475 
9. The Shock Wave for Cylindrical Symmetry 
The theoretical description of underwater shock waves has so far 
been limited to the case of spherical symmetry. This case is the simplest 
one that corresponds to a situation that can be realized experimentally; 
and it is a good approximation, particularly at large distances, to the 
shock wave produced by charge shapes commonly employed. However, the 
theoretical investigation of shock waves of different symmetry is of in- 
terest for the information that it can give on the effect of symmetry upon 
the wave. 
The methods of the kinetic enthalpy propagation theory of Kirk- 
wood and Bethe have been employed by Rice and Gine112/ for a theoretical 
treatment of the one-dimensional case of an infinite cylinder of explosive 
undergoing instantaneous adiabatic isometric conversion to its products. 
The shock-front conditions of Rankine and Hugoniot and the equation of 
state are the same as for the spherical case, the differences between spher- 
ical and cylindrical symmetry appearing in the fundamental equations of 
hydrodynamics. The initial conditions resulting from adiabatic constant 
volume explosion are also unaffected by the symmetry. 
In the acoustic approximation, cylindrical waves undergo a change 
of type as they are propagated, and the variation of some property of the 
fluid, such as pressure, as r elt = r/c.) » Where F, is an arbitrary 
function, is valid only asymptotically. The corresponding variation as 
ye (t- m/e.) for an acoustic spherical wave is valid at any distance, 
A finite amplitude theory, in which the approximations are suggested by the 
acoustic case, will therefore be less simply related to the wave. In the 
85 
