Abstract
The analytical expression for the quadrupole moment of a charged conducting droplet caused by the presence of the self- and induced charges on the droplet surface is obtained. The droplet is assumed to be motionless in the superposition of gravitational and electrostatic fields. The analytical calculations are carried out in the first order in the dimensionless oscillation amplitude of the droplet. The intensity of electromagnetic radiation of the droplet generated by time variation in its quadrupole moment is estimated in the second order of smallness with respect to the square of the ratio of the characteristic linear droplet size to the length of emitted wave.
Similar content being viewed by others
References
Crawford, F.S., Jr., Waves. Berkeley Physics Course, Vol. 3, McGraw-Hill, 1968; Moscow: Nauka, 1976.
Astakhov, A.V. and Shirokov, Yu.M., Kurs fiziki. Tom 2: Elektromagnitnoe pole (Physics Course. Vol. 2: Electromagnetic Field), Moscow: Fizmatgiz, 1980.
Sivukhin, D.V., Obshchii kurs fiziki. Tom 3: Elektrichestvo, Ch. 2 (General Physics Course. Vol. 3: Electricity, Pt. 2), Moscow: Nauka, 1996.
Kalechits, V.I., Nakhutin, I.E., and Poluektov, P.P., On possible mechanism of radio-frequency radiation of convective clouds, Dokl. Akad. Nauk SSSR, 1982, vol. 262, ##no. 6, 1344–1347.
Levich, V.G., Kurs teoreticheskoi fiziki. Tom 1 (Course of Theoretical Physics. Vol. 1), Moscow: Fizmatgiz, 1969.
Landau, L.D. and Lifshitz, E.M., The Classical Theory of Fields (3rd ed.), Oxford: Pergamon, 1971; Nauka: Moscow, 1973.
Belotserkovskii, A.V., Divinskii, L.I., Ekaterinicheva, N.K., Ivanov, B.D., Kachurin, L.G., Osipov, Yu.G., Osokina, E.V., and Psalomshchikov, V.F., Active-Passive Radiolocation of Hearth Thunderstorms and Thunderous Dangers in Clouds, Kachurin, L.G. and Divinskii, L.I., Eds., St.-Petersburg: Gidrometeoizdat, 1992.
Kachurin, L.G., Fizicheskie osnovy vozdeistviya na atmosfernye protsessy (Physical Fundamentals of the Impact on Atmospheric Processes), Leningrad: Gidrometeoizdat, 1990.
Gorelik, A.G., Kozlov, A.I., and Sterlyadkin, V.V., Scattering of microwaves by nonspherical and oscillating raindrops, Nauchnyi Vestnik MGTU GA, 2012, no. 176, 25–30.
Frenkel, Ya.I., Teoriya yavlenii atmosfernogo elektrichestva (Theory of Phenomena of Atmospheric Electricity), Leningrad-Moscow: Gostekhneorizdat, 1949.
Grigoryev, A.I. and Shiryaeva, S.O., Electromagnetic radiation of an oscillating charged viscous drop of finite conductivity, Fluid Dynamics, 2002, vol. 37, ##no. 5, pp. 74–80.
Bogatov, N.A., Electromagnetic field generated by capillary drop oscillations, in: Abstracts of the 6th Intern. Conf. “Solar-Terrestrial Relations and Foreshock Physics,” Petropavlovsk-Kamchatskii, September 9–13, 2013, Petropavlovsk-Kamchatskii: Far East Branch of the Russian Academy of Sciences, 2013, pp. 10–11.
Grigor’ev, A.I., Kolbneva, N.Yu., and Shiryaeva, S.O., Dipole electromagnetic radiation by a charged drop oscillating in a uniform electrostatic field, Fluid Dynamics, 2018, vol. 53, ##no. 2, pp. 234–247.
Grigor’ev, A.I., Kolbneva, N.Yu., and Shiryaeva, S.O., Quadrupole electromagnetic radiation by an oscillating charged drop, Zh. Teor. Fiz., 2017, vol. 87, ##no. 6, pp. 914–920.
Abbas, M.A. and Latham, J., The disintegration and electrification of charged water drops falling in an electric field, Quart. J. Roy. Met. Soc., 1969, vol. 95, pp. 63–76.
Grigor’ev, A.I., Shiryaeva, S.O., and Belavina, E.I., Equilibrium shape of a charged drop in the electric and gravitational fields, Zh. Tekhn. Fiz., 1989, vol. 59, ##no. 6, pp. 27–34.
Frenkel, Ya.I., On the Tonks theory of liquid surface rupture by a uniform electric field in vacuum, Zh. Eksper. Teoret. Fiz., 1936, vol. 6, ##no. 4, pp. 348–350.
Beard, K.V. and Tokay, A.A., The field study of small raindrop oscillation, Geophysical Research Letters, 1991, vol. E1, no. 12, pp. 2257–2260.
Sterlyadkin, V.V., Field measurements of precipitation drop oscillations, Izv. Akad. Nauk SSSR, Fizika Atmosfery i Okeana, 1988, vol. 24, ##no. 6, pp. 613–621.
Landau, L.D. and Lifshitz, E.M., Fluid Mechanics (2nd ed.), Oxford: Pergamon, 1987; Moscow: Nauka, 1986.
Hendrics, C.D. and Schneider, J.M., Stability of conducting droplet under the influence of surface tension and electrostatic forces, J. Amer. Phys., 1963, vol. 1, ##no. 6, pp. 450–453.
Naifeh, A.H., Perturbation Methods, New York: Wiley, 1973; Moscow: Mir, 1976.
Landau, L.D. and Lifshitz, E.M., Electrodynamics of Continuous Media, Oxford: Pergamon Press, 1960; Moscow: Nauka, 1982.
Varshalovich, D.A., Moskalev, A.N., and Khersonskii, V.K., Kvantovaya teoriya uglovogo momenta (Quantum Theory of Angular Momentum), Leningrad: Nauka, 1975.
Mazin, I.P. and Shmeter, S.M., Oblaka. Stroenie i fizika obrazovaniya (Clouds. Structure and Physics of Formation), Leningrad: Gidrometeoizdat, 1983.
Mazin, I.P., Khrgian, A.Kh., and Imyanitov, I.M., Oblaka i oblachnaya atmosfera. Spravochnik (Clouds and Cloudy Atmosphere. Handbook), Leningrad: Gidrometeoizdat, 1989.
Author information
Authors and Affiliations
Corresponding author
Additional information
Russian Text © The Author(s), 2019, published in Izvestiya RAN. Mekhanika Zhidkosti i Gaza, 2019, No. 5, pp. 70–82.
Rights and permissions
About this article
Cite this article
Grigor’ev, A.I., Kolbneva, N.Y. & Shiryaeva, S.O. Quadrupole Electromagnetic Radiation of a Charged Drop Oscillating in the Superposition of Collinear Gravitational and Electrostatic Fields. Fluid Dyn 54, 658–670 (2019). https://doi.org/10.1134/S0015462819050045
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462819050045