Notes on Nonuniform Shock Propagation

Abstract

The propagation of a spherical or cylindrical shock wave in a gas, the propagation of a plane shock in a stratified atmosphere, and the travel of a shock through ducts of various kinds belong to a family of closely related physical problems involving thoroughly nonlinear acoustics. In all such situations, the changes in the shock are partly due to the nonuniformity of the environment into which the shock travels, but the development of the shock is also determined in part by nonlinear acoustic wave interactions occurring behind the shock. A discussion of the physical process taking place behind the shock leads to the derivation of a wave-strength relation offering a precise comparison of the relative influence which the environment and the acoustic waves have on the local development of the shock. One interpretation of this wave-strength relation leads to Whitham's approximation for the case of negligible wave influence. Another interpretation leads to a higher approximation for the initial stage of shock propagation. The connection with some recent asymptotic work is also indicated.