Transient growth in a two-fluid channel flow under normal electric field

Abstract

A linear model of a layered channel flow of two perfectly dielectric viscous fluids in the presence of uniform normal electric field is built. The effect of the normal electric field on transient growth of small disturbances is studied at two values of Weber number. The numerical result shows that the electric field enhances the transient growth for both two-dimensional and three-dimensional disturbance cases. The contours of optimal energy growth are represented in the wave number plane. When the electric field is small, the optimal disturbance that corresponds to the peak value of optimal growth is two dimensional. It is governed by the lift-up mechanism and is little influenced by the electric field. However, when the electrical Euler number exceeds a critical value, the optimal disturbance is three dimensional with streamwise uniform wave number and is partially dominated by the electric field, and moreover, the spanwise wave number has a linear relationship with the electrical Euler number. The comparison of exponential growth and transient growth is performed. It is shown that exponential growth becomes profound and even predominant over transient growth when the electric field is sufficiently strong. In addition, the mechanism of transient growth is discussed and it is found that the existence of material interface may cause transient growth in the absence of shear in basic flow.