70 



6. DEPARTURES FROM SPHERICAL SHAPE 



In the analysis of Appendices 4 and 5, which has just 

 been discussed, the effects of gravity and of nearby surfaces are 

 treated as small perturbations on the motion. As is shovm in 

 these appendices, the perturbed motion is in first approximation 

 merely a superposition of radial and translatory motions, without 



any change in the spherical shape of the bubble. Moreover, 



22 

 Taylor has shown that the observed motion of bubbles can be 



approximately calculated, even when the migration is large, by a 

 theory in which the bubble is constrained to be spherical at all 

 times. However, it is clear that in higher approximations depar- 

 tures from sphericity will occur, and photographs taken during 



23 

 the later war years do in fact show that in the contracted 



stages the bubble becomes flattened in a plane, normal to its 



direction of migration, and sometimes develops a mushroom-like 



shape. As this flattening has a significant effect on the rate 



of migration and on the intensity of the pressure pulse, some 



theoretical study has been devoted to it ^. The present section 



22 



See the article by Taylor in this volume. 



23 

 -^See the article "Motion and Shape of the Hollow Produced by 



an Explosion in Liquid" by Taylor and Davies in this volume. 



See for example the article of Penney and Price in this 

 volume. 



