The effect of an axial electric field on the nonlinear stability between two uniform stream flows of finitely conducting cylinders

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