112 



DEEP-WATER TRANSMISSION 



5.3.3 



Average Layer Effect 



Differences in transmission anomaly between shal- 

 low and deep hydrophones are characteristic of 

 isothermal water overlying a thermocline. Some evi- 

 dence for a correlation of this difference with oceano- 

 graphic conditions has been fomid. These results are 



1000 



RANGE IN YARDS 

 2000 3000 



Figure 24. Average transmission anomalies, above 

 and below thermocline. 



1000 



4000 



5000 



2000 3000 



RANGE IN YARDS 



Figure 25. Difference in transmission anomaly above 

 and below thermocline. 



given later in this section. Since these results are 

 subject to some uncertainty, it is useful to obtain an 

 average value for this difference in transmission be- 

 tween a shallow hydrophone in isothermal water and 

 a deep hydrophone below the layer. Such an average 

 has been obtained by averaging together all UCD WR 

 runs made off San Diego under these conditions. 



The average curves found at 24 kc are shown in 

 Figure 24. These curves include all runs in which the 

 water was isothermal to more than 40 ft. The 

 probable error of each curve, determined from the 



quartile deviation of the individual points, divided 

 by the square root of the number of runs, is about 

 1 db. The increased anomaly at short ranges for the 

 deep hydrophone results from the vertical directivity 

 of the sound projector. The difference between these 

 two curves is plotted as a function of range in Figure 

 25. It is evident that this difference, in decibels, in- 

 creases linearly with range. The dotted line at less 

 than 1,000 yd indicates the difference in anomaly 

 that would presumably be found for a nondirectional 

 projector. The dashed line represents the semi- 

 empirical formula (13) discussed below. 



5.3.4 Studies of Layer Effect 



at 24 kc 



The average effect is large and significant. The 

 way in which thermoclines of different depth and 

 sharpness weaken the sound intensity below them 

 is a detailed problem of both scientific and practical 

 interest. First, the theoretical expressions for sound 

 intensity below a thermocline are discussed and ap- 

 plied to the average observational results. Secondly, 

 the effect which thermocline depth and sharpness 

 has on the measured sound intensity at depth is 

 discussed in detail. Some early UCDWR studies 

 are reported which fail to show the expected effects; 

 a more detailed study is then given which indicates 

 that general theoretical expectations are, in fact, 

 fulfilled. 



Theory 



One might expect that at least in some cases the 

 theory developed in Chapter 3 could be used to pre- 

 dict the sound intensity below a layer of sharp tem- 

 perature gradient. This expectation is supported by 

 the discussion in Section 9.2.2, which shows that the 

 intensities of explosive pulses agree rather well with 

 the intensity calculations based on the ray theory. 

 It is evident from Figure 23, on comparison of the 

 solid line drawn through the circles with the dashed 

 theoretical curve, that at ranges less than 2,000 yd, 

 layer effect can in fact be explained on the basis of the 

 simple ray theory. The predicted decrease of intensity 

 results from the increased divergence of rays, which 

 are bent sharply downward on passing through a 

 temperature gradient. This increase of divergence is 

 shown in the ideahzed diagram in Figure 26. The rays 

 are close together in the ideal isovelocity layer, and 

 the intensity is therefore high; but below the layer 

 of sharp gradient they are much further apart, re- 

 sulting in much reduced intensity. 



