Breaker and O'Neil 



from another. This phenomenon has been observed by virtually every- 

 one who has ever worked in underwater acoustics and has long been 

 known to be largely due to spatial variations in the local acoustic- 

 propagation velocity within the ocean. 



Another familiar phenomenon is the fluctuation over time in 

 the amplitude of a signal observed at a hydrophone whose position, 

 with respect to the source, is constant. This temporal fluctuation 

 is less well understood than the spatial variation but it has long 

 been felt by many that they were related (see, for instance, Ref . 1) . 

 For suppose that the structure of local acoustic-propagation 

 velocities itself fluctuated over time; might this not cause variation 

 in constant-geometry received amplitudes very much like that seen 

 when the propagation-velocity structure is fixed while the geometry 

 is varied slightly? (Ref. 2 provides direct empirical evidence that 

 this is, in fact, the case.) 



In passing from this idea to a definite model of trans- 

 mission-loss fluctuation one is faced with two chief problems. The 

 first is to learn what sort of fluctuations in the structure of 

 propagation-velocities might be expected in the ocean while the 

 second is to predict the effects of these fluctuations on acoustic 

 propagation. The first problem, clearly, is especially formidable 

 theoretically and complex empirically. The difficulty of solving the 

 second problem would seem to depend upon the answer to the first. 



The velocity of sound in the ocean increases regularly 

 with pressure. More important, for our purposes, is that it also 

 varies with water temperature and salinity. If a patch of warmer 

 (or more saline) water happens to occur within a body of colder (or 

 less saline) water then in the absence of outside influences, 

 hydrodynamic forces will eventually break it up and disperse it 

 throughout the "host" body. In the ocean, with its constant but 

 spatially and temporally irregular receipts and drains of heat and 

 salts, such "patches" are continually being generated. 



This breakup and dispersion process can be viewed in terms 

 of the particle-velocity field generated by the hydrodynamic forces. 

 (This field within a region is to be distinguished from the net 

 average velocity of the region as a whole due to large-scale currents, 

 etc.) In seawater, with its low kinematic viscosity, these particle 

 velocities are generally non-zero and random for scales greater than 

 a centimeter. Such random motion is of course described as turbulent. 



Any fluid will have an inner scale of turbulence /o. set 

 by the scale at which viscosity tends to strongly damp fluid motion, 

 and an outer scale of turbulence Lq, set by the geometry of the fluid 

 as a whole and generally of the same order as the minimum of the 

 dimensions of the body of fluid. (Of course, unless Iq«Lq 

 turbulence of the sort we are about to discuss cannot occur.) For 



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