The Inviscid Instability in an Electrically Conducting Fluid Affected by a Parallel Magnetic Field

We investigate inviscid instability in an electrically conducting fluid affected by a parallel magnetic field. The case of low magnetic Reynolds number in Poiseuille flow is considered. When the magnetic field is sufficiently strong, for a flow with low hydrodynamic Reynolds number, it is already known that the neutral disturbances are three-dimensional. Our investigation shows that at high hydrodynamic Reynolds number (inviscid flow), the effect of the strength of the magnetic field on the fastest growing perturbations is limited to a decrease of their oblique angle, i.e., angle between the direction of the wave propagation and the basic flow. The waveform remains unchanged. A detailed analysis of the linear instability provided by the eigenvalue problem shows that the magnetic field has a stabilizing effect on the electrically conducting fluid flow. We find also that at least, the unstability appears if the main flow possesses an inflexion point with a suitable condition between the velocity of the basic flow and the complex stability parameter according to Rayleigh's inflexion point theorem.