Analysis of spherically imploding shocks

Abstract

The self-similar solution of spherically imploding shock waves is derived analytically for a perfect gas with a constant ratio γ =cp/cv. The basic conservation equations are reduced to a first-order differential equation in the x- y plane. The requirement of a maximum for the pressure curve dictates the values of the self-similar exponent αm. These values are compared with the previously derived numerical values of αm. When γ=2+√3, the maximum of the pressure occurs at the shock front. The pressure curve then decreases monotonically.