8 



THE SEQUENCE OF EVENTS 



wave. The expansion continues for a relatively long time, the internal 

 gas pressure decreases gradually, but the motion persists because of the 

 inertia of the outward flowing water. The gas pressure at later times 

 falls below the equilibrium value determined by atmospheric plus hj^dro- 

 static pressure, the pressure defect brings the outward flow to a stop, 

 and the boundary of the bubble begins to contract at an increasing rate. 

 The inward motion continues until the compressibility of the gas, which 

 is insignificant in the phase of appreciable expansion, acts as a powerful 

 check to reverse the motion abruptly. The inertia of the water to- 



FIRST 

 MAXIMUM 



SECOND 

 MAXIMUM 



FIRST PERIOD 



SECOND PERIOD 



Fig. 1.3 Pulsations of the gas products from an underwater explosion. 



gether with the elastic properties of the gas and water thus provide the 

 necessary conditions for an oscillating system, and the bubble does in 

 fact undergo repeated cycles of expansion and contraction. Ordinarily 

 the original state of the bubble is approximately spherical and the radial 

 nature of the later flow results in an asymmetrical oscillation about the 

 mean diameter, the bubble spending most of its time in an expanded 

 condition. These phases in bubble oscillation are shown schematically 

 in Fig. 1.3, which shows the bubble size as a fimction of time. The 

 period of oscillation, in the absence of disturbing effects due to bound- 

 aries, turns out to be quite simply related to the internal energy of the 

 gas and the hydrostatic pressure (and hence depth below the surface of 

 the water), being proportional to the cube root of energy and inverse 

 five-sixths power of pressure. 



Oscillations of the gas sphere can persist for a muul^er of cj^clcs, ten 



