Instability of Flow between Parallel Planes with a Coplanar Magnetic Field

Abstract

The equations determining the growth of three-dimensional disturbances in the presence of a coplanar magnetic field, which is not parallel to the flow, are shown to be similar to those which determine the growth of two-dimensional disturbances when the field is parallel to the flow. When the field is not parallel to the flow the critical Reynolds number for the flow is shown to be finite for disturbances propagated in a certain direction. A consequence of this result is that the analog of Squire's theorem does not hold, in general, when the magnetic field is not in the flow direction.