Viscous Potential Flow Analysis of Electrohydrodynamic Rayleigh-Taylor Instability

A linear analysis of Rayleigh-Taylor instability in the presence of tangential electric field has been carried out using viscous potential flow theory. In viscous potential flow theory, viscosity is not zero but viscous term in the Navier- Stokes equation is zero as vorticity is zero. Viscosity enters through normal stress balance and tangential stresses are not considered in viscous flow theory. A dispersion relation has been obtained and stability criterion has been given in the terms of critical value of electric field. It has been observed that tangential electric field influences stability of the system. A comparison between the results obtained by viscous potential analysis and inviscid potential flow has been made and found that viscosity reduces the growth of instability.