Fabula 



-40 



-50- 



-60- 



Qj -70- 



■80 - 



100 



500 



FREQUENCY , cps 



Fig. 17 - Relative spectral levels in Solution 

 PC-4 at x/M = 10.7, 20.2, 35, and 64 



containing 83 ppm of Polyox coagulant, was only 8 hours old, and there was ex- 

 treme raggedness at both xM = 10.7 and 20,2. 



The falseness of a velocity interpretation of the raggedness can be seen as 

 follows. Under conditions of extreme raggedness, such as seen in Fig. 17 for 

 x/M = 10.7 and 20.2, the relative spectral level curves generally had a slope of 

 about -20 db per decade over the frequency range of roughly 10 cps to the upper 

 limit of frequency analysis, typically about 200 or 300 cps. If such a frequency 

 spectrum were interpreted as a true velocity spectrum and converted to a wave- 

 number spectrum ^(k), the latter would behave as k' ^ in the corresponding 

 wavenumber range. Thus the viscous dissipation spectrum, k^st(k), would be 

 nearly flat over that range, while the water dissipation spectrum drops to very 

 low levels. Therefore a dissipation increase by a factor of perhaps 10 could be 

 implied. Such an increase in dissipation is seen to be completely out of the 

 question, as follows. For water, the decrease in turbulence energy due to vis- 

 cous dissipation between x m = 10.7 and 20.2 is roughly 50%. Since the ragged- 

 ness spectral distortion can be severe enough to imply the factor of 10 increase 

 in dissipation at both x/M = 10.7 and 20.2, and, therefore, over the interval in 

 between, the decrease in turbulence energy implied by the spectra would be an 

 impossible 500%. 



60 



