No abstract

Weakly nonlinear streaming instability of two conducting fluids with an interface is presented for cylinders of circular cross section. The two fluids are subjected to a uniform axial electric field. Gravitational effects are neglected. The method of multiple scale perturbation is used to obtain a dispersion relation for the first-order problem and two nonlinear Schrödinger equations for the higher orders. The nonlinear Schrödinger equation, generally, describes the competition between nonlinearity and a linear dispersion relation. One of these equations is used to determine the nonlinear cutoff electric field separating stable and unstable disturbances, while the other is used to analyze the stability of the system. The stability criterion is expressed theoretically in terms of various parameters of the problem. Stability diagrams are obtained for different sets of physical parameters. New instability regions in the parameter space, which appear due to nonlinear effects, are indicated. PACS Nos.: 47.20, 47.55.C, 47.65

No 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 axisymmetric. 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 Schro¨dinger 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.