Hydromagnetic Stability of Current-Induced Flow in a Small Gap Between Concentric Cylinders

Abstract

A linear stability analysis has been carried out for hydromagnetic current-induced flow. A viscous electrically conducting fluid between concentric cylinders is driven electromagnetically by the interaction of a superimposed radial current and a uniform axial magnetic field. The assumption of small-gap approximation is made and the governing equations with respect to nonaxisymmetric disturbances are derived and solved by a direct numerical procedure. Both of the two different types of boundary conditions, namely ideally conducting and weakly conducting walls, are considered. For 0 ≤ Q ≤ 5000, where Q is the Hartmann number, which represents the strength of magnetic field in the axial direction, it is found that the instability sets in as a steady secondary flow for the case of weakly conducting walls but not for ideally conducting walls. For ideally conducting walls, it is demonstrated that the onset mode is due to nonaxisymmetric rather than axisymmetric disturbances as Q exceeds a certain critical value. The transition of the onset of instability from axisymmetric modes to nonaxisymmetric modes is discussed in detail and the possibility of axisymmetric oscillatory modes is examined. The values of the radial current density required for the appearance of secondary flow are also determined. Furthermore, the predictions of present numerical results are found to be in agreement with previous experimental studies.