THE SEQUENCE OF EVENTS 5 



pressure, and in sea water at 18° C. is about 4,900 ft. /sec. This state 

 of affairs is realized in underwater sound transmission, but temperature 

 and density changes also affect the velocity. If the motion is one- 

 dimensional so that plane waves are generated, the wave travels with- 

 out significant change of magnitude or shape. If the waves are radiated 

 from a spherical source, the amplitude decreases with distance from the 

 source and the water motion is modified by the pressure differences 

 resulting from this spherical divergence, a phenomenon known as the 

 surge or afterflow. 



In the regions of water surrounding an explosion the pressures are so 

 large that the wave velocity cannot be assumed independent of pres- 

 sure. This has the physical result that the form of the wave depends 

 on the magnitude of the pressure and displacement of the water as it 

 progresses. These complications for waves of finite amplitude are ex- 

 pressed in much more difficult mathematical statements than those 

 which suffice to explain the propagation of small amplitude waves. 



If, on the other hand, the disturbances affecting the water are slowly 

 changing, and the water can accommodate itself to them before the 

 disturbance has changed appreciably, it may suffice to neglect entirely 

 the wave propagation by which the accommodation takes place. We 

 may then consider the water as an incompressible medium in which the 

 disturbance spreads instantaneously to all points in the liquid. Motion 

 which can be accounted for in this way is usually described as incom- 

 pressive flow. 



1.3. The Shock Wave 



The first cause of disturbance to the water in an explosion is the ar- 

 rival of the pressure wave in the reacting explosive at the water bound- 

 ary. Immediately upon its arrival, this pressure, which is of the order 

 of 2-10^ lb. /in. 2 for TNT, begins to be relieved by an intense pressure 

 w^ave and outward motion of the water. The extremely dense mass of 

 gas left when detonation or burning is complete then begins to expand, 

 its pressure diminishes and the pressure in the water also falls off rapidly. 

 In the case of a detonating high explosive, such as TNT, the pressure 

 rise is for all practical purposes discontinuous, and is then followed by 

 a roughly exponential decay, the duration being measured in times of a 

 few milliseconds at most. The pressure level about a 300 pound spheri- 

 cal charge shortly after complete detonation is sketched in Fig. 1.1(a). 



Once initiated, the disturbance is propagated radially outward as a 

 wave of compression in the water, the steep fronted wave being de- 

 scribed as the "shock wave." As compared to waves of infinitesimal 

 amplitude, this shock wave has the following characteristics : 



(i) . The velocity of propagation near the charge is several times the 

 limiting value of about 5,000 ft. /sec, this value being approached quite 



