233 



the water retains the expanding motion which brought about the cavitation. 

 If contraction of the bubbles occurs near a part of the boundary at which 

 7) = 0, this part of the boundary will advance Into the cavltated region as 

 a closing-front. A closing-front of this type may be called an intrinsic 

 one; the analysis shows that it must advance at a speed exceeding the speed 



of sound, else it will at once change Into the other 

 type, to be described next. 



When recession of the boundary of the cav- 

 ltated region Is caused by conditions in the un- 

 broken water, the boundary may be called a forced 

 closing-front. Figure 3. Its motion is essentially 

 an impact process, similar to that which occurs when 

 a locomotive picks up the slack in a long string of 

 cars. Layer after layer of the cavltated water is 



Figure 3 - A Forced compressed impulsively from p^ to some higher pres- 

 Closing-Front 



sure p, and its component of velocity normal to the 



boundary is likewise changed. It is assumed in the 

 idealized theory, as already stated, that the cavitation bubbles close In- 

 stantly as the closing-front passes over them. If, in reality, they contain 

 a kernel of air or other foreign gas which requires time to redissolve in the 

 liquid, the process will be modified. 



It can be shown that a forced closing-front cannot move faster than 

 sound, relatively to the unbroken liquid behind it, but exact equations cov- 

 ering its motion are difficult -to formulate in the general case. The reason 

 can be said to lie in diffraction of the waves that are incident on the 

 boundary . ' 



THE ONE-DIMENSIONAL CASE 



The one-dimensional case, on the other hand. Is easily treated in 

 more detail. If the motion is confined to one dimension, use may be made of 

 the familiar fact that any one-dimensional disturbance in unbroken liquid is 

 equivalent to two superposed trains of plane waves traveling in opposite di- 

 rections. One of these two trains will fall at normal Incidence upon the 

 plane boundary of the cavltated region, while the other will be leaving it 

 continually as a reflected train of waves. Simple equations can then be 

 written in terms of these trains. 



Let p' denote the pressure in the incident wave train, and let v^ 

 denote the particle velocity in the cavltated region, measured positively now 

 toward the cavltated side of the boundary. Then the analysis (2) indicates 

 that, if 



p' ^ -9-(Pe + pcv,) 



