SPINDEL: PHASE FLUCTUATIONS, COHERENCE AND INTERNAL WAVES 



data fall off with a slope of approximately of -2 as predicted by the 

 model, and in this respect these data lend credence to the model. Data 

 taken at greater depth show more rms phase fluctuation which supports 

 the notion of an equivalent internal wave layer. Rays to the deeper 

 phone have spent a greater fraction of their travel time in or about 

 the layer. There is no cut-off at the bouyancy frequency, contrary 

 to the model prediction. This result has appeared in the work of 

 others, Stanford (1974) for example. At present we attribute this 

 lack of abrupt fall-off to the contaminating effects of microstructure 

 which may begin to dominate at higher frequencies. We shall return 

 to this point below. 



It seems safe at this juncture in our current understanding of 

 phase fluctuations to assert that internal waves are the dominant 

 cause of fluctuations at these acoustic frequencies and that such 

 fluctuations range in period from several minutes to a day. It is 

 important to appreciate that the term "internal waves" can cover a 

 host of phenomena, including tidal waves, Rossby waves, more classic 

 internal waves, and wavelike behavior of microstructure. 



COHERENCE 



Oceanic induced phase fluctuations establish limits on array 

 performance. Upper bounds on coherent array processing gains are only 

 approached when the signal received across the array is phase coherent 

 from array element to element. The pointing accuracy or resolving 

 power of an array is critically dependent on the phase coherence of 

 the acoustic transmission path. Figure 12 illustrates these ideas. 

 A simple two-element array of length L receiving energy from a distant 

 acoustic source (point source) is said to be working at the utmost 

 limit of its resolving power when the random phase difference along 

 the two paths is less than 1/2 cycle. This phase difference is 



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