Ekman Convective Layer Flow of a Viscous Incompressible Fluid

Analytical solutions for generalizing the Ekman stationary flow of a viscous incompressible fluid in an infinite layer are obtained. The solution of an overdetermined system of the Oberbeck–Boussinesq equations is considered. It is suggested to use a class of exact solutions for this problem. It is shown that the structure of the solutions allows one to preserve the advective derivative in the heat-conductivity equation; this makes it possible to model the stratification of the temperature and pressure fields and describe the oceanic countercurrents.