Inhomogeneous isothermal equatorial Poiseuille - Ekman flow

An inhomogeneous solution describing the laminar large-scale isothermal Poiseuille-Ekman flow of the viscous incompressible fluid in the equatorial zone is constructed. At the free boundary, tangent stresses are set to simulate the effect of wind. The slip conditions for the Navier fluid are set on the solid surface. The condition of compatibility of the redefined system of equations describing the laminar flow is obtained. The compatibility condition imposes restrictions on the boundary conditions. The solution is constructed in the form of polynomials.