534 



ROLE OF BUBBLES IN ACOUSTIC WAKES 



of air in one cu cm of water is then given by the 

 integral 



u = I u(Rr)dRr, 



(2) 



where /Jmax, the maximum radius of any bubble 

 present, is assumed to be much less than 1 cm. 



Since the attenuation coefficient Ke is directly pro- 

 portional to the bubble density u{Rr), and since also 

 the damping constant 5 discussed in Section 28.2 does 

 not affect Ke, measurements of acoustic attenuation 

 provide a sensitive determination of the amount of 

 air present in wakes. The actual attenuations ob- 

 served, however, are somewhat complicated by the 

 geometry, since the wake is never sufficiently deep to 

 ensure that no sound reaches the measuring hydro- 



To find the absorption in decibels per yard, the re- 

 sulting transmission losses have been divided by the 

 wake widths for the destroyers given in Section 

 31.3.1. The values of Ke for a destroyer speed of 15 

 knots are listed in Table 1, together with the cor- 

 responding values of u{Rr). The values of u{Rr) for 

 different ages of the wakes were plotted against Rr 

 for destroyer speeds of 10, 15, 20, and 25 knots, re- 

 spectively, and the areas under these curves were 

 determined by graphical integration. The resulting 

 values of u, the relative amount of air present, in 

 bubbles of all sizes for different destroyer speeds and 

 wake ages are given in Table 2. Starred values are 

 uncertain, since they are based primarily on the 

 extrapolated parts of the graphs. 



Apparently no direct estimates have been made of 

 air present as bubbles in destroyer wakes. The only 



T.\BLE 1. Attenuation coefficient and density of resonant bubbles — destroyer at 15 knots. 



phone below the wake. As a result of this uncertainty, 

 the bubble densities found by use of equations (1) 

 and (2) are somewhat indefinite, though they are 

 probably not in error by a factor of more than two. 



Bubble densities may be computed from acoustic 

 measurements for destroyers at different speeds and 

 for different wake ages. They may also be computed 

 for a small high-speed propeller with no forward 

 motion. 



34.2.1 Wakes of Destroyers and 

 Destroyer Escorts 



The computations for destroyers and similar ves- 

 sels are based on the extensive transmission measure- 

 ments across wakes reported in Section 32.3.1. The 

 smoothed curves represented by equations (10) and 

 (11) of Chapter 32 have been used, and an average 

 taken for source outside the wake and source inside 

 the wake, since these represent lower and upper 

 limits to the absorption in the top 10 ft of the wake. 



Table 2. Fraction of air present as bubbles in de- 

 stroyer wakes. 



* Uncertain. 



attempts to collect bubbles in ship wakes are ap- 

 parently the attempts made with a 78-ft yacht.' 

 About 1 cu cm per minute of air was collected through 

 a ring 8 in. in diameter, 6 ft behind a propeller 38 in. 

 in diameter rotating at tip speeds between 50 and 60 

 ft per second. Cavitation bubbles could be seen in the 

 water, but the bubble density computed for a slip- 

 stream speed of 5 ft per second is only 5 X 10"' parts 

 of air by volume in 1 part water. This value is in 



