PHASE FLUCTUATIONS, COHERENCE AND INTERNAL WAVES 



R. C. Spindel 



Woods Hole Oceanographic Institute 

 Woods Hole, Massachusetts 



Observations of low-frequency, long-range acoustic 

 transmissions have revealed a correspondence between 

 acoustic phase variations and internal oceanic effects 

 such as tidal cycles, transport phenomena, geostrophic 

 flow and internal gravity waves. For periods less than 

 the local inertial period and greater than the local 

 bouyancy (Brunt- Vaisala) period, internal waves appear 

 to be the predominant cause of acoustic phase fluctuations 

 (in the absence of severe multipath) . Measurements of 

 220 Hz and 406 Hz transmissions at ranges from 200 to 

 1200 km using free-drifting receivers of varying depth 

 have substantiated this conjecture. The empirical acoustic 

 phase spectrum is proportional to a theoretical phase 

 spectrum constructed by using a simple ray theory in con- 

 junction with a hypothesized internal wave spectrum (Garrett 

 and Munk) . Furthermore, a predicted dependence of fluctu- 

 ation energy on depth is observed in these data. 



These measurements have been used to determine a 

 mixed space-time coherence function as a function of range 

 which establishes the oceanic limit of array resolution. 

 The simple ray- internal wave theory predicts coherence 

 parameters that compare favorably with data. Data collected 

 to date have suggested several important areas for future 

 consideration . 



INTRODUCTION 



Recent observations of low-frequency, long-range acoustic trans- 

 missions have revealed a correspondence between acoustic phase vari- 

 ations and internal oceanic effects such as tidal cycles, transport 

 phenomena, geostrophic flow and internal Rossby and gravity waves 

 (Steinberg, et al., 1973; Weinberg, et al., 1974; DeFarrari, 1974; 

 Baer and Jacobson, 1974; Franchi and Jacobson, 1973; Spindel, et al . , 

 1974; Porter, et al., 1976; and Stanford, 1974). From a physical 



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