Instability Increments for Waves with Different Symmetries on a Space-Charged Jet Moving Relative to a Material Medium

Abstract

We have studied the instability increments of capillary waves with an arbitrary symmetry (arbitrary azimuthal numbers m) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible material dielectric medium. It is shown that for not very high jet velocities, the axisymmetric mode (m = 0) is the first to become unstable upon an increase in the space charge density, and then the kink mode (m = 1) and flexural-strain mode (m = 2) exhibit instability. It is this sequence of realization of instability of azimuthal modes that determines the regularities of charged jet dispersion in experiments. For jet velocities comparable with those critical for aerodynamic instability realization, the mode with m = 1 is the first to lose its stability. The dependences of maximal increments on wavenumbers have been determined for all azimuthal modes.