Electrogravitational instability of an annular fluid jet coaxial with a very dense fluid cylinder under radial varying fields

Abstract

The electrodynamic instability of a self-gravitating dielectric annular fluid jet possessing a very dense fluid (of negligible inertia) cylinder mantle surrounded by another dielectric self-gravitating medium pervaded by a radial varying electric field is investigated. A general eigenvalue relation valid for all possible symmetric m = 0 and asymmetric m ≠ 0 perturbation modes is derived and discussed. The electrodynamic force has a strong destabilizing influence not only to m = 0 but also to m ≠ 0 disturbance modes. The self-gravitational force is stabilizing to all pure m ≠ 0 modes, while to m = 0 it is stabilizing or destabilizing according to conditions. The destabilizing effects of the internal and exterior varying electric fields shrink the gravitationally stable states and simultaneously increase the unstable ones. The electrogravitodynamic instability character of the model can be minimized if the electrodynamic force effect is extremely small in comparison with that of the self-gravitational force, but the instability will never be suppressed.