10 



6 - 



2 ~ 



„ D-. ^ 



D O- 



O 



10 15 20 . 25 30 35 40 



X/M 



Figure JO. From Uberoi (11), by permission of the Journal of Aeronautical Sciences. 



15 



Superficially distinct from the characteristic time criteria is the obvious require- 

 ment that the locally isotropic spectral region be at wave numbers much larger than 

 those at which energy is fed into the turbulence. With a mixing-length type of behavior 

 qualitatively in mind, we may estimate the latter as 



A/4 



1 dU 



> 

 v' dy 



(18) 



so that we cannot expect local isotropy at wave numbers which do not satisfy the 

 inequality 



1 dU 

 k » . 



v' dy 



Hence, for dissipative local isotropy, a necessary condition is that 



/ <t> y i su 



K = — » . 



\ , 3 / v' dy 



At the same boundary layer position, 



(19) 



(20) 



dU 



dy 



45, 



(21) 



which is enough greater than unity to be consistent with locally isotropic dissipation. 



385 



