Intervals of an unsteady electrohydrodynamic Kelvin-Helmoltz stability

An analysis is made of the stability of a basic flow of streaming fluids in the presence of an oblique periodic electric field. The particular profile investigated is the classical Kelvin-Helmholtz profile modified by the addition of the influence of mass and heat transfer across the interface. The intervals of electrohydrodynamic Kelvin-Helmholtz instability are considered. It is shown that a linear model of the interface is governed by Hillʹs differential equation. Characteristic values and intervals of stability are discussed. The special case of the Mathieu differential equation type is obtained. From the latter equation, the various criteria are discussed for both Rayleigh-Taylor and Kelvin-Helmholtz problems in the presence of an oblique periodic electric field, with and without mass and heat transfer across the interface.