The paper presents a particular analytical solution to the Navier—Stokes equations for describing the stationary Benard convection of the viscous incompressible fluid flow in the infinitely extended horizontal layer. It analyzes velocity field in the vertical vortex flow. The large-scale fluid flow is considered in approximation to a thin layer with the non-deformable boundaries. Two horizontal velocity vector components are taken into account. Shear flow appears when the lower boundary is heated/cooled, and the pressure gradient is at the upper boundary. Temperature and pressure are taken as the linear forms. Linear form coefficients depend on the vertical (transverse) coordinate. The priori unknown functions include polynomials describing the velocity field and are precisely determined from the sixth-order system of ordinary differential equations. The polynomials spectral properties are identified in the solution domain. Analysis of the polynomials zero distribution defining the velocity field makes it possible to determine the fluid layer stratification. The paper provides a detailed study of the stable reverse flows in the convective fluid flow of the Couette—Poiseuille—Benard type.

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