538 



ROLE OF BUBBLES IN ACOUSTIC WAKES 



on a 40-ft motor launch gave a value of 2 db for W; 

 later measurements on the same ship, with more 

 standard equipment, gave a value of —21 db. In view 

 of the failure of the later measurements to reproduce 

 the early high values, these early values can probably 

 be neglected. Until more detailed information is avail- 

 able it may therefore be assumed that on the average 

 the wake strength of large moving surface vessels, 

 measured with long pulses, are all close to the theo- 

 retical maximum values found from equation (5); 

 that is, about — 16 db for rms amplitudes and — 10 db 

 for average peak amplitudes, at 24 kc. 



The high values of W found at 60 kc are not easily 

 explained. These values are believed to be less ac- 

 curate than those at 24 kc, since the equipment had 

 not yet been wholly standardized. It is perhaps sig- 

 nificant that in one of the most careful tests — the 

 measurements on the wake of the Scripps discussed 

 in Section 33.4 — the value of W at 60 kc was actu- 

 ally less than that at 24 kc (see Table 9 of Chapter 

 33). Moreover, use of this same underwater sound 

 equipment in measurements of target strengths of 

 submarines has yielded results at 60 kc which are also 

 10 to 20 db above the 24 kc results, in contradiction 

 to theoretical expectations (see Sections 21.4.3 and 

 23.6.2). It is also important that measurements on 

 submarine wakes, made with different equipment and 

 discussed below, show a decrease of W with increas- 

 ing frequency rather than an increase. It is possible 

 that the bubble density at 60 kc is sufficiently high 

 and the wake boundary sufficiently sharp that specu- 

 lar reflection of sound at the wake boundary is suf- 

 ficient to account for the high wake echoes observed; 

 this possibility has not been investigated theoreti- 

 cally. Until the high wake strengths found at 60 kc can 

 be either explained or shown to be the result of ob- 

 servational error, they will remain a serious discrep- 

 ancy in the study of wakes. 



34.3.2 



Submarines 



Values of W for submarines both submerged and 

 surfaced are presented in Table 4 of Chapter 33. For 

 surfaced submarines no estimates are available at 

 20 kc; but at 45 kc, the value of W found for two sub- 

 marines is — 13 db. When 6 db is subtracted to give 

 the wake strength in terms of the average intensity, 

 this value is in close agreement with the maximum 

 wake strength of about — 16 db found at 24 kc. While 

 no experimental data are available on the value of the 

 damping constant 8 at 45 kc. Figure 1 suggests that 



the value of 10 log ((Ts/Sirae) at 45 kc does not differ 

 by more than a few decibels from its value at 24 kc. 

 Thus it may be inferred that the wake strength for a 

 surfaced submarine is quite comparable with that for 

 any large moving surface vessel. The decrease of W 

 shown at 60 kc in Table 4 of Chapter 33 is probably 

 not significant. 



This same Table 4 shows that the wake of a sub- 

 merged submarine is a much poorer reflector than the 

 wake of a surfaced submarine. Since the wake 

 strength is less than its maximum value, W should 

 vary with the bubble density, and therefore with 

 submarine depth and speed. While the measurements 

 are not very conclusive, they indicate that for a sub- 

 marine at 6 knots and a depth of 45 to 90 feet, W is 

 about — 25 db at 45 kc ; this estimate may well be in 

 error by as much as 5 db. As before, an additional 

 6 db must be subtracted to convert to an intensity 

 scale, giving -31 db for W. If 10 log (3/85) at 45 

 kc is taken from Table 5, equation (8) gives 



10 log u{Rr) = -31 - 0.8 - 10 log /i 



- 10 log w - 19.6. (9) 



If the wake is 10 yd deep and 30 yd across, the bubble 

 density u{Rr) is about 3 X 10~^, less than a hundredth 

 of the values for destroyer wakes 1 minute old at 15 

 knots found in Table 1 ; the assumed wake dimensions 

 are somewhat uncertain, but any reasonable varia- 

 tion of these figures would not change the order of 

 magnitude of u{Rr). If the curve of u(Rr) against Rr 

 were the same as the typical curves for destroyers, 

 the total fraction u of the wake volume occupied by 

 air bubbles would be only about 1 X 10~'. While no 

 other quantitative measurements are available, prac- 

 tical echo-ranging tests indicate that the bubble 

 density decreases with increasing submarine depth 

 as would be expected at the greater pressure. 



In the top 60 ft this decrease is about as rapid as 

 would be expected from the experiments with model 

 propellers. Both the transmission measurements dis- 

 cussed above and the reflection measurements dis- 

 cussed below show that with a 10-in. propeller all 

 acoustic effects are much reduced at depths below 

 30 ft. However, the reflection measurements indicate 

 that the acoustic effects have largely disappeared at 

 depths below 60 ft, while echoes from submarine 

 wakes have been reported at greater depths. This 

 difference may be due to lack of sensitivity of the 

 acoustical equipment used for the model propeller 

 experiments. Alternatively, the greater size of the 

 full-scale propellers may enable the formation of 



