116 



DEEP-WATER TRANSMISSION 



mocline while for the circles the hydrophone depth 

 was more than 100 ft below the top. From intensity- 

 contour diagrams like those shown in Figure 25 of 

 Chapter 3, it is evident that for thermoclines within 

 less than 100 ft from the surface, the computed in- 

 tensity increases appreciably as the hydrophone goes 

 from just below the layer to considerably greater 

 depths. No simple formula has been derived for the 

 increase of intensity in this case. The points plotted 

 in Figure 28 indicate that for these deeper thermo- 

 clines also, the value of Riu tends to increase some- 

 what with increasing depth of hydrophone below the 

 top of the thermocline, provided the value of AT is 

 less than about 2 degrees. This result is also in gen- 

 eral accordance with the predictions of intensity-con- 

 tour diagrams. 



3000 



u 2500 



" 1500 



a 1000 



500 

 50 



HYDROPHONE 100 FEET OR LESS 

 BELOW TOP OF THERMOCLINE 



HYDROPHONE MORE THAN 100 FEET 

 BELOW TOP OF THERMOCLINE 



■ THEORETICAL CURVE FROM EQUATION 13 



USING AT EQUAL TO Z.5° 

 1 I I 



100 150 200 250 



DEPTH TO TOP OF THERMOCLINE IN FEET 



300 



Figure 29. Correlation between Rm and depth to ther- 

 mocline. Temperature difference in top 30 feet of 

 thermocline, 1.6 degrees to 4.0 degrees. 



The curve in Figure 28 is computed directly from 

 equation (13), with a thermocline depth of 150 ft and 

 a surface temperature of 70 F. It is evident from 

 Figure 28 that the change of ^40 with changing tem- 

 perature difference is, if anything, somewhat greater 

 than can be explained on the basis of equation (13). 

 This result is the reverse of that found in the empiri- 

 cal equation (14). The many different points plotted 

 in Figure 28 are not all completely independent since 

 many were taken on the same day. Thus, the sam- 

 pling error may be larger than might be expected from 



the number of points plotted. However, the data 

 shown in Figure 28 are more extensive than those 

 used in reference 32, and the result should therefore 

 be more reliable. 



Similar data may be used to show the dependence 

 of Rio on thermocline depth. Values of Rto obtained 

 with hydrophones below the thermochne, and with 

 temperature differences of 1.6 to 4.0 F in the top 30 ft 

 of the thermochne are shown in Figure 29. The circles 

 and crosses have the same meaning as before. It is 

 apparent that, for the shallower layers, the increase 

 in intensity at depths well below the thermocline can 

 become quite marked; this is in accordance with the 

 theoretical expectations schematically presented in 

 the intensity-contour diagrams of reference 31. 



The curve in Figure 29 shows theoretical values, 

 computed from equation (13), with a velocity differ- 

 ence Ac of 12 ft per sec, corresponding to a tempera- 

 ture change of 2.5 F at a surface temperature of 70 F. 

 The change in the median R40 is approximately that 

 predicted by equation (13). The quartile deviation, 

 however, is of the same order of magnitude as the 

 increase in median Rio when the depth of the isother- 

 mal layer is increased from 70 ft to 200 ft. 



The general trend in Figures 28 and 29 seems to 

 indicate that equation (13) gives a rough approxima- 

 tion to the median observed transmission. Though 

 the spread is large, the data are not in disagreement 

 with the predictions of that equation about the effect 

 of changes in layer depth and thermocline sharpness. 

 Thus equation (13) gives a moderately good fit to 

 UCDWR transmission data. 



Additional data are required, of course, for more 

 conclusive results. In particular, the niunber of varia- 

 bles that might enter the problem is so great that other 

 factors may be responsible for the apparent agree- 

 ment between observations and the simple theory. 

 Nevertheless Figures 28 and 29 indicate that equa- 

 tion (13) provides a moderately satisfactory empirical 

 fit for the present data. 



Some of these same results have been obtained in 

 greater detail in an analysis of average transmission 

 anomaly curves. This analysis^"* classifies the data 

 according to the temperature code discussed in Sec- 

 tion 5.1.3. The average anomaly curves for hydro- 

 phones in or below the thermocline with ^2 equal to 

 4 and to either 5 or 6 are given in Figures 30 and 31, 

 respectively. These correspond to isothermal layers 

 between 40 and 80 ft thick, and between 80 and 320 ft 

 thick, respectively. In Figure 30, curve III, with the 

 hydrophone between 20 and 160 ft below the top of 



