Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 39. no. 2. pp. 80–90. ISSN 2079-6641

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MATHEMATICAL MODELING

MSC 86A10

Research Article

Modeling the growth of flat snow crystals in clouds with fractal structure

T. S. Kumykov

Institute of Applied Mathematics and Automation KBSC RAS, 360004, Nalchik, Shortanova st., 89 a, Russia

E-mail: macist20@mail.ru

In this paper, a universal model is proposed to describe the growth process of flat round-shaped snow crystals in mixed-type clouds with a fractal structure. Snow crystals were chosen as the object of research, as they can have a significant impact on the weather conditions and climate of the Earth. In an analytical form, the solution of the equation of the model is found, in which the fractal property of the cloud environment is taken into account through a phenomenological parameter that determines the intensity of the growth of snow crystals using the fractional integro-differentiation apparatus. It is shown that the growth of snow crystals under sublimation and coagulation growth mechanisms mainly depends not only on temperature and water content, but also on the fractal parameter of the cloud environment. The snow crystal growth curves are presented depending on the experimental parameters of the fractality of the cloud medium in the general case and with rapid diffusion. It is noted that the fractality index is responsible for the intensity of the process, the greater the fractality, the more intense the process of snow crystal growth. The considered model can be used to calculate the growth of snow crystals taking into account the fractal parameters of the cloud environment.

Key words: snow crystal, dynamic model, fractal medium, cloud water content.

DOI: 10.26117/2079-6641-2022-39-2-80-90

Original article submitted: 04.08.2022

Revision submitted: 14.09.2022

For citation. Kumykov T. S. Modeling the growth of flat snow crystals in clouds with fractal structure. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 39: 2, 80-90. DOI: 10.26117/2079-6641-2022-39-2-80-90

Competing interests. The authors declare that there are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)

© Kumykov T. S., 2022

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