In this paper, a three-dimensional, nonstationary numerical model of convective clouds is presented. Hydrothermodynamical, microphysical, and electrical processes are described in detail; results of studies of changes in thermodynamical, microstructural, and electrical parameters in time are given. The hydrothermodynamical block of the model consists of equations of motion that describe the wet convection in the Boussinesq approximation. The equations of the microphysical block describe the processes of nucleation, condensation, coagulation, sublimation, accretion, aggregation, and freezing of drops, deposition of cloud particles in the gravity field, their transport by air flows, and interaction of cloud particles under the influence of electric fields of clouds. Numerical experiments based on the model developed were carried out to study the formation of convective clouds for various stratifications of the atmosphere and the structure of the wind field in the atmosphere. Thermodynamical and microstructural parameters in the zone of a powerful convective cloud are determined. The system of equations of the model was solved by the methods of splitting in physical processes and component-wise splitting.
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B. A. Ashabokov, M. N. Beytuganov, G. V. Kupovykh, A. V. Shapovalov, K. A. Prodan, and V. A. Shapovalov, “Numerical simulation of electrical characteristics of convective clouds,” Izv. Vyssh. Ucheb. Zaved. Sev.-Kav. Region, No. 6, 65–68 (2012).
B. A. Ashabokov, L. M. Fedchenko, V. O. Tapaskhanov, A. V. Shapovalov, V. A. Shapovalov, M. K. Makuashev, A. Kh. Kagermazov, L. T. Sozaeva, A. A. Tashilova, and L. A. Kesheva, Physics of Hail Clouds and Active Effects on Them: State and Directions of Development [in Russian], Pechatny Dvor, Nalchik (2013).
B. A. Ashabokov, A. Kh. Kagermazov, A. V. Shapovalov, and V. A. Shapovalov, “On an approach to the formation of initial conditions for modeling convective clouds,” Tr. Glavn. Geofiz. Observ. Voeikova, No. 582, 159–173 (2016).
B. A. Ashabokov and A. V. Shapovalov, Convective Clouds: Numerical Models and Simulation Results in Natural Conditions and with Active Exposure [in Russian], Nalchik (2008).
B. A. Ashabokov, A. V. Shapovalov, Z. S. Gaeva, L. D. Novikova, V. A. Shapovalov, I. Kh. Mashukov, and M. A. Sherieva, “Numerical modeling of hail clouds when exposed to crystallizing reagent,” Tr. Glavn. Geofiz. Observ. Voeikova, No. 582, 174–183 (2016).
B. A. Ashabokov, A. V. Shapovalov, and V. A. Shapovalov, “Mathematical Model of a Hail Cloud with a Detailed Calculation of Electrical Processes,” in: Innovative Methods and Tools for Research in the Field of Atmospheric Physics, Hydrometeorology, Ecology, and Climate Change [in Russian], Proc. II Int. Conf., Stavropol (2015), pp. 212–215.
B. A. Ashabokov, V. A. Shapovalov, A. G. Ezaova, and M. A. Shapovalov, “Study of the formation of ice phase in powerful convective clouds based on a three-dimensional numerical model,” Estestv. Tekhn. Nauki, No. 5 (73), 78–83 (2014).
A. G. Butkovsky, Control Methods for Distributed Systems [in Russian], Nauka, Moscow (1975).
T. Clark, “Numerical simulation with a three-dimension cloud model: Lateral boundary condition experiments and multiceller severe storm simulations,” J. Atm. Sci., 36, No. 11, 2191–2215 (1979).
A. S. Dennis, Weather Modification by Cloud Seeding, Academic Press, New York, etc. (1980).
S. K. Godunov and V. S. Ryaben’kii, Finite-Difference Schemes [in Russian], Nauka, Moscow (1977).
E. L. Kogan, I. P. Mazin, B. N. Sergeev, V. I. Khvorostyanov, Numerical Simulation of Clouds [in Russian], Gidrometeoizdat, Moscow (1984).
V. A. Shapovalov, I. Kh. Mashukov, K. A. Prodan, N. N. Skorbezh, and M. A. Shapovalov, “Some results of numerical modeling of microstructural and electrical characteristics of convective clouds,” in: Sustainable Development: Problems, Concepts, Models, Proc. Int. Conf. Dedicated to the 20th Anniversary of the Kabardino-Balkar Scientific Center of the Russian Academy of Sciences, Vol. 2, Nalchik (2013), pp. 216–219.
S.M. Shmetter, Thermodynamics and Physics of Convective Clouds [in Russian], Gidrometeoizdat, Leningrad (1987).
R. D. Orville and F. J. Kopp, “Numerical simulation of the life history of a hailstorm,” J. Atm. Sci., 34, No. 10, 1596–1618 (1977).
F. P. Vasil’ev, Numerical Methods for Solving Extremal Problems, Nauka, Moscow (1988).
E. A. Volkov, Numerical Methods, Nauka, Moscow (1987).
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 154, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, 2018.
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Ashabokov, B.A., Shapovalov, A.V., Shapovalov, V.A. et al. Numerical Modeling of Thermodynamical and Microstructural Parameters of Convective Clouds in the Process of Their Evolution. J Math Sci 253, 478–487 (2021). https://doi.org/10.1007/s10958-021-05244-2
Keywords and phrases
- mathematical model
- system with distributed parameters
- numerical integration
- splitting method
- microstructural parameters
AMS Subject Classification