Shock Propagation in Spherically Symmetric Exponential Atmospheres

Abstract

Computer calculations have been made of the propagation of the shock from an explosion at the origin of a spherically symmetric, exponential, ideal-gas atmosphere. A generalization of Sachs scaling has been devised which allows a very convenient systematization of the pressure-distance curves, and which shows that, for a suitable normalization, these curves are straight lines throughout a significant range of yield, distance, and degree of atmospheric inhomogeneity. This technique is also used to investigate the validity of modified Sachs scaling, an approximate method of generating pressure-distance curves for an inhomogeneous atmosphere from the known results for a homogeneous atmosphere. It is found that modified Sachs scaling yields results which deviate from the hydrodynamic code calculations by at most 20% in the weak shock regime. This result is essentially independent of yield. Some comments are made on the applicability of these methods to the problem of shocks from explosions in horizontally stratified, real-gas atmospheres.