That is to say, 



2 







lim 



A/-*o ^f 



P{f) = lim 



This was the procedure used in the work reported here. 



It is desirable to present the measured data in dimensionless form. Since the spectral 

 density of the pressure fluctuations has the dimensions of (pressure)^ x time, the dimension- 

 less spectral density was chosen to be P (O/p-^ f/^ S* where p, Uq, and S* are the fluid density, 

 free steam velocity, and boundary layer displacement thickness , respectively. The 

 frequency f was nondimensionalized as f 8*/Uq. 



The dimensionless spectral density curves are shown in Figure 4. The data exhibits 

 some lack of similarity over the velocity range studied. As mentioned earlier, the work sec- 

 tion of the tunnel was not long enough to 

 permit observations further downstream so 

 as to prove that the boundary layer was ex- 

 hibiting similarity. 



The coefficient 





\ fl A 





D Ujj= 1500 cm/sec 

 o U;,= 3000 cm/sec 

 fl Ug=6000 cm/sec 



a ( 



■sia 



A 



2 











8 











S 











[ 



D 





K = 



(p') 



2\y2 



P^o' 



Figure 4 — Spectral Density of the 

 Pressure Fluctuations 



can be obtained either by integrating over 

 the spectral density or by direct measurement 

 of p-^. In view of the lack of similarity ex- 

 hibited in Figure 4, a definite value cannot 

 be obtained. The values obtained for K have 

 an average value of about 9.5 x 10~^ which 

 in excess of the value obtained by Willmarth.^ 

 A surprising feature of the spectral 

 density is that it does not decrease appreciably at the lowest frequencies measured. For 

 these frequencies, which correspond to wave numbers much smaller than the reciprocal of 

 the characteristic lengths of the boundary layer, Xraichnan has argued that the spectral density 

 should be proportional to the square of the frequency.^ There is some evidence that inter- 

 mittency of the boundary layer has a strong influence on the pressure fluctuations at the 

 lower frequency. Qualitative observations at the lower frequencies revealed an intermittency 

 in the amplitude of the spectral density which could not be accounted for by the randomness of 

 the process. This intermittency gave pressure versus time records not unlike those observed 



