SPINDEL: PHASE FLUCTUATIONS, COHERENCE AND INTERNAL WAVES 



The result of this processing is a signal at dc, the fluctuations of 

 which are due to fluctuations in the ocean transmission path. 



Figure 3 illustrates the ray path geometry between the point of 

 signal transmission and a receiver located about 210 km away. Typical 

 samples of received acoustic phase are shown in Figure 4 for a receiver 

 at a depth of 300 meters. Over an approximate 3-hour interval spanning 

 an aperture of 3.5 km, peak-to-peak phase fluctuations are about 7 

 cycles. Two more examples of raw phase fluctuations are shown in 

 Figures 5 and 6. Here we have compared fluctuations at two frequencies 

 approximately an octave apart. Both frequencies were recorded and 

 processed simultaneously. Careful examination of these figures 

 indicates that observed phase fluctuations are approximately twice 

 as great in the 405 Hz data. This suggests that the scale of 

 inhomogeneities encountered by the acoustic transmission is large 

 compared to a wavelength. Thus, the transmissions are affected 

 independently, and notions of simple frequency scaling appear to hold. 



One implication is that large-scale phenomena, internal waves 

 for example, are primarily responsible for fluctuations in this 

 frequency range. 



INTERNAL WAVES AND PHASE FLUCTUATIONS 



Some rather simple theoretical ideas contribute strongly to our 

 assxjmption that internal waves are the predominant factor in generating 

 phase fluctuations at these acoustic frequencies and ranges. The 

 frequency of internal wave oscillation is bounded at the lower end 

 by the local inertial frequency and at the upper end by the local 

 bouyancy frequency, n(z), a function of depth. Figure 7 illustrates 

 the relationship between sound velocity variations and internal wave 

 parameters. Sound velocity fluctuations are proportional to the 



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