SPINDEL: PHASE FLUCTUATIONS, COHERENCE AND INTERNAL WAVES 



amplitude of the internal wave S and the temperature gradient T , 

 which in turn is proportional to the bouyancy frequency. Thus, 

 maximum variations in sound speed due to internal wave action occur 

 at the depth where n(z) is greatest. This is usually near the main 

 thermocline as illustrated by the sample bouyancy frequency profile 

 shown. 



On the basis of this analysis, the internal wave field is modeled 

 as affecting a traveling acoustic wave only in a thin layer at thermo- 

 cline depth as shown in Figure 8. A ray passing through the layer 

 will experience a phase advancement or retardation depending upon 

 whether the immediate sound velocity of the layer is greater or less 

 than the average sound velocity. Figures 9 and 10 outline the 

 theoretical analysis necessary to complete the internal wave-acoustic 

 wave interaction model. The internal wave field is modeled as a random 

 superposition of waves concentrated in a layer of thickness ri. The 

 field is characterized by a frequency-wavenumber spectrum proportional 

 to the internal wave model proposed by Garrett and Munk (1972) . 



The phase change AO of an acoustic signal due to a single passage 

 through the internal wave layer is proportional to acoustic frequency, 

 the angle with which the ray enters the layer , and the internal wave 



y 



spectrum. The spectrum of the resulting acoustic phase variations 



F (co ) is proportional to the number of times the ray has passed through 



the layer, M, and the square of the acoustic frequency. It is also 



a function of the inertial frequency oj . and cuts off at the local 



bouyancy frequency n . 



Figure 11 shows a plot of this theoretical spectrum as a heavy 

 solid line together with measured phase spectra for receivers at two 

 different depths. The light solid line represents data at 1500 m, 

 the dashed line at 305 m. Transmission range was about 200 km. These 



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