%0 Journal Article
%T On the Stability of a Compressible Axial Flow with an Axial Magnetic Field
%A M. Subbiah
%A M. S. Anil Iype
%J Journal of Fluids
%D 2013
%R 10.1155/2013/869324
%X We consider the stability problem of inviscid compressible axial flows with axial magnetic fields following the work of Dandapat and Gupta (Quarterly of Applied Mathematics, 1975). A numerical study of the stability of some basic flows has been carried out and it is found that an increase in the magnetic field strength has a stabilizing effect on subsonic flows and a destabilizing effect on supersonic flows. An analytical study of the stability problem has also been done in the present paper, but this analytical study is restricted by the approximation and , where is the Mach number and is the imaginary part of the complex phase velocity . A semicircular region depending on the magnetic field parameter and the Mach number is found for subsonic disturbances and as a consequence it is found that sufficiently strong magnetic field stabilizes all subsonic disturbances. Under a weak magnetic field, it is shown that short subsonic disturbances are stable. 1. Introduction The stability of inviscid shear flows of a compressible fluid was studied in Blumen [1]. In order to simplify the stability problem, Blumen [1] focused attention on the stability of basic parallel shear flow of a perfect gas whose thermodynamic state is constant. From the equations of motion, the pressure of the shear flow is a constant only and if the basic flow temperature is also a constant, it follows that the basic flow density is also a constant. In the context of magnetogasdynamics, Dandapat and Gupta [2] studied the stability of a parallel flow of an inviscid perfectly conducting gas in the presence of a uniform magnetic field. Following Blumen [1], Dandapat and Gupta [2] also considered the case of a constant basic thermodynamic state. In Dandapat and Gupta [3] the stability of a nondissipative axial flow of a compressible conducting fluid between two concentric cylinders in the presence of a uniform axial field was studied. In cylindrical polar coordinates they considered the basic flow with velocity , magnetic field , where is a constant, is the pressure, and is the density. In the absence of the swirl component of the velocity in the basic flow it follows from the equations of magnetohydrodynamics that is a constant. In their stability analysis, Dandapat and Gupta [3] noticed that the equation involving the density perturbation is not needed in deriving the stability equation. Dandapat and Gupta [3] explained this by observing that there is no basic swirl velocity and therefore the mechanism of the centrifugal acceleration playing the role of a radial effective gravity is absent
%U http://www.hindawi.com/journals/fluids/2013/869324/