248 21 



At the instant 1 , a small part of the Incident wave has already- 

 been converted at the surface into the reflected wave, shown by the light 

 curve abc; the remainder of the incident wave is represented by the curve 

 def. Together these two components make up the total pressure represented 

 by the heavy curve im. Cavitation is just beginning at Q, where the pres- 

 sure has sunk to -600 pounds per square inch. 



From this time onward, the curve of total pressure is clipped off 

 at -600 pounds per square inch by the breaking-front. Hence, at the time 2, 

 for example, the curve has its minimum at -600 at B, and to the right of this 

 point, or toward the surface, lies a cavitated region, in which the pressure 

 has the small negative value p^. Just under the surface, however, in un- 

 broken water, larger negative pressures will probably occur. The distribu- 

 tion of pressure at this instant will thus be as shown by the heavy curve 222. 



The breaking-front will finally cease advancing when V^ as given by 

 Equation [2] becomes equal to c. In applying this criterion, it is more con- 

 venient to transform Equation [2] by substituting, from the theory of sound 

 waves, 



dvx ' dvy dv^ _ 1 dp 

 dx dy dz pc'^ dt 



The actual formula employed in making the rough estimate was Equation [46] in 

 Reference (2), Using the author's provisional estimate of the later part of 

 the pressure curve, as represented on page 15 of Reference (6), it was con- 

 cluded in the manner just described that cavitation might ultimately extend 

 throughout a volume such as that shaded in Figure 1U, or to a horizontal 

 radius of nearly TOO feet, but only to a maximum depth in the center of 10 

 feet. 



After the boundary of the cavitated region has ceased advancing as 

 a breaking-front, it will undoubtedly begin to recede as a closing-front. No 

 attempt has been made to follow this process, however, since it seems to be 

 possible to infer the gross features of the subsequent motion of the water 

 from more general considerations. 



The particle velocity just behind the front may be estimated from 

 Equation [3]. Just above the top of the cavitated layer, v^,^, representing 

 the resultant particle velocity due to incident and reflected waves, adds 

 numerically to the last term in Equation [3] and gives a total upward par- 

 ticle velocity v^^ in the cavitated layer of about 49 feet per second. The 

 simultaneous value at the surface is twice that in the incident wave or per- 

 haps 34 feet per second. V/here the descending part of the front halts, how- 

 ever, the positive direction for v^^ is downward, whereas the actual particle 

 velocity is due almost entirely to the reflected wave and Is upward. Thus 



