Magnetogasdynamic Shock Waves in a Rotating Gas with Exponentially Varying Density

J P Vishwakarma,G Nath

doi:10.5402/2012/168315

Abstract

Nonsimilar solutions are obtained for one-dimensional adiabatic flow behind a magnetogasdynamic cylindrical shock wave propagating in a rotating or nonrotating perfect gas in presence of a constant azimuthal magnetic field. The density of the gas is assumed to be varying and obeying an exponential law. In order to obtain the solutions, the angular velocity of the ambient medium is assumed to be decreasing exponentially as the distance from the axis increases. The shock wave moves with variable velocity and the total energy of the wave is nonconstant. The effects of variation of Alfven-Mach number and time are obtained. Also, a comparison between the solutions in the cases of rotating and non-rotating media with or without magnetic field is made.

Highlights

Hayes 1, Laumbach and Probstein 2, DebRay 3, Verma and Vishwakarma 4, 5, Vishwakarma 6, Vishwakarma and Nath 7, and Vishwakarma et al 8 have discussed the propagation of shock waves in a medium where density varies exponentially and obtained similarity or nonsimilarity solutions
Chaturani studied the propagation of ISRN Mathematical Physics cylindrical shock waves through a gas having solid body rotation and obtained the solution by similarity method adopted by Sakurai
Nath 18 obtained the similarity solution for the magnetogasdynamic shock wave generated by a moving piston in a rotational axisymmetric isothermal flow of perfect gas with variable density according to power law

Summary

Introduction

Hayes 1 , Laumbach and Probstein 2 , DebRay 3 , Verma and Vishwakarma 4, 5 , Vishwakarma 6 , Vishwakarma and Nath 7 , and Vishwakarma et al 8 have discussed the propagation of shock waves in a medium where density varies exponentially and obtained similarity or nonsimilarity solutions. These authors have not taken into account the effects of rotation of the medium. A comparison between the solutions in the cases of rotating and nonrotating media is made for both the magnetic and nonmagnetic cases

Fundamental Equations and Boundary Conditions

Solution to the Equations

Results and Discussion