Nonlinear Streaming Instability of Cylindrical Structures in Finitely Conducting Fluids under the Influence of a Radial Electric Field

Abstract

Linear and weakly nonlinear stabilities of two-layer flows between two concentric circular cylinders are investigated. Two different dielectric inviscid fluids are assumed to flow with different velocities in the two separate layers, whose interface is cylindrical. Hence the flow field is assumed to be axi-symmetric. The two fluids are influenced by a radial electric field due to surface charges at the interface. The critical magnitude of the electric field is obtained as a function of the velocity difference in the linear stability analysis. Based on the multiple scales technique, two nonlinear Schrödinger and Klein-Gordon equations are derived. The modulation instability of a finite wavetrain solution is discussed and compared with the linear instability condition. The analytical results are numerically confirmed, hence stability diagrams are obtained for different sets of physical parameters. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.