Analytical solution of the equation for the current function in the model of flows with variable wind action in space

Abstract

The paper considers a mathematical model of wind currents in a rectangular reservoir of constant depth. The analysis is carried out for the model in dimensionless form with the subsequent exclusion from the system of equations of terms describing advection and horizontal diffusion. The analytical solution for the integral components of the horizontal components of the flow velocity is obtained by specifying the components of the tangential friction stress of the wind according to a special law that allows describing various wind situations. The solutions found can be used as reference when testing various difference schemes and algorithms used in reservoir circulation models. Numerical modeling of ocean dynamics is an important and urgent task in solving which it is necessary to use methods and algorithms that allow obtaining solutions corresponding to objective reality. But the models themselves and especially the modeling object are quite complex, so most often the comparison of the results obtained from different models are compared with each other. Therefore, it is preferable to simplify the model itself and the object of study to such an extent that we have the opportunity to build an analytical solution to the problem and test the schemes and methods used in the numerical implementation of hydrodynamic models on such an example. The use of adequate schemes and methods does not exclude the use of high sampling. However, the development of the models themselves and the methods of their numerical implementation allows us to obtain similar results using less computing resources.