Transition to dimensionless problem in wind circulation model

Abstract

It is difficult to overestimate the importance of numerical modeling for solving problems of ocean dynamics, for solving actual problems of environmental monitoring and problems related to weather forecasting. The development of computer technology has allowed significant progress in this matter, especially by increasing the sampling. But, the direction associated with the development of the models themselves, difference schemes and methods of their numerical implementation is far from exhausted. When choosing a model describing the dynamic processes in the ocean, the results obtained from different models are often compared with each other. Therefore, the presence of an analytical (accurate) solution of a problem allows you to make a reasonable choice of the schemes and algorithms used. The ocean dynamics models themselves are quite complex. There are some analytical solutions for the simplest statements, for example, the Stommel model. In this paper, the transition to the dimensionless problem of the model of wind circulation in a rectangular pond with a flat bottom is carried out to obtain a test analytical solution of the three-dimensional problem of wind circulation. The correctness of such a transition is verified by considering the dimension of the corresponding multipliers.  Expressions for barotropic velocity components are given, which can be used for testing and analysis of difference schemes and algorithms in the construction of hydrodynamic models of water bodies dynamics.