Magnetohydrodynamic stability of streaming liquid cylinder with doubly perturbed interfaces having a streaming fluid mantle jet

Abstract

The magnetohydrodynamic (MHD) stability of streaming liquid cylinder with doubly perturbed interfaces coaxial with a streaming fluid mantle jet has been developed. A general dispersion relation is derived, discussed and some reported works are described. The analytical results are confirmed numerically and interpreted physically. The streaming is purely destabilizing while the capillary force is such as for small axisymmetric perturbations only. The magnetic field has a strong stabilizing influence and it gives a measure of rigidity in the fluids. The radii (liquid-fluid) ratio plays an essential role in increasing the MHO stabilizing domains. The densities (liquid-fluid) ratio have a very small stabilizing effect. If the magnetic field strength is so strong that the Alfvèn wave velocity is much greater than the streaming speed, the capillary and streaming destabilizing character is completely suppressed and stability sets in. The present results are in good agreement with the experimental results of Kendall (1986) since we neglect here both the magnetic field influence and the inertia force of the interior fluid jet.