Propagation of magnetogasdynamic shock waves in a self-gravitating gas with exponentially varying density

Abstract

Non-similarity solutions are obtained for one-dimensional adiabatic flow behind a magnetogasdynamic spherical (or cylindrical) shock wave propagating in a self-gravitating perfect gas in the presence of a constant azimuthal magnetic field. The density of the gas is assumed to be varying and obeying an exponential law. The shock wave moves with variable velocity, and the total energy of the wave is non-constant and varies with time. The effects of variation of the Alfven-Mach number and time are obtained. It is investigated that the presence of gravitational field reduces the effects of the magnetic field. Also, the presence of gravitational field increases the compressibility of the medium, due to which it is compressed and therefore the distance between the inner contact surface and the shock surface is reduced. A comparison between the solutions in the cases of the gravitating and the non-gravitating medium with or without magnetic field is made. The solutions are applicable for arbitrary values of time. MSC: 76L05, 76W05