Physical Oceanography Physical Oceanography 1573-160X 20230302 Analysis of observations and methods of calculating hydrophysical fields in the ocean Research Article Calculation of the Total Flow Components in the Models of Wind Fluid Motion https://orcid.org/0000-0002-6767-1218 AAG-4209-2020 Kochergin V. S.
Russian Federation
vskocher@gmail.com https://orcid.org/0000-0002-3583-8351 AAAG-4206-2020 Kochergin S. V.
Russian Federation
svkocher@mail.ru https://orcid.org/0000-0001-6985-6155 Sklyar S. N.
Kyrgyz Republic
sklyar51@gmail.com Marine Hydrophysical Institute of RAS 2 Kapitanskaya Str. Sevastopol 299011 Russian Federation American University in Central Asia 7/6 Tokombaeva Str. Bishkek 720060 Kyrgyz Republic 30 06 2023 30 3 274 287 04 04 2022 09 01 2023 09 03 2023 Copyright ©; 2023, V. S. Kochergin, S. V. Kochergin, S. N. Sklyar 2023 V. S. Kochergin, S. V. Kochergin, S. N. Sklyar https://creativecommons.org/licenses/by-nc/4.0/ https://physical-oceanography.ru/repository/issues/2023/03/02/

Purpose. The object of the work is to construct an effective numerical method to solve the problem for a stream function and to determine subsequently the total flow components in the models of fluid wind motion in a reservoir. Its efficiency was analyzed, and the work of the proposed difference approximations was illustrated using a class of test problems with the known analytical solutions.

Methods and Results. The difference scheme and the corresponding computational algorithm were constructed based on the projection variant of the integro-interpolation method, which permitted (within a single approach) to solve the problem for the stream function, to calculate its derivatives, and to determine subsequently the total flow horizontal components.

Conclusions. The used discretization method permits to preserve automatically the most important features of the initial differential model at switching to its discrete analog. In particular, its application makes it possible to reproduce correctly the behavior of the stream function derivatives, and hence, the behavior of the total flow horizontal components in the areas of its highest intensity.

 wind currents stream function total flow component singularly perturbed problem analytical solution difference scheme The study was carried out within the framework of the state task on theme FNNN-2021-0005 "Complex interdisciplinary studies of oceanological processes which determine functioning and evolution of the ecosystems of coastal zones of the Black and Azov seas".

Article text not included.

REFERENCES O'MalleyR.E. Jr. Introduction to Singular Perturbations New York Academic Press 1974 206 RoacheP.J. Computational Fluid Dynamics Albuquerque Hermosa Publishers 1976 434 EkmanV.W. On the Influence of the Earth's Rotation on Ocean-Currents Arkiv för Matematik, Astronomi och Fysik 1905 2 11 1 53 StommelH. The Westward Intensification of Wind-Driven Ocean Currents EOS, Transactions, American Geophysical Union 1948 29 2 202 206 10.1029/TR029i002p00202 StommelH. The Gulf Stream. A Physical and Dynamical Description Berkeley and Los Angeles, USA University of California Press 1965 243 KocherginV.S. KocherginS.V. SklyarS.N. Analytical Test Problem of Wind Currents ChaplinaT. Processes in GeoMedia — Volume I Cham Springer Geology 2020 17 25 10.1007/978-3-030-38177-6_3 KocherginV.S. KocherginS.V. SklyarS.N. Analytical Solution of the Test Three-Dimensional Problem of Wind Flows ChaplinaT. Processes in GeoMedia — Volume II Cham Springer Geology 2021 65 71 10.1007/978-3-030-53521-6_9 KocherginV.S. KocherginS.V. SklyarS.N. Analytical Solution of the Equation for the Stream Function in the Model of Flows with Variable Wind Action in Space Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation 2022 19 1 16 24 10.31429/vestnik-19-1-16-25 (in Russian) SklyarS.N. A Projective Version of the Integral-Interpolation Method and Its Application for the Discretization of the Singular Perturbation Problems AlekseevA.S. BakhvalovN.A. Advanced Mathematics, Computations and Applications. Proceedings of the International Conference AMCA-95 Novosibirsk NCC Publisher 1995 380 385 EremeevV.N. KocherginV.P. KocherginS.V. SklyarS.N. Mathematical Modeling of Hydrodynamics of Deep-Sea Basins Sevastopol ECOSI-Gidrofizika 2002 238 (in Russian) KocherginV.P. SklyarS.N. SultanovR.K. On the Problem of Numerical Ocean Hydrodynamics Modelling Soviet Journal of Physical Oceanography 1990 2 2 89 98 10.1007/BF02196859 KocherginV.P. SklyarS.N. SultanovR.K. On the Calculation of the Barotropic Components of Motion in Models for General Circulation of the Ocean Physical Oceanography 1995 6 1 19 24 10.1007/BF02197293 KocherginV.P. DunetsT.V. Computational Algorithm for the Evaluation of Inclinations of the Level in the Problems of the Dynamics of Basins Physical Oceanography 2001 11 3 221 232 10.1007/BF02508869 Il'inV.P. Iterative Preconditioned Methods in Krylov Spaces: Trends of the 21st Century Computational Mathematics and Mathematical Physics 2021 61 11 1750 1775 10.1134/S0965542521110099 KocherginV.S. KocherginS.V. SklyarS.N. Testing of Numerical Methods for Solving the Stream Function Problem in a Model of Stationary Fluid Motion ChaplinaT. Processes in GeoMedia — Volume VI Cham Springer Geology 2023 513 521 10.1007/978-3-031-16575-7_46 BuleevN.I. TimukhinG.I. Numerical Solution of Hydrodynamics Equations for the Planar Flow of a Viscous, Incompressible Liquid Izvestiya SO AN SSSR, Series of Technical Sciences 1969 1 3 14 24 (in Russian)