On blast waves in exponential atmospheres

Abstract

The paper presents a comprehensive analysis of gas motion created by a strong explosion in an atmosphere whose density is an exponential function of altitude. For the near field (i.e. short times after initiation), an exact analytical solution of the equations of motion is obtained by means of a perturbation technique. For the far field (i.e. long times after initiation), a similarity solution associated with a logarithmic front trajectory is derived. The two are shown to be well matched with each other. Finally, a fully-algebraic approximate solution is given that qualitatively reproduces all the salient features of the exact and asymptotic solutions, while quantitatively it is in fair agreement with their results.