24 



To 



16- 



Turbulent Shear Stress Fluctuations 

 Boundary Layer 



(data from Klebanoff) 



o 



\ 

 ^"^o 



T = mean surface stress 





J L 



.2 .4 .6 .8 y 1.0 



Fig. 12 I 



noted that in the fully turbulent zone, T T decreases monotonically with increasing y/S, 



r r 



T x T X 



so that — goes to even larger values than -^ . 



T x 



If (39) is indeed a proper identification, then the large values of :=r describes 



T T 

 a process in which instantaneous transfer against the mean gradient is only a little less 

 frequent than instantaneous transfer down the mean gradient. 



Parenthetically we may look at the fluctuations in the molecular transport of 

 laminar flow. In the gas kinetic formulation of momentum transport at low Mach 

 numbers, the expression analogous to (39) is dominated by the (uv — iiv) term since 

 molecular velocities are much higher than "drift" velocities. Hence the gas kinetic 



t't . 

 quantity corresponding to our — - is 





u l v l 



- ~ 1, (41) 



uv' 1 



where u and v are, for this discussion only, molecular velocity components. If we 

 assume u and v to be jointly normal, 



u 2 v 2 = uV + 2uv' 2 , and 



=-V 



u-v- U V 



- + 1 » , (42) 



uv uv 



which is much larger than unity if the inverse of the mean strain rate is much larger 

 than the mean free time of the molecules. 



390 



