Pressure flow stability between coaxial cylinders in a longitudinal magnetic field

A system of equations of magnetohydrodynamics for an incompressible fluid is used to study flow stability between coaxial cylinders, which arises under the action of a longitudinal pressure gradient, in the case where a uniform magnetic field is directed along the cylinder axis. The differential sweep method is applied to investigate the dependences of the critical Reynolds numbers on the value of electrical conductivity and the strength of the external magnetic field. The existence of two ranges of electrical conductivity values is established, in which the stabilizing effect of the magnetic field is most significant. An abrupt increase in the critical Reynolds numbers and the detachment of closed instability regions from neutral curves are revealed.