C,8 • SPECTRAL THEORY OF ISOTROPIC TURBULENCE 



c 



>> 



SI 

 D 



>^ 



-^- 



'^ 



C 

 cu 



\— 



cu 



C 

 CD 



O 



Q. 



100 200 300 



Frequency, hertz 



400 



Fig. C,8. Experimental verification of the Fourier transform relation between space 

 correlation and time spectrum for turbulent fluctuations behind a grid in a wind 

 tunnel (after Stewart and Townsend [22]). 



This leads to an equation of the form 



dF 



dt 



+ Tf = -2vk'F 



(8-7) 



In the above equation, W{k, t) is connected with the triple correlation 

 function h{r, t) by the following relations: 



W{K,t) =^[Km['(K) - kH[{k)] 



(8-8) 



( 213 ) 



