so that 



d# To 



or 



Hence 



— = , (67) 



dx pU x ~ 



d(x) = To(x l )dx l . 



pU a 



1 



i? 2 (a:) = / / to(xi)t (x2) dx-idxi. (69) 



P 2 U a 



This integral was evaluated by assuming the skin friction spatial autocorrelation to be 

 equivalent to the time correlation by (A*) ^ U (At), a very poor assumption near the 

 wall as shown experimentally by Klebanoff [7]. With the further assumptions of similar- 

 ity and 8 <~~> x% mean growth rate of the boundary layer, the momentum thickness 

 fluctuation was estimated from (69) as 



— « .001, (70) 



8 



at the boundary layer position where the computed value is .014. The failure of this 

 estimate may be due in part to the erroneous shear stress correlation and in part to the 

 general omission of z-variations both in the differential equation and the surface stress. 



ACKNOWLEDGEMENT 



A number of people have contributed to the calculations in this report. I should 

 particularly like to thank F. Lien, J. L. Lumley, W. G. Rose, and R. R. Mills. Dr. 

 R. W. Stewart of the University of British Columbia was kind enough to point out some 

 errors in the first draft. 



SYMBOLS 



398 



