Kinematics of spherical shock waves in an interstellar ideal gas clouds with dust particles

Abstract

In this article, a system of partial differential equations governing the one‐dimensional motion of inviscid, self‐gravitating, spherical dusty gas cloud is considered. The evolutionary behavior of spherical shock waves of arbitrary strength in an interstellar dusty gas cloud is examined. By utilizing the method based on the kinematics of the one‐dimensional motion of shock waves, we derived an infinite set of transport equations governing the strength of shock waves and induced discontinuity behind it. By applying the truncation procedure to the infinite set of transport equations, we get an efficient system of finite number ordinary differential equations describing shock propagation, which can be regarded as a good approximation of the infinite hierarchy of the system. The truncated equations describing the shock strength and the induced discontinuity are used to analyze the growth and decay behavior of shock waves of arbitrary strength in the dusty gas medium. We considered the first two truncation approximations and the obtained results for the exponent from the successive approximation and compared our results with Guderley's exact similarity solution and the characteristic rule.