C • STATISTICAL THEORIES OF TURBULENCE 



called respectively the skewness factor and the flatness factor. Fig. C,3b 

 and C,3c show the experimental values of these factors as obtained by 

 Stewart {[11], also as quoted in [12]). For exact joint-Gaussian distribu- 

 tion, the former should be zero, and the latter should have the value 3. 

 Thus, the hypothesis of a joint-Gaussian distribution is not exact, but it 

 may still be used for certain approximations (cf. Art. 16). One should 



0.75 



r/M 



Fig. C,3b. Skewness factor for turbulent fluctuations 

 behind a grid (after Stewart [11]). 



3.6 



3.4 

 3.2 

 3.0 

 2.8 







0.08 



r/(x'M)^ 



0.16 



0.24 



0.32 



X + 5M) 



0.40 



Fig. C,3c. Flatness factor for turbulent fluctuations behind a grid across a 

 uniform air stream (after Stewart, as quoted in [12]). 



especially note the departure of the experimental value of the flatness 

 factor from the value 3 for a small value of r. 



C,4. Homogeneous Fields of Turbulence. As noted in Art. 1, 

 theoretical investigations of turbulent flow are often limited to the ideal- 

 ized case of an infinite field of turbulence which is statistically homogene- 

 ous or even isotropic, and devoid of mean motion. Homogeneity means 

 that the statistical properties of the field are independent of the particular 



( 200 > 



