Analytical solutions for a non-stationary model of wind currents
UDC
51.7DOI:
https://doi.org/10.31429/vestnik-19-3-17-24Abstract
In this paper, we consider a simplified three-dimensional mathematical model of wind currents in a reservoir obtained by analyzing a model based on a system of complete nonlinear equations of hydrothermodynamics written in traditional approximations. The analysis is carried out on the basis of the procedure for resizing the model with the subsequent exclusion from the system of equations of terms describing advection and horizontal diffusion. The problem is considered in a rectangular area with the assignment of the components of the tangential friction stress of the wind in a special way that allows you to describe complex wind situations. Within the framework of the above limitations, an analytical solution was found for the integral components of the horizontal velocity components of the wind flow model. The accepted restrictions are quite soft and allow you to preserve the most important properties of the simulated processes in the model. This makes it possible, when choosing the main parameters in the model that reflect the specifics of the reservoir, to obtain some properties of the currents in this reservoir "in the first approximation". In this paper, the components of the shear stress of wind friction are set in accordance with a special law that allows describing complex wind situations, and an analytical solution of the non-stationary problem is obtained.
Keywords:
dimensionless problem, wind currents, test problem, analytical solution, current function, integral velocityFunding information
The work was carried out for the state assignment on the topic 0555-2021-0005 "Comprehensive interdisciplinary studies of oceanological processes that determine the functioning and evolution of ecosystems in the coastal zones of the Black and Azov Seas" (code "Coastal studies").
References
- Марчук, Г.И., Саркисян, А.С., Математическое моделирование циркуляции океана. Наука, Москва, 1988. [Marchuk, G.I., Sarkisyan, A.S., Matematicheskoe modelirovanie cirkulyacii okeana = Mathematical modeling of ocean circulation. Nauka, Moskva, 1988. (in Russian)]
- Stommel, H., The westward intensification of wind-driven ocean currents. Trans. Amer. Geoph. Un., 1948, vol. 29, pp. 202–206.
- Stommel, H., The Gulf Stream. A Physical and Dynamical Description. University of California Press, 1965.
- Стоммел, Г., Гольфстрим. Москва, ИЛ, 1965. [Stommel, G., Gulfstream = Gulfstream. Moscow, Inostrannaya Literatura, 1965. (in Russian)]
- Еремеев, В.Н., Кочергин, В.П., Кочергин, С.В., Скляр, С.Н., Математическое моделирование гидродинамики глубоководных бассейнов. Севастополь, Экоси-Гидрофизика, 2002. [Eremeev, V.N., Kochergin, V.P., Kochergin, S.V., Sklyar, S.N., Matematicheskoe modelirovanie gidrodinamiki glubokovodnyh bassejnov = Mathematical modeling of hydrodynamics of deep-water basins. Sevastopol, Ekosi-Gidrofizika, 2002. (in Russian)]
- Kochergin, V.P., Dunets, T.V., Computational algorithm of the evaluations of inclinations of the level in the problems of the dynamics of basins. Physical oceanography, 2001, vol. 11, iss. 3, pp. 221–232.
- Kochergin, V.S., Kochergin, S.V., Sklyar, S.N., Analytical Test Problem of Wind Currents. In: Chaplina T.O (ed.) Processes in GeoMedia. Volume I. Springer Geology. Springer, Cham., 2020, pp. 17–25. DOI: 10.1007/978-3-030-38177-6_3
- Kochergin, V.S., Kochergin, S.V., Sklyar, S.N., Analytical solution of the test three-dimensional problem of wind flows. In: Chaplina T.O. (ed.) Processes in GeoMedia. Volume II. Springer Geology. Springer, 2021, pp. 65–71. DOI: 10.1007/978-3-030-53521-6_9
- Кочергин, В.С., Кочергин, С.В., Скляр, С.Н., Аналитическая тестовая задача ветровых течений. Процессы в геосредах. 2019. № 2. С. 193–198. [Kochergin, V.S., Kochergin, S.V., Sklyar, S.N., Analytical test problem of wind currents. Processes in geoenvironments, 2019, no. 2, pp. 193–198. (in Russian)]
- Кочергин, В.С., Кочергин, С.В., Скляр, С.Н., Аналитическое решение тестовой задачи ветровых течений при постоянном ветре. Экологический вестник научных центров Черноморского экономического сотрудничества. 2021. Т. 18, № 1. С. 32–35. [Kochergin, V.S., Kochergin, S.V., Sklyar, S.N., Analytical solution of the test problem of wind currents at constant wind. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva = Ecological Bulletin of Scientific Centers of the Black Sea Economic Cooperation, 2021, vol. 18, no. 1, pp. 32–35. (in Russian)] DOI: 10.31429/vestnik-18-1-32-35
- Кочергин, В.С., Кочергин, В.С., Скляр, С.Н., Аналитическое решение уравнения для функции тока в модели течений с переменным по пространству ветровым воздействием. Экологический вестник научных центров Черноморского экономического сотрудничества, 2022, т. 19, № 1, с. 16–25. [Kochergin, V.S., Kochergin, S.V., Sklyar, S.N., Analytical solution of the equation for the stream function in the model of flows with spatially variable wind action. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva = Ecological Bulletin of Scientific Centers of the Black Sea Economic Cooperation, 2021, vol. 19, no. 1, pp. 16–25. (in Russian)] DOI: 10.31429/vestnik-19-1-16-24
Downloads
Downloads
Dates
Submitted
Accepted
Published
How to Cite
License
Copyright (c) 2022 Кочергин В.С., Кочергин С.В., Скляр С.Н.
This work is licensed under a Creative Commons Attribution 4.0 International License.
