Nonlinear Monopole and Dipole Acoustic Radiation of a Weakly Charged Droplet Oscillating in a Uniform Electrostatic Field

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.