Abstract
The linear electrohydrodynamic Taylor-Helmholtz instability between a dielectric liquid of constant shear and a vacuum, when there is a constant vorticity in the liquid and under the effect of a constant electric field acting tangentially to the interface between the two media is studied. The interfacial stability conditions are obtained for constant shear, wavenumber (or wavelength) and electric field values. It is found that each of the constant shear, surface tension and the tangential electric field has a stabilizing effect. In the absence of the electric field, the corresponding pure hydrodynamical case is recovered and corrected The case when the applied electric field is acting normally to the interface between the two media is also investigated for the cases when there are and there are not surface charges present at the interface, and stability conditions are obtained for both cases. It is found that the shear has a stabilizing effect, while the electric field has always a destabilizing influence, and the instability is more effective in the second case than in the first one.