On the evolution of compression pulses in an exploding atmosphere: initial behaviour

Abstract

The development in space and time of a plane initial disturbance to a spatially uniform exploding atmosphere is analysed on the assumption that the disturbance amplitude is comparable in magnitude with the inverse (dimensionless) activation energy of the explosion reaction. Particular attention is focused on the shock-fitting problem, which has features that distinguish it from its inert-atmosphere counterpart.Using the positive half of a sine wave to typify an isolated compression perturbation, it is found that the amplifying effect of the ambient reaction leads to very rapid shock wave development, which depends significantly on the spatial extent of the disturbance. The latter also influences the question of whether local explosion (local explosion is recognized here as a logarithmically unbounded growth of the disturbance amplitude; in other words as a local breakdown of the present approximations) occurs at the shock wave or some distance behind it. The subsequent evolution of these two states will no doubt be significantly different, but the answer to this speculation must await extension of the present theory to encompass the rapid events that ensue near the local explosion regions.