Nonlinear periodic waves on the charged surface of a deep low-viscosity conducting liquid

An analytical expression for the profile of a finite-amplitude wave on the free charged surface of a deep low-viscosity conducting liquid is derived in an approximation quadratic in wave amplitude-to-wavelength ratio. It is shown that viscosity causes the wave amplitude to decay with time and makes the wave profile asymmetric at surface charge densities subcritical in terms of Tonks-Frenkel instability. At supercritical values of the surface charge density, taking account of viscosity decreases the growth rate of emissive protrusions on the unstable free surface, slightly broadens them for short waves, and narrows for long ones. Analytical expressions for the wave frequencies, damping rates, and instability growth rates with regard to viscosity are found. (C) 2004 MAIK "Nauka / Interperiodica".