C • STATISTICAL THEORIES OF TURBULENCE 



A more definite verification of case (c) is provided by their measure- 

 ment of the spectrum, which is reproduced in Fig. C,15c and C,15d. 

 Fig. C,15c gives the one-dimensional spectrum Fi{k) which shows a large 

 departure from similarity at low values of k. Fig. C,15d shows that, for 



200 



mlrc 



-v 



w 



CN 



l£" 



150 



TOO 



50 







0.2 



0.1 

 k/Ks 



Fig. C,15c. Spectrum of u fluctuations [k« = {Ze/2v^)^ 



0.2 



(N 



.^ 0.1 



il^l^ 







4>^ 



x/M Rm 

 o 60) 



-i- 80 ^ 2625 

 X lOOJ 

 ® 40) 

 e 60^ 5250 

 ® 80j 



13 301 



a 40 H 0500- 



E 60j 



A 30 21000 



^S^ 



«:;x 



^ 



0.1 



0.2 



0.3 

 k/Ks 



0.4 



0.5 



0.6 



Fig. C,15d. Spectrum of du/dt fluctuations. 



each experiment, all the points for kWi(k) fall on a single curve. Similar 

 results are obtained for k^Fi{k) and kWi{k) by Stewart and Townsend [££]. 

 Thus, all the moments 



fj K'-F,iK)dK, 



n> 1 



<234> 



