Chapter 34 

 ROLE OF BUBBLES IN ACOUSTIC WAKES 



THE PREVIOUS CHAPTERS havc developed a general 

 theoretical background for the study of wakes 

 and have presented the results of acoustic measure- 

 ments on wakes. In this chapter, a review is first 

 given of the evidence that bubbles are the chief source 

 of the acoustic properties of wakes. Ne.xt, the quanti- 

 tative acoustic measurements are compared with the 

 theoretical formulas derived in Chapter 28. From this 

 comparison, conclusions are drawn as to the amount 

 of air present in wakes. Finally, the rate of decay of 

 acoustic wakes is discussed, and shown to be roughly 

 similar to the rate at which air bubbles disappear in 

 sea water. 



34.1 EVIDENCE FOR AIR BUBBLES IN 

 WAKES 



At the present time it seems almost certain that 

 small air bubbles are responsible for the observed re- 

 flection and absorption of sound by surface ship and 

 submarine wakes. The evidence for this is of two 

 general types, qualitative and quantitative. 



From a qualitative standpoint, air bubbles provide 

 the only mechanism yet proposed which can explain 

 the general behavior of wake echoes. In particular, 

 no other explanation seems capable of explaining the 

 very marked dependence of scattering and absorbing 

 power on the depth of the wake. The measurements 

 with the model propeller, described in Sections 32.5 

 and 33.5, show unmistakably a pronounced weaken- 

 ing of both attenuation and scattering when the pro- 

 peller is below about 30 ft. Measurements of echoes 

 from submarine wakes show a similar decrease of 

 about 5 to 10 db in wake strength when the sub- 

 marine dives from the surface to periscope depth. 

 Practical echo-ranging trials confirm the disappear- 

 ance of wake echoes when the submarine dives below 

 200 or 300 ft. These observations cannot be explained 

 on the assumption that turbulence or temperature 

 effects are responsible for the acoustic properties of 

 wakes, but they follow naturally from the assumption 

 that bubbles are the important agents. 



From a quantitative standpoint, the magnitude of 

 the observed effects is enormously greater than can 

 apparently be explained by any assumed mechanism 

 besides the presence of small bubbles in the wake. It 

 has already been noted, in Chapter 29, that on the 

 basis of present acoustic theory, neither turbulence 

 nor temperature irregularities could account for any 

 appreciable scattering or attenuation by wakes. The 

 absorbing and scattering power of a single resonant 

 bubble, analyzed in Section 28.1, is so great, how- 

 ever, that a relatively small number of bubbles is 

 required to explain the observed acoustic effects. 



Any theory of the acoustic properties of wakes can- 

 not be regarded as completely confirmed until reliable 

 quantitative data are shown to be in close numerical 

 agreement with the theoretical predictions. Until in- 

 dependent nonacoustic measurements are made of 

 the bubble density in wakes, or until accurate and 

 reproducible acoustic data can be obtained on wakes 

 under a variety of conditions, it is not possible to 

 verify the "bubble hypothesis" explaining the origin 

 of the acoustic wake. Nevertheless, the general evi- 

 dence seems sufficiently strong to make this hy- 

 pothesis highly probable. 



34.2 TRANSMISSION THROUGH WAKES 



The attenuation of sound by air bubbles in water 

 has been discussed in Section 28.2. The conclusion 

 reached was that probably most of the attenuation 

 is produced by bubbles whose radii are close to the 

 radius Rr of a resonant bubble. Integrating the con- 

 tributions to the attenuation from all bubbles near 

 resonant size leads to equation (67) of Chapter 28 for 

 Ke, the attenuation coefficient in decibels per yard: 



Ke= 1.4 X 105M(/?r) , 



(1) 



where u{Rr)dR is the volume of air per cu cm in 

 bubbles whose radii lie between Rr and Rr + dR. 

 If Ke is known at all frequencies, equation (1) gives 

 uiRr) for bubbles of any radius. The total volume u 



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