73 



7. THE ETTERGY BALATrCE 



It has already been merit lonedt In Section 4 above 

 that the energy loat between auocesslve pulsations seems to 

 be considerably greater than the acoustic energy racJlated. 

 This Is Illustrated In Fig. 4, which shows, on a smaller scale, 

 the successive pulsations of the same bubble as Pig. 2 . The 

 energies of the first two pulsations are roughly proportional 

 to the cubes of the maximum radii, hence are in about the 

 ratio 1;0.31 . As a check, the kinetic energies shortly 

 before and shortly after the first minimum appear to be In 

 about the same ratio. Although no acoustic measurements of 

 the bubble pulse were made for this explosion, it seems quite 

 certain from other cases in which such measurements have been 

 taken that nowhere near 70^ of the energy of the first 

 oscillation could have been radiated acoustically. Several 

 processeB may be considered in an effort to find a cause 

 for this additional dissipation: 



(1) Turbulence. It has been noticed that for some 

 cases, where the bubble is migrating rapidly the non-acoustlo 

 dissipation of energy is of the same order of magnitude as 

 that which would be expeated for the dissipation in the 

 turbulent wake of a \jnlformly moving solid sphere of the same 

 slie and- velocity as the bubble at Its minimum, in a time 

 of the same order as the duration of the contracted stage. 

 Since the Reynolds number for such oases may be of the order 



27 



See for example A. B. Arons and D. R. Yennie, Bev. 



Mod. Phys. 20, 519 (19^8), also Volume I of this Compendium, 



