540 



ROLE OF BUBBLES IN ACOUSTIC WAKES 



At any rate, equation (10) and the corresponding 

 one for long pulses, resulting from putting Tq/w equal 

 to 1, seems to account qualitatively for the shape of 

 curves obtained by plotting wake strength against 

 wake age, as illustrated by Figure 8 in Chapter 33. 

 Generally, W remains constant during the first 5 

 minutes after the wake has been laid, or it may even 

 increase slightly. Thereafter W decreases linearly 

 with time. However, the transmission loss Hy, of the 

 wake appears to decrease linearly with time right 

 from the beginning of the wake. The explanation is 

 that for young wakes the factor F in equation (10) is 

 so much smaller than 1 that dW/dt equals 0. After 

 about five minutes Hw seems to have decreased to 

 such an extent that F becomes of the order of one, or 

 dW/dt and dHw/dt have reached the same order of 

 magnitude. 



The observed rates of decay of wake echoes, noted 

 in Chapter 33, are mostly between 1 and 2 db per 

 minute; the much higher values recorded in Table 6 

 of Chapter 33 may be caused by the rather shallow 

 depth of the wake of the launch, as distinguished from 

 the much deeper wakes of the larger surface vessels. 

 In the interpolation formula for H,„ — equation (10) 

 in Chapter 32 — Hy, was assumed to decrease linearly 

 with increasing time. An exponential decay would be 

 more consistent with the observations of wake echoes, 

 if equation (10) of this section is fulfilled; the meas- 

 urements are not sufficiently accurate, however, to 

 indicate which type of decay is actually followed. 



Thus it may be concluded that the observed decay 

 rates for scattering and attenuation are mutually con- 

 sistent, as far as the rather scanty evidence goes. 

 Even if future wake observations would establish 

 beyond doubt that equation (10) is satisfied, these 

 results would by no means suffice to confirm the 



bubble hypothesis. It should be realized that equa- 

 tion (10) represents a relationship of a quite formal 

 nature and physically does not imply more than the 

 plausible proposition that the acoustic effects of 

 wakes are proportional to the volume density of some 

 unspecified agent. 



The total time required for wakes to decay, how- 

 ever, is consistent with the time required for small 

 bubbles to disappear by resolution in sea water. The 

 experiments discussed in Section 27.2.2 indicate that 

 a bubble whose initial radius is 0. 10 cm will disappear 

 in about 30 minutes by gradual resolution of air back 

 into the water. Turbulent motion is needed to keep 

 air bubbles from reaching the surface but cannot pro- 

 long the life of a wake beyond the time limit set by 

 the resolution process. Thus 30 minutes is an upper 

 limit for the life of an acoustic wake if the greatest 

 air bubbles present are initially 0.10 cm in radius. 

 Since bubbles of this size resonate to sound of 3 kc, 

 the transmission loss observations described in Sec- 

 tion 32.3.1 indicate that bubbles of this size are 

 present initially. The observed length of time during 

 which echoes are observed from a surface ship wake 

 averages in the neighborhood of 30 minutes. Thus the 

 observed rate of decay of acoustic wakes is at least 

 generally consistent with the hypothesis that bubbles 

 are responsible for the wake's acoustic properties. In- 

 formation on turbulence in wakes would be necessary 

 for more detailed comparison. However, this general 

 consistency lends added support to the "bubble 

 hypothesis," especially when added to the data al- 

 ready discussed on (1) the variation with depth of the 

 cross section for scattering and extinction, and (2) 

 the value of the ratio (Xs/(ye, and its variation with 

 frequency, which affects the absolute values of the 

 wake strength. 



