Nonlinear electrohydrodynamic stability of a finitely conducting jet under an axial electric field

The nonlinear analysis of the electrohydrodynamic Rayleigh–Taylor instability of a cylindrical interface separating two conducting fluids of circular cross section is investigated in the absence of gravity. The fluids are assumed to be stressed by a uniform axial electric field. The analysis is based on the method of multiple scale perturbation. The linear dispersion relation, nonlinear Schrödinger equations and a nonlinear Klein–Gordon equation are obtained. The stability conditions of the perturbed system are discussed both analytically and numerically and stability diagrams are obtained. The stability diagrams are discussed in terms of various parameters of the problem. Regions of stability and instability are identified.