74 



of 10', it Is certainly worth while to examine seriously the 

 possibility of turbulent dissipation. However, there are two 

 considerations which make it seem unlikely that this is the 

 principal cause of the energy loss. In the first place, there 

 Is to the author's knowledge no evidence that the disappearance 

 of energy is significantly less serious f:)r bubbles which do 

 not migrate than for bubbles which migrate rapidly; since one 

 expects turbulence to be much less serious for a stationary bubble, 

 a large energy disappearance for such cases would probably have 

 to be attributed to other mechanisms. In the second place. It 

 is questionable whether turbulence could develop quickly enough 

 to oroduce a steady-state rate of dissipation in the very short 

 time covered by the contracted stage. For there are no solid 

 boundaries to heln start the turbulence, and a calculation of 

 the stresses due to viscosity in the velocity field of Taylor's 

 theory shows these stresses to be negligible in comparison with 

 the hydrostatic oressure. 



(ii) Cavitation. It is Just possible that the pressure 

 a short distance above a rising bubble may be low enough to 

 produce a cavitation. However, even if this should occur for 

 a rising bubble it would not explain the energy loss of a 

 stationary bubble. 



(ill) Transfer of heat from the compressed gas to the 

 water. Loss of energy through thermal conduction can easily be 

 shown to be negligible if the vr.oticn of the gas in the bubble 

 Ib non-turbulent. If an appreciable portion of the energy of 

 the gas is to be lost by conduction, the drop in temperature be- 

 tween center and boundary of the bubble must be distributed over 



an aporeclable f-actlon of the radius a. In such a case the 



