Analytic Solutions for the Blast-Wave Problem with an Atmosphere of Varying Density.

The adiabatic motion of a gas behind an inflinitely strong shock wave is examined in the case when the density of the gas ahead of the shock front varies as a power of the distance from the origin. It is found that if the decrease in density is greater than a certain critical value, a discontinnity occurs in the gas at some point behind the shock front, and cavitation appears. A complete investigation is made for the case of spherically symmetric flows, and the nature of the discontinuity is examined in each case.