Volume 10, no. 3Pages 16 - 24 Mathematical Modelling of the Formation of a Difference in the Potentials During Crystallization of Cloud Droplets in View of Fractal Media
T.S. KumykovIn this paper, we consider the mechanism of a potential difference occurrence while cloud drops are crystallizing in the convective clouds. Differential equations of fractional order have been applied. We have shown the occurrence of the potential difference at droplets crystallization in the convective clouds essentially depends not only on the rate of the ice growth and dispersion of the bubbles, but also on the fractal environment. Simulation results based on the numerical solution of the graphs depending on different values of the governing parameters.
Full text- Keywords
- cloud drop; fractal dimension; mathematical model; convective cloud.
- References
- 1. Iudin D.I., Trakhtengerts V.Y., Hayakawa M. Fractal Dynamics of Electric Discharges in a Thundercloud. Physics Review E, 2003, vol. 68, p. 016601. DOI: 10.1103/PhysRevE.68.016601
2. Mareev E.L., Iudin D.I., Trakhtengerts V.Y. [Modern Problems of Research of Lightning Electricity]. Design and Technology of Electronic Means, 2004, pp. 7-16. (in Russian)
3. Zhekamuhov M.K., Kambiev M.M. [On One Possible Mechanism of Large Potentials in the Crystallization of Aqueous Solutions]. Russian Journal of Physical Chemistry A, 1985, vol. 10, no. 11, pp. 2884-2886. (in Russian)
4. Andreev A.O. Oblaka: proiskhozhdenie, klassifikatsiya, raspoznavanie [Clouds: Origin, Classification, Recognition]. St. Petersburg, Russian State Hydrometeorological University, 2007.
5. Rys F., Val'dfogel' A. [Analysis of the Fractal Dimension of Clouds with Powerful Convective Currents]. Fractals in Physics: Proceedings of the VI International Symposium on Fractals in Physics, Trieste, 1985, pp. 644-649. (in Russian)
6. Kumykov T.S., Parovik R.I. Mathematical Modeling of Changes in the Charge Cloud Droplets in a Fractal Environment. Bulletin KRASEC. Physical and Mathematical Sciences, 2015, vol. 10, no. 1, pp. 12-17. (in Russian) DOI:10.18454/2079-6641-2015-10-1-12-17
7. Brownscombe J.L., Hallett J. Experimental and Field Studies of Precipitation Particles Formed by the Freezing of Supercooled Water. Quarterly Journal of the Royal Meteorological Society, 1967, vol. 93, no. 398, pp. 455-473. DOI: 10.1002/qj.49709339805
8. Adzhiev A.H., Kupovyh G.V. Atmosfernye ehlektricheskie yavleniya na Severnom Kavkaze [Atmospheric Electrical Phenomena in the North Caucasus]. Taganrog, Taganrog, 2008.
9. Kumykov T.S. Modeling the Dynamics of Bubbles’ Charge in the Fractal Cloud Droplets. News of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, 2015, vol. 1, no. 6, pp. 23-27. (in Russian)
10. Rekhviashvili S.Sh. [Fractional Derivative Physical Interpretation]. Nonlinear World, 2007, vol. 5, no. 4, pp. 194-198. (in Russian)
11. Rekhviashvili S.Sh. The Lagrange Formalism with Fractional Derivatives in Problems of Mechanics. Technical Physics Letters, 2004, vol. 30, no. 1, pp. 55-57. DOI: 10.1134/1.1646715
12. Zhekamuhov M.K., Karov B.G., Kumykov T.S. [Electrization and Spatial Charge Separation at the Air Bubbles Exhalation that Occurs During the Coagulation Growth of Hail Particles in a Cloud. Part 1. Kinetics of the Bubbles Exhalation Process Caused by Increasing Temperature of Overcooled Cloud Drops]. Meteorologiya i Gidrologiya, 2008, no. 11, pp. 44-52. (in Russian)