Two-Dimensional Surface Periodic Flows of an Incompressible Fluid in Various Models of the Medium

Abstract

A comparative analysis of the properties of two-dimensional infinitesimal periodic perturbations propagating over the incompressible fluid surface in various representations of the medium density profiles is carried out. Stratified and homogeneous in density viscous or ideal liquids are considered. Calculations are carried out by methods of the theory of singular perturbations. Dispersion relations and dependences of phase and group velocities for surface waves in physically observed variables are given. The change in the meaning of dispersion relations during the transition from ideal liquids to viscous and from homogeneous to stratified is shown. Taking into account the influence of electric charge does not qualitatively change the nature of two-dimensional dispersion relations. An increase in the surface density of the electric charge leads to a decrease in the wavelength at a fixed frequency and has no noticeable effect on the fine structure of the periodic flow.