The development of numerical modeling of the dynamics of water bodies for solving environmental problems is of great importance. In recent years, modern computer technology has made it possible to significantly increase the discretization of the problems to be solved for more accurate reproduction of dynamic processes. However, the direction associated with the development of the models themselves, algorithms and methods of their integration is not exhausted, since the joint use of modern computer power and new computational approaches can lead to a positive effect in solving such problems. When choosing a model that describes the dynamics of a reservoir, it is necessary to evaluate the quality of the schemes and algorithms used. Therefore, the presence of an analytical solution to a particular problem allows you to perform such testing. Dynamic models are quite complex. In the literature, some classical analytical solutions for the simplest statements are known, for example, the Stommel model. In this paper, we consider a problem whose solution allows us to obtain an analytical solution for its three-dimensional additional part and vertical component. The solution is obtained for the formulation in a dimensionless form. In this paper, an analytical solution is obtained under constant wind action.

В работе найдено аналитическое решение простейшей задачи ветровой циркуляции, необходимое для тестирования разностных схем и алгоритмов при построении динамических моделей водоемов. Найдено точное решение задачи для различных компонент скорости, в том числе вертикальной. В данной работе решение поставленной задачи выписано при постоянном ветровом воздействии. Показано, что в данной постановке при использовании данного касательного напряжения ветра, баротропные компоненты скорости равны нулю. В целом полученные аналитические выражения удобны для их программирования и сравнения с численным аналогом используемой модели.