Unsteady isothermal flow behind a magnetogasdynamic shock wave in a self-gravitating gas with exponentially varying density

G Nath

doi:10.1007/s40094-014-0131-y

Abstract

The propagation of spherical (or cylindrical) shock wave in an ideal gas with or without gravitational effects in the presence of a constant azimuthal magnetic field is investigated. Non-similarity solutions are obtained for isothermal flow between the shock and the piston. The numerical solutions are obtained using the Runge–Kutta method of the fourth order. 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, gravitational parameter and time are obtained. It is investigated that the presence of gravitational field reduces the effect 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. The shock waves in conducting perfect gas can be important for description of shocks in supernova explosions, in the study of central part of star burst galaxies, nuclear explosion, rupture of a pressurized vessel and explosion in the ionosphere. Other potential applications of this study include analysis of data from exploding wire experiments and cylindrically symmetric hypersonic flow problems associated with meteors or re-entry vehicles etc. A comparison is made between the solutions in the cases of the gravitating and the non-gravitating medium with or without magnetic field. The obtained solutions are applicable for arbitrary values of time.

Highlights

Shock phenomena such as a global shock resulting from a stellar pulsation or supernova explosion passing outward through a stellar envelope or perhaps a shock emanating from a point source such as a man-made explosion in the Earth’s atmosphere or an impulsive flare in the Sun’s atmosphere have tremendous importance in astrophysics and space sciences
It is investigated that the presence of gravitational field reduces the effects of the magnetic field
The presence of gravitational field increases the compressibility of the medium, due to which it is compressed and, the distance between the inner contact surface and the shock surface is reduced

Summary

Introduction

Shock phenomena such as a global shock resulting from a stellar pulsation or supernova explosion passing outward through a stellar envelope or perhaps a shock emanating from a point source such as a man-made explosion in the Earth’s atmosphere or an impulsive flare in the Sun’s atmosphere have tremendous importance in astrophysics and space sciences. Shock waves are common in the interstellar medium because of a great variety of supersonic motions and energetic events, such as cloud–cloud collision, bipolar outflow from young protostellar objects, powerful mass losses by massive stars in a late stage of their evolution (stellar winds), supernova explosions, central part of star burst galaxies, etc. According to the observational data, the unsteady motion of a large mass of gas followed by sudden release of energy results flare-ups in novae and supernovae. A qualitative behavior of the gaseous mass may be discussed with the help of the equations of motion and equilibrium taking

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