Abstract
The complete dispersion relations of a flat free surface periodic perturbations with a positive definite frequency and a complex wavenumber taking into account spatial attenuation in a viscous stratified charged liquid were obtained in a linear approximation for the first time by methods of the theory of singular perturbations. Regular components of the complete solution describe plane gravitational-capillary waves. Singular components characterize ligaments – thin flows that are absent in the model of an ideal medium. The obtained dispersion relations in extreme cases uniformly transform into known expressions for inviscid stratified, viscous homogeneous and ideal liquids. The calculated dependencies of the wavelength and thickness of the ligament, the group and phase velocity of the components on the frequency at different values of the media parameters are given.
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