On the control and suppression of the Rayleigh-Taylor instability using electric fields

It is shown theoretically that an electric field can be used to control and suppress the classical Rayleigh-Taylor instability found in stratified flows when a heavy fluid lies above lighter fluid. Dielectric fluids of arbitrary viscosities and densities are considered and a theory is presented to show that a horizontal electric field (acting in the plane of the undisturbed liquid-liquid surface), causes growth rates and critical stability wavenumbers to be reduced thus shifting the instability to longer wavelengths. This facilitates complete stabilization in a given finite domain above a critical value of the electric field strength. Direct numerical simulations based on the Navier-Stokes equations coupled to the electrostatic fields are carried out and the linear theory is used to critically evaluate the codes before computing into the fully nonlinear stage. Excellent agreement is found between theory and simulations, both in unstable cases that compare growth rates and in stable cases that compare freq...