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Asymptotic calculations of the second order of smallness for a small dimensionless amplitude of the oscillation of droplets of natural origin in a material environment in an intracloud or ground-level electric field are used to show that, among other modes, the zero and the first mode of droplet oscillations are excited, which do not occur in calculations made in the first order of smallness. The intensity of acoustic radiation in such modes is calculated using the model of an ideal noncompressible electrically conductive fluid. The monopole acoustic radiation of a droplet is shown to be six orders of magnitude more intense than the dipole radiation. In an approximation quadratic in terms of the dimensionless oscillation amplitude, the monopole radiation intensity does not depend on the droplet radius and the strength of the external electric field, while the dipole-radiation intensity greatly depends on the droplet radius. The dependence of the strength of the electric field only appears in the third order of smallness. Oscillating rain droplets emit acoustic radiation in the audible frequency range, while cloud and fog droplets, in the ultrasonic range. The time dependence of acoustic radiation of a droplet of both monopole and dipole type under the initial excitation of a finite segment of the continuous spectrum of modes has the form of beats. [ABSTRACT FROM AUTHOR]

The intensity of acoustic radiation of droplets and the width of the frequency range for which this radiation is accounted are evaluated in asymptotic calculations of the first order of smallness with respect to the dimensionless oscillation amplitude and equilibrium deformation of natural weakly charged droplets. The calculations are carried out using the ideal incompressible conducting fluid model. It is shown that acoustic radiation of fluid-droplet aerosol of natural origin, namely, clouds and fogs, is accounted for the ultrasonic frequency range, while acoustic radiation of rain occurs over the sonic range and such radiation can be hearable. The boundary between the ultrasonic and sonic acoustic radiations with respect to the droplet radius depends on the physical characteristics of the medium and the droplet and can be displaced both to one or another side. [ABSTRACT FROM AUTHOR]

The dispersion relation for capillary waves of an arbitrary azimuthal symmetry on an elliptic cross-section jet in a uniform electrostatic field which is perpendicular to the axis of symmetry of the jet is derived. The stability of the first three azimuthal modes is investigated. It is shown that the stability of capillary waves on the jet reduces with increase in the external electrostatic field strength and the related eccentricity of transverse jet cross-section, as well as with increase in the polarization charge on the jet surface. Comparison with a jet in a radial electrostatic field is carried out. In the case of the transverse electrostatic field the instability growth rates of the capillary waves of any symmetry on the jet surface are turned out to be significantly higher than those in the case of the radial electrostatic field. [ABSTRACT FROM AUTHOR]

In the approximation linear in the amplitude of capillary waves (generally nonaxisymmetric) on the surface of a volumetrically charged dielectric fluid jet accelerated in an external electrostatic field collinear to the jet axis, a dispersion equation is derived and analyzed. It is shown that for certain values of physical parameters the effect of the external electric field stabilizing the capillary waves and the destabilizing effect of the capillary forces and the electrostatic forces exerted by the jet charge may compensate one another for both axisymmetric and nonaxisymmetric, with a high degree of asymmetry, waves. The instability of flexural waves cannot be suppressed completely and can be realized for sufficiently small wave numbers. [ABSTRACT FROM AUTHOR]

Analytically, on the basis of asymptotic methods, the problem of the nonlinear oscillations of a charged ideal incompressible electroconductive fluid drop levitated at rest in gravity and homogeneous electrostatic fields is solved in the quadratic approximation in two small parameters: the initial drop shape deformation amplitude and the stationary eccentricity of the equilibrium drop shape in the electrostatic field. The calculations are performed in fractional powers of the nonlinear oscillation amplitude. The nonlinear corrections to the oscillation frequencies are always negative and already present in the second-order approximation due to the stationary deformation of the drop in the external fields rather than nonlinear interaction between the modes. In the case considered, in contrast to the nonlinear oscillations of a free charged drop, the expression for the generator of the nonlinearly oscillating drop shape contains terms proportional to the oscillation amplitude to the power 3/2. [ABSTRACT FROM AUTHOR]