employed semi-quantitatively to explain 

 some features of shear turbulence. Townsend [1] has apparently done considerable 

 work along this line. 



In a discussion of local isotropy in shear flow, it is pertinent to note the strong 

 departures from local isotropy in the homogeneous strain experiments, at least out as 

 far as the spectral region contributing to mean square first derivatives. In Figure 10, 

 for example, we see Uberoi's evidence at a strain-rate of about 30 per second. From 



the decay rate just before the contraction, ( — j may be estimated as 16 per second, 



evidently not an order of magnitude larger than 30. This is consistent with the lack 

 of local isotropy. 



Taking Klebanoff's boundary layer data [7] as typical and considering a point 



y 



— = 0.2, in the fully turbulent region, we may check inequality (15) by estimating 



8 



(17) 



dy 



This implies that local isotropy is more likely here than in the homogeneous cases 

 reported. 



384 



