Abstract
Nonlinear interaction of capillary waves for the first azimuthal modes of an elliptical jet in an electric cross-section field is examined by the product of two independent small parameters. The interaction itself arises due to the ellipticity of the section perpendicular to the jet. Three azimuth modes participate in the interaction: either even or odd ones. When compared with a jet in a radial electrostatic field, the stability of the jet in a perpendicular uniform electrostatic field is reduced. It turned out that the characteristic time for implementing instability decreases with an increase in the initial amplitudes of the interacting modes and with an increase in the intensity of the external electrostatic field, and it also depends on the value of the wave number.
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