Degenerated internal nonlinear resonance interaction of the waves on the surface of an uncharged dielectric jet in a longitudinal electrostatic field

Abstract

Using the asymptotic analytical procedure of the second order of smallness with respect to the ratio between the amplitude of a wave and the radius of a jet for the calculation of the wave motion of a finite amplitude on the surface of a cylindrical jet of an ideal incompressible dielectric liquid, it was found that the nonlinear corrections for the jet’s profile and the potential of the fields of the rates and electrostatic potentials inside and outside of the jet have a resonance character. In a degenerate resonance interaction between the wave, which determines the initial deformation and the waves that become excited owning to the nonlinearity of the hydrodynamic equations, the waves with different symmetry (with different azimuthal numbers) can participate.