A Self-Similar Flow behind a Magnetogasdynamic Shock Wave Generated by a Moving Piston in a Gravitating Gas with Variable Density: Isothermal Flow

G Nath,A K Sinha

doi:10.1155/2011/782172

Abstract

The propagation of a cylindrical (or spherical) shock wave in an ideal gas with azimuthal magnetic field and with or without self-gravitational effects is investigated. The shock wave is driven out by a piston moving with time according to power law. The initial density and the initial magnetic field of the ambient medium are assumed to be varying and obeying power laws. Solutions are obtained, when the flow between the shock and the piston is isothermal. The gas is assumed to have infinite electrical conductivity. The shock wave moves with variable velocity, and the total energy of the wave is nonconstant. The effects of variation of the piston velocity exponent (i.e., variation of the initial density exponent), the initial magnetic field exponent, the gravitational parameter, and the Alfven-Mach number on the flow field are obtained. It is investigated that the self-gravitation reduces the effects of the magnetic field. A comparison is also made between gravitating and nongravitating cases.

Highlights

The explanation and analysis for the internal motion in stars is one of the basic problems in astrophysics
According to the observational data, the unsteady motion of large mass of the gas was followed by sudden release of energy results flare-ups in novae and supernovae
Numerical solutions for self-similar adiabatic flows in self-gravitating gas were obtained by Sedov [1] and Carrus et al [2], independently

Summary

Introduction

The explanation and analysis for the internal motion in stars is one of the basic problems in astrophysics. Nath et al [5] have studied the above problem assuming the flow to be adiabatic and selfsimilar and obtained the effects of the presence of a magnetic field. Vishwakarma and Singh [11] obtained the similarity solution for the flow behind a shock wave in a gravitating or nongravitating nonuniform gas with heat conduction and radiation heat flux in the case of adiabatic flow. The purpose of this study is, to obtain the selfsimilar solutions for the propagation of magnetogasdynamic cylindrical (or spherical) shock wave generated by a moving piston in a nonuniform gas with or without self-gravitational effects, in the presence of an azimuthal magnetic field, under isothermal flow condition. Effects of viscosity and rotation are not taken into account

Equations of Motion and Boundary Conditions

Self-Similarity Transformations

H D dH dη

Results and Discussion