=• 3 



•j 



- 2 



«? 



Effect of contraction on homogeneous turbulence 

 2 Subsequent approach to isotropy 



20 



25 



30 35 



X/M 



40 



^> L_ 



45 



4 U/U, 



50 



55 



_J 



Contraction Channel 



Figure 8. Curves from Uberoi (11), by permission of the Journal of Aeronautical Sciences. 



There must also be a general inertial tendency toward isotropy through the 

 pressure-velocity correlations at all wave numbers. 



A necessary condition for local isotropy is that there exist a wave number 

 beyond which the spectral times characterizing inertial and viscous mechanisms favoring 

 isotropy [#,(&) and {} v (k)] are much smaller than the time characterizing the gross 

 1 



straining process, 



E 1 



$i{k) and # t .(fc) « - 



dU 



by 



(8) 



Of course, in a purely inertial range only the #, inequality is necessary, while 

 in the purely viscous range (if a thing exists in stationary turbulence), only the & v 

 inequality is necessary. 



With E{k) as turbulent energy spectrum, we may follow Onsager's definition 

 [13] of inertial time, 



1 

 M® = , • (9) 



Vk 3 e(k) 



Similar reasoning leads to 



382 



1 



vk 2 



(10) 



