IV-33 



Ignoring t±ie very low wave number range, we obtain the form of the Kolmogoroff 

 spectrum which we shall henceforth use: 



E(k) = 



0.4<u^> 



for k < k 







(IV-73) 







<-ir> 



for k < k 







In Figure IV-11, we show a number of actual measured correlation functions, in- 

 cluding the fairly long range portion of the correlation function, as compared with 

 a correlation function of the Kolmogoroff type. The general qualitative agreement 

 seems to be very good, certainly much better than the exponential or Gaussian 

 approximation, which turns out to be an appropriate approximation only for relatively 

 small values of the correlation distance. As we shall see in the next section, the 

 low wave number (large wavelength) portion of the spectrum is very important in 

 most scattering calculations. 



To summarize the results of this section, we present below a table of the 

 three correlation functions, and their associated spectra, that have been used as 

 various degrees of approximation of the micro- structure of the index of refraction. 



TABLE IV-2 



OCEAN MICRO- STRUCTURE CORRELATION FUNCTIONS 

 AND ASSOaATED SPECTRA 



Correlation Function R (r) 



Spectrum E (k) 



Remarks 



,-r/a 



4 < u^ > a 



n 



(ka)= 



Exponential 



(l+(kaff 



e 



vrT 2 



Gaussian 



See Figure IV- lie 



°-' k 

 ^0 



1 for k < k 

 (k^/kf/^ fork>kQ 



Kolmogoroff 



artftur Sl.ILittlcJnir. 



S-7001-0307 



