where 



Breaker and O'Neil 



f.= ^ .P^-- ,'? . , u = f/f 



27r A/ L yi^FXr ' " ' - (6) 



P(£) can be computed by numerical integration and is plotted in Fig. L 



While it was not possible to consider phase effects in 

 this experiment it is of interest to note that this same theory 

 predicts significant phase fluctuations as well. In fact, the two- 

 dimensional phase-fluctuation spectnam analogous to Eq. (4) is 



Fs(/c,0) = 0.0337rCnK^L(l+-^sin-^^J/c"'!/3 (7) 



From this may be derived phase fluctuation and difference spectra 

 along a line, analogous to Eq. (5). 



The physical interpretation of the foregoing is fairly 

 straightforward. The turbulence takes the form of nested eddies of 

 all scales from i to the largest scale of the fluid body 

 (of ten > Lp) . The largest eddies (of scale near L ) are anisotropic 

 while the smallest (near / ) are affected by viscosity. These eddies 

 produce corresponding inhomogeneities with respect to temperature 

 and salinity and, thus, with respect to the refraction index. It 

 is the inhomogenities with scales near^XL which account for the 

 fluctuations in the acoustic signal. These inhomogeneities do not 

 evolve rapidly and may be regarded as "frozen-in" the fluid when 

 -\/XL«Lo . Comparing Eq. (4) we see that the theory should be valid 

 for/o«ytL«Lo- 



All of the foregoing is discussed in detail in Tatarski's 

 book (Ref. 3). (Generally his approach and notation have been used 

 here although our numerical constants differ because we will work 

 in decibels.) Briefer summaries occur in References 4 and 5. The 

 validity of the theory is well established for acoustic (and electro- 

 magnetic) waves in the atmosphere. 



But there are certainly reasons to wonder whether it 

 applies equally well in the ocean. This is especially so when one 

 reflects that the relatively stable vertical stratification of the 

 ocean due to buoyancy forces must seriously limit the scales over 

 which truly isotropic turbulence can exist. This implies that L^ 

 would be small and thus that our condition,yXL«Lo might not be 

 satisfied for interesting values of X or L. (Still further 

 limitations might be expected ne&r the surface where wave motions 

 may strongly modify the turbulent velocity field.) 



Dunn, Ref. 4, reports evidence for isotropy but his data 

 extend to scales only up to about 5 meters. This problem of the 

 scale of isotropic turbulence in the ocean was taken up in 1965 by 

 a group of Bissett-Berman Corporation personnel headed by 



370 



