The cloud droplets evolution in view of the impact of fractal environment: mathematical modeling
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 4 (2018), pp. 97-108
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In this paper, we investigate the effect of the medium with fractal structure on the growth of small cloud droplets at the initial condensation stage of cloud formation using a fractional differential equation. An electrodynamic model of coagulation of droplets under the action of an electric field is constructed in the cloud medium with a fractal structure. Numerical experiments are performed for assessment of the effect of the medium with fractal structure on the growth of cloud particles involving various combinations of microphysical parameters. A general dependence of the growth of cloud particles on different parameters of fractal structure in medium is established.
Keywords: cloud droplet, mathematical model, convective cloud.
Mots-clés : fractal dimension
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T. S. Kumykov. The cloud droplets evolution in view of the impact of fractal environment: mathematical modeling. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 4 (2018), pp. 97-108. http://geodesic.mathdoc.fr/item/VKAM_2018_4_a9/

[1] Mandelbrot V. V., “Fractals in physics: Squig clusters, diffusions, fractal measures, and the unicity of fractal dimensionality”, J. Stat. Phys., 34 (1983), 895–930 | DOI | MR

[2] Feder E., Fractals, Mir, M., 1991, 214 pp. | MR

[3] Rys F., Waldfogel A., “Analysis of the fractal dimension in clouds with powerful convective currents”, Fractals in Physics Proceedings of the VI International Symposium on Fractals in Physics, ICTP, Trieste, Italy, 1985, 644–649

[4] Iudin D. I., Trakhtengerts V. Y., Hayakawa M., “Fractal dynamics of electric discharges in a thundercloud”, Phys. Rev. E., 68 (2003), 016601 | DOI

[5] Kumykov T. S., Parovik R. I., “Mathematical modeling of changes in the charge cloud droplets in a fractal environment”, Bulletin KRASEC. Phys. and Math. Sci., 10:1 (2015), 11–15 | MR

[6] Kumykov T. S., “Dynamics of cloud drops charge in fractal medium”, Mathematical modeling, 2016, no. 12, 56–62 | MR | Zbl

[7] Kumykov T. S., “Modeling the emergence of fractal structures "babstons" in the atmosphere”, Scientific Bulletins of BelGU. Series: Mathematics. Physics, 44:20 (2016), 145–153

[8] Samko S. G., Kilbas A. A., Marichev O. I., Integrals and derivatives of fractional order and some of their applications, Science and Technology, Minsk, 1987, 688 pp. | MR

[9] Pshu A. V., Boundary value problems for partial differential equations of fractional and continual order, Publishing house KBSC RAS, Nalchik, 2005, 185 pp. | MR

[10] Timofeev M. P., Shvets M. E., “Evaporation of small drops of water”, Meteorology and Hydrology, 1948, no. 2, 14–18

[11] Taukenova F. I., Shkhanukov-Lafishev M. Kh., “Difference methods for solving boundary value problems for fractional differential equations”, Comput. Math. Math. Phys., 46:10 (2006), 1785-–1795 | DOI | MR

[12] Sweilam N. H., Khader M. M., Mahdy A. M. S., “Numerical studies for solving fractional-order logistic equation”, International Journal of Pure and Applied Mathematics, 78:8 (2012), 1199–1210 | MR

[13] Alikhanov A. A., “Apriori estimates of solutions to boundary value problems for fractional-order equations”, Differential equations, 46:5 (2010), 658–664 | DOI | MR | Zbl

[14] Shishkin N. S., Clouds, rainfall and thunderstorms, Gidrometeoizdat, L, 1964, 402 pp.