Similarly, ^^j^^^ ''^ obtained by using a time delay 



^fo 



where f^ is here the midband frequency of the narrow filter. The imaginary part of the nor- 

 malized cross spectral density v^^{f) is 



v,,{f) = 



^12(/) 



iP,if)P2ift^ 



It is noted that the measurement of w,, (/) ^.nd v^^{f) yields more information than the 

 more commonly measured normalized cross correlation since the normalized cross correlation 

 may be obtained by integration. 



For this work PAf) = Pjif) since the two measurement points are sufficiently close 

 together that the boundary layer has not changed in character. 



The real and imaginary parts of the cross spectral density as a function of f^x/O.SUQ 

 are shown in Figure 5. The distance between the two measurement points has been desig- 

 nated as X, and the midband frequency of the narrow filter has been designated as f^. The 

 factor of 0.8 will now be accounted for. 



By measuring the cross correlation in a narrow band of frequencies, and by determining 

 the time delay T that maximized this correlation, an effective convection velocity U^ = x/T 

 of the spectral pattern was determined. For all frequencies up to 2000 cps (the upper limit 











/ \ ^ 



o 



k- 



^^!^^^i 



OS. 



o^ 



rvf> 



^-^ 



'^ o 



o 









1.0 

 0.8 U„ 



Figure 5 - Real and Imaginary Parts of the Longitudinal Cross Spectral Density 



