Rezumat
CZU 532.69
DOI https://doi.org/ 10.5281/zenodo.4455839
Features of realization of instability of Kelvin-Helmholtz on the charged interface the ideal conducting liquid – the ideal dielectric environment are investigated at various interface geometry: flat, cylindrical, and spherical. It is noted that for a flat interface in the region of its stability to each wave number there correspond two waves with various frequencies running in one direction. With an increase in speed, the difference of frequencies decreases, and at the time of realization of instability of Kelvin-Helmholtz (in the region of instability), it became zero, and there appears one wave whose amplitude exponentially increases in time. For a cylindrical border, the situation is same, but there are distinctions connected with the existence of the azimuthal symmetry of waves. In case of a spherical interface, such effect is not present, the change of the modes of the existence of waves is different: the oscillatory instability like Kevin-Helmholtz is implemented at the paired interaction of the modes, and at a further increase in speed, it is replaced by a periodic instability, however, the general picture of the realization of instability is significantly more difficult. It is supposed that the reason of such distinction of the realization of instability is connected with the extremity of the surface area of the sphere and its infinity in one measurement for the cylindrical limit of the section and infinity in two mutually perpendicular directions for the flat one.
Keywords: ideal conductive liquid, dielectric environment, electric charge, Kelvin-Helmholtz instability.