Suppression of Kelvin–Helmholtz instability by an electric field

This study investigates the dynamics of the Kelvin–Helmholtz instability in perfectly dielectric fluids in the presence of a tangential electric field. The motion of the interface is described by a vortex sheet. We show that the interface is linearly stable for Re<2|Aϵ|, where Re denotes the ratio of the inertial force to the electric force, and Aϵ represents the Atwood number for electric permittivity. We perform numerical simulations for the interface evolution for both stable and unstable regimes. The numerical results show the stabilizing effect of the electric field on the interface evolution when the electric field is sufficiently strong. In the stable regime, a nonlinear surface wave appears and propagates along the interface. Notably, the interface is nonlinearly unstable for Re≈2|Aϵ| in the linearly stable regime. We compare the unstable evolutions of the interface for wide ranges of parameters Re and Aϵ. As Re decreases, the spiral turns are significantly weakened and the spiral core is deformed. Increasing |Aϵ| has a similar effect on the interface as decreasing Re. Reversing the sign of Aϵ makes the interface morphology symmetric with respect to the center of the initial interface.