Autocorrelation Functions at Wall 



skin friction fluctuations 



(Klebanoff , boundary layer in air ) 



— static pressure fluctuations 

 (Einstein- Li , open channel flow of oil) 



J I 



20 40 60 80 100 120 140 160 180 



Fig. 17 



time autocorrelation of the skin friction fluctuations. The time interval is made 

 dimensionless by the characteristic sublayer time, 



— . (57) 



dy /o 



Einstein and Li [26] have measured the autocorrelation of surface static pressure 

 fluctuations on the bottom of a turbulent open channel flow of oil. Their curve, some- 

 what smoothed, is plotted on the same sheet as the skin friction correlation. Consider- 

 ing the differences between the two flow systems, the general consistency is remarkable. 

 The situations are doubtless too diverse to permit drawing detailed conclusions, but it 

 does appear that the two kinds of surface force fluctuations have about the same dura- 

 tion of autocorrelation. 



Boundary layer thickness fluctuations 



Recent attempts at prediction of sound radiation by a turbulent boundary layer 

 have taken two apparently diverse paths. Working from the viewpoint of Lighthill's 

 formulation, Phillips [25] has related sound radiation to skin friction fluctuations. Work- 

 ing from a more explicit picture of how the free stream "sees" a boundary layer, 

 Liepmann [27] has focussed attention upon the fluctuations in boundary layer displace- 

 ment thickness, presumably acting as a random distribution of pistons. 



Of course there must be some analytical connection between skin friction fluctua- 

 tions and boundary layer thickness fluctuations, although we may expect to find the 

 connection with momentum thickness rather than displacement thickness. 



396 



