385 
THEORY OF THE SHOCK WAVE PRODUCED BY AN 
UNDERWATER EXPLOSION 
By Stuart R. Brinkley, Jr. and John G. Kirkwood 
ABSTRACT 
The effect of an underwater shock wave from an explosive source 
upon a target structure is determined by the amplitude and duration of the 
shock wave. The theoretical description of an underwater shock wave is thus 
of importance in the determination of the effectiveness of different explo- 
sives for use in underwater ordnance. 
The kinetic enthalpy propagation theory of Kirkwood and Bethe is 
developed from the assumption that level values of a function G =r (w+ u°/2) 
are propagated outward from the generating charge with a velocity €=c+u, 
where r is the distance from the charge, w the enthalpy increment of the 
water for pressure p, u the particle velocity, and c the sound velocity at 
pressure p. Kirkwood and Bethe have estimated an upper bound of the error 
resulting from their basic assumption and have developed the relations neces- 
sary for the calculation of underwater shock-wave parameters as functions of 
distance from the charge. 
In the similarity restraint propagation theory of Kirkwood and 
Brinkley, the explicit integration of the equations of hydrodynamics is 
avoided by the assumption of an exponential Lagrange energy-time curve and 
tne utilization of the second law of thermodynamics to determine at an 
arbitrary distance from the charge the partition of the initial shock-wave 
energy between dissipated @mergy residual in the fluid already traversed by 
