Axisymmetric Steady Flow of a Slightly Conducting Gas in a Magnetic Field

Abstract

The axisymmetric steady flow of an infinite or cylindrically bounded, inviscid, compressible fluid is investigated assuming that the magnetic Reynolds number and the interaction parameter are small. For the unbounded flow the radial velocity alone is evaluated with reference to the potential theory. For the channel flow, the solutions are obtained using the finite Hankel transform and they consist of two parts, namely, the convolution integral term and the magnetic field integral term. In the subsonic case, the first term is negligible because of its exponential damping so that the flow field is explicitly determined by the magnetic field applied. In the supersonic case, the first term is rather dominant and periodic so that the flow field remains oscillatory to infinity downstream. This oscillatory behavior results from the existence of discontinuity (Mach cones or lines) continuing by reflection off the wall of the cylinder.