SPINDEL: PHASE FLUCTUATIONS, COHERENCE AND INTERNAL WAVES 



CONCLUSIONS, PROBLEMS, AND RECOMMENDATIONS 



This paper has presented some illustrative data and theoretical 

 notions that summarize much of our current appreciation for the phase 

 fluctuation problem in long-range acoustic transmissions. We have 

 restricted our presentation to Woods Hole data because we feel that 

 they illustrate the major effects of internal waves on phase stability, 

 and its consequences regarding array performance. Some large data 

 sets obtained by other researchers support our notions, while others 

 give us pause. Longer time series illustrate effects not seen in our 

 data, such as tidal cycles and variations resulting from seasonal 

 changes. These are important, too, and critically so if acoustics 

 is to be used as a tool for studying large-scale oceanographic 

 phenomena. 



An example of the type of behavior we do not fully understand 

 is shown in Figures 14A and 14B.* It shows the amplitude and phase 



spectra of a 367 Hz tone transmitted between Eleuthera and Bermuda. 



2 

 The phase spectrum falls off as f with no apparent cut-off at the 



local buoyancy frequency. The amplitude spectrum, however, falls 

 rapidly at the buoyancy frequency. Our feeling has been that environ- 

 mental effects would be most visible in the acoustic phase, and that 

 multipath effects would so distort the amplitude fluctuations as to 

 make environmental-acoustic amplitude comparisons difficult indeed. 

 Apparently this is not the case for data such as these have been 

 obtained by the Institute for Acoustical Research and others. A 

 similar spectrum of amplitude fluctuations calculated at Woods Hole 

 using transmissions from free-drifting SOFAR floats at 270 Hz and a 

 range of 600 miles is shown in Figure 15.** Again the buoyancy 



* Reproduced from a paper by G. Stanford (1974) 

 ** Figure 15 courtesy of L. Baxter III. 



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