Nonlinear analysis of the Rayleigh-Taylor instability at the charged interface

An asymptotic solution to the problem of analyzing the nonlinear stage of the Rayleigh-Taylor instability at the uniformly charged interface between two (conducting and insulating) immiscible ideal incompressible liquids is derived in the third order of smallness. It is found that the charge expands the range of waves experiencing instability toward shorter waves and decreases the length of the wave with a maximum growth rate. It turns out that the characteristic linear scale of interface deformation, which arises when the heavy liquid flows into the light one, decreases as the charge surface density increases in proportion to the square root of the Tonks-Frenkel parameter characterizing the stability of the interface against the distributed self-charge.