72 



at the sides where the fluid moves tangentially to the sphere. 

 It is therefore to be expected that an explosion bubble will 

 flatten if Taylor's constraint of sphericity is replaced by the 

 boundary condition that the pressure be constant over the boundary. 



Small-scale distortions of the surface of the bubble 

 tend to become greatly exaggerated during the contracted stages. 

 This is illustrated by the fact that near the minimum radius 

 bubbles usually present a decidedly prickly appearance. The 

 phenomenon can be understood mathematically in terras of the treat- 

 ment given by Penney and Price for the motion of a bubble depart- 

 ing slightly from spherical shape. Qualitatively, the cause 

 seems to be that illustrated in Fig. 3. Here the top curve may 

 be taken to represent a small portion of the surface of the bubble, 

 as distorted by some accidental ripples. This surface is of course 

 a contour of constant pressure. As we go away from the surface 

 into the water (down in the figure) the contours of constant 

 pressure must become smoother, as shown. This means that the 

 pressure gradient must be numerically greater at the "troughs" 

 of the ripples in the figure than at the crests. If the pressure 

 is higher in the bubble than a short distance outside it, as is 

 the case in the contracted stages, the troughs will be accelerated 

 downward much more than the crests, and the amplitude of the 

 riples will increase. If on the other hand the pressure gradient 

 is in the opposite direction, as it is when the bubble is large, 

 the troughs will be accelerated upward relatively to the crests, 

 and the ripples will be leveled out. 



See the article by Penney and Price in this volijune. 



