Stagnation points of an inhomogeneous solution describing convective Ekman flow in the oceanic equatorial zone

An inhomogeneous analytical solution describing a stratified large-scale isothermal Ekman–Poiseuille flow of a viscous incompressible fluid in the equatorial zone is obtained. A set of stagnation points of this solution is studied. Temperature is set at the flow boundaries. Tangential stresses simulating the effect of wind are specified at the free boundary. The Navier slip conditions are specified on the solid surface. The solution is constructed in the form of functions, linear in horizontal coordinates, with the coefficients dependent on the vertical coordinate. The coefficients of the linear functions are obtained as polynomials. The condition of consistency of the overdetermined equation system describing the specified flow is obtained. The consistency condition imposes restrictions on the boundary conditions. It is shown that the set of stagnation points lies on a straight line.