Comparison between algebraical and numerical solutions of the characteristic equation for ripple motion in the presence of a surface film

Numerical solutions of the characteristic equation for ripple motion in the presence of a surface film due to a tensioactive substance are obtained. A comparison between numerical solutions and algebraical approximate ones, obtained by several authors, is made. The role of tensioactive substances in increasing the vorticity of waves in the gravito-capillary frequency region is evidentiated by the dynamics of water under the surface. In particular the main dynamical differences between the two possible wave modes of water in such conditions (Laplace and Marangoni waves) are examined.