On derivation of the analytical expression for damping ratios in a low-viscosity approximation

Abstract

The damping ratios of waves and oscillations in nonlinear dispersion equations are found for planar, cylindrical, and spherical geometries as applied to finite-volume liquids. For a cylindrical jet and a plane interface between viscous liquids, the damping ratios are determined for the first time. When the radius of curvature of the liquid jet surface decreases, so does the damping ratio of capillary waves. In a system of immiscible liquids, the damping ratio may be both larger and smaller than that for the pure liquid depending on the viscosity of the liquids and the ratio of their densities. This is because the damping ratio depends on the kinematic viscosities of pure liquids. The damping ratio is also estimated for waves arising at the liquidgas interface due to a tangential discontinuity of the velocity field.