454 



FORMATION AND DISSOLUTION OF AIR BUBBLES 



Figure 6. Underwater photograph of cavitation spot near bow of a PT boat travehng at 9.5 knots. 



The analogy with transport in a river is not complete, 

 since the turbulence at any fixed position in a wake 

 dies out gradually and the bubbles, once they have 

 reached the surface, are likely to disintegrate. 



A semi-theoretical analysis of the lifetime of wakes 

 has been presented which aims at finding precisely 

 how much turbulence is needed in order to account 

 for the observed ages of acoustic wakes. ^ In this 

 work, the intensity of turbulence is measured by a 

 certain empirical parameter, and it is shown that the 

 theoretical lifetime of the wake passes through a 

 broad but well-defined maximum if the turbulence 

 parameter is increased steadily. 



This theoretical maximum has a simple qualitative 

 physical explanation. While weak or moderately 

 strong turbulence tends to lengthen the lifetime of a 

 wake, as pointed out before, a very large degree of 

 turbulence will speed the decay of a wake by in- 

 creasing the probability of the bubbles reaching the 

 ocean surface and breaking up, namely, when the 



average value of the upward components of the tur- 

 bulent motion exceeds the speed of the rise of bub- 

 bles with gravitational force alone. The existence of 

 these opposing effects for very small and very large 

 turbulence accounts for the maximum lifetime 

 reached at some intermediate value of the turbulence 

 parameter. The predicted maximum happens to agree 

 with the average observed lifetime of acoustic wakes, 

 which is from 15 to 45 minutes. Gratifying as this 

 result is, there are not available any measurements of 

 the intensity of turbulence in wakes, and hence the 

 actual value of the turbulence parameter is unknown. 

 Moveover, should the observations necessary to 

 specify the value of the turbulence parameter be 

 made, the analysis ^ would require some modifica- 

 tion before an exact comparison with the observed 

 lifetime of wakes could be made. In particular, the 

 concentration of bubbles at the ocean surface was 

 assumed to vanish, according to the premise that the 

 bubbles reaching the surface are immediately de- 



