On an exact solution of the Navier-Stokes equations describing non-isothermal large-scale flow in a rotating fluid layer with a free upper boundary

The paper provides analytical presentation of an exact solution of the Navier-Stokes equations describing fluid flow in a rotating horizontal layer with a rigid and thermally insulated bottom boundary and a free upper boundary. At the upper boundary a constant tangential stress of the external force is set and heat transfer according to Newton's law occurs. The temperature of the medium above the surface layer is a linear function of horizontal coordinates. The solution is found from the boundary-value problem for ordinary differential equations for velocity and temperature. The type of solution is investigated depending on the Taylor, Grashof, Reynolds and Biot numbers.