Propagation of spherical and cylindrical blast waves in a nonhomogeneous atmosphere with counterpressure taken into account

Abstract

We present an approximate method for calculating the propagation of a weak spherical or cylindrical shock wave (with counterpressure taken into account) into a nonhomogeneous exponential atmosphere. In the case of a cylindrical wave with an arbitrary orientation of the cylinder axis the three-dimensional problem is reduced to a two-dimensional one upon introducing the principle of planar sections, i.e., motions of the gas along the cylinder axis are neglected. By means of a parametrization with respect to the positional angle the two-dimensional problem is reduced to a one-dimensional one. To solve the one-dimensional problem, we use the method of “parallel layers”: the atmosphere is partitioned into a number of parallel layers of small thickness in each of which the atmosphere may be considered to be homogeneous, and the passage of the wave through a boundary of the layers may be regarded as a passage across the boundary separating two media.