I0 2 



oT 3 

 'o 



O. tO. 



'1° 



10' 



10 



10 



10" 



0.01 



0.1 



10 



100 



Strouhal Number fD/U 



Figure 19. The spectral densities of the fluctuating pressure and the fluctuating velocity in the wake 

 of a cylinder, at a downstream distance of 24 diameters. The measurements were made in air. 



where the normalized dimensionless spectral densities* of both the pressure and the 

 velocity are plotted against the Strouhal number (/£>/£/„), based on cylinder diameter 

 D and free-stream velocity U . The two sets of points indicate that the measured spectra 

 of the pressure are essentially the same as those of the velocity. This is an unexpected 

 result, not at all what would be anticipated from the theoretical relations for isotropic 

 turbulence. 



However, any comparison between measured values of fluctuating pressure and 

 the theoretical predictions based on isotropic turbulence is subject to two uncertainties: 



1. The validity of the measurements is in some question. There is no con- 

 clusive evidence that the probes used to measure the pressure do actually indicate the 

 fluctuating pressure that would have existed in the absence of the probe. 



2. The measurements were performed in flows which were not isotropic. In 

 this connection, Kraichnan [50] has estimated the pressure fluctuations in several simpli- 



* The spectral density of a quantity is defined so that the integral of the spectral 

 density on frequency is equal to the mean-square of the fluctuating component of the quantity. 

 In particular, for the spectral density G P (f) of the fluctuating pressure, f^°G p {f)df = (p s ) 2 

 = </V>ap. Also, if G p (f) is normalized by division by (p s )' and non-dimensionalized by 

 multiplication by (U a /D), the integral on Strouhal number is then unity. 



267 



