III-14 



B. SCATTERING FROM AIR BUBBLES 



Small air bubbles may be found throughout the ocean, and appear very 

 often in conjunction with other scatterers. For example, they occur immediately 

 below the surface of the ocean, due to the breaking of surface waves or the in- 

 cidence of spray or rain on the surface; they are generated in the wake or turbu- 

 lent boundary layers of ships; they may even take the form of gas bladders in 

 fish. Typical air bubbles are quite small, usually less than one centimeter in 

 diameter even though an occasional piscine bladder may be somewhat larger. 

 The density of air bubbles is normally quite low, but their effect on the scatter- 

 ing of acoustic waves is far greater than one would expect from their low frac- 

 tional volume. 



We may obtain a general idea of the effect of air bubbles on sound 

 waves through the analysis of the previous section. Consider the air bubble 

 simply as a small sphere of air surrounded by an infinite expanse of water. We 

 are concerned primarily with sound of 100 cps to 10, 000 cps, in other words, 

 sound with a wavelength in water of between 15 centimeters and 15 meters. 

 Since the air bubbles are very small compared to the wavelength, we are indeed 

 in a situation analyzed in the preceding section for the case ka < < 1 . 



From that analysis emerged Equation III- 15, which showed that the 

 scattering of a plane wave from a small fluid sphere consists of "breathing" and 

 a "sloshing" mode. For the case of air in the ocean, just below the surface, the 

 two parameters g and h (the ratios of the densities and sound velocities of air 

 and water) are given approximately by g = Po/Po =1.3x10 , h = Co /co =0.2. 

 In this case, therefore, the relative compressibility gh^ is so small (0.52x10 ) 



that the breathing mode will completely dominate. The resulting scattered wave 



(ka)s 

 is isotropic, and its amplitude at the surface of the bubble is „ a Pjj^^, as given 



by (III- 15). From this it would appear that the scattering strength of the bubble 

 increases quadratically with the frequency of the incident sound. This is indeed 

 true for sufficiently small ka, but not for the entire range ka < < 1. If ka be- 

 comes of the same order of magnitude as 3 gh^, so that the amplitude of the 

 scattered wave would appear to be approximately the same as that of the incident 

 wave, we must consider a more careful approximation of the breathing mode. 

 According to (III- 13), a plane incident wave of the form given in (III-8) will pro- 

 duce a spherically scattered "breathing" mode wave: 



i p ikr-iuut p. ikr-iuut 



. . mc e mc e „^^ ,o\ 



;artbur SI.ILittleJnt. 



S-7001-0307 



