Analytical test problem of wind currents in the sea of Azov

Abstract

Numerical modeling of dynamic processes in reservoirs is of great importance for solving urgent problems of environmental monitoring. Due to the increase in computing power of the used computer systems, it became possible to make significant progress in this issue, mainly by reducing the steps in space and time. However, problems related to the development of the models themselves, difference schemes and methods for their numerical implementation are of great scientific interest. Comparison and analysis of the results of calculations based on a particular model describing dynamic processes in the ocean is most often carried out based on the ideas about the flow of dynamic processes and the experience of the researcher. Therefore, having an accurate (analytical) solution to the problem, we can make a reasonable choice of the schemes and algorithms used. The ocean dynamics models themselves are quite complex, so an analytical solution is not possible for them. But there are analytical solutions for simple statements, such as the Stommel model. In this paper, based on the analytical solution of the three-dimensional problem of wind circulation in a rectangular reservoir with a flat bottom, a solution is obtained that is compared with the numerical solution of a dynamic model with similar input parameters. Input parameters for both models were selected based on the size and average depth of the sea of Azov. The results of calculations showed a good correlation between the obtained solutions. Expressions for barotropic velocity components are given, which can be used for testing and analyzing difference schemes and algorithms in the construction of hydrodynamic models.