Capillary instability of a streaming cylindrical liquid jet submerged in a streaming fluid under the influence of magnetic fields

Abstract

The instability of a streaming cylindrical liquid jet embedded in a streaming different fluid, acted upon by the capilarity, electromagnetic and the fluids inertia forces is investigated analytically and numerically for all axisymmetric and non-axisymmetric disturbances. The non-streaming system is capillary unstable only for small axisymmetric disturbances and in that domain the area under the instability curves is decreased with increasing densities ratio but never suppressed. The magnetic fields interior and exterior to the cylindrical jet have strong stabilizing influences on all different parameters of the problem. Above a certain value of the basic magnetic field the capillary instability is completely suppressed. The streaming has a strong destabilizing influence on all different parameters of the system. Due to the streaming effect, there will be unstable states, not only in the axisymmetric disturbances but also in the non-axisymmetric modes, whether the system is acting upon the capilarity force or electromagnetic force or the combined effect on both. The streaming system is magnetohydrodymanics stable if and only if the perturbed Alfvén wave velocity is greater than the velocity of the basic flow, and this is confirmed numerically. Numerous reported works are obtained as limiting cases from the present general result.