A large-scale layered stationary convection of a incompressible viscous fluid under the action of shear stresses at the upper boundary. Velocity field investigation

The exact solution of the definition of convective motions in a layered large-scale flows of a viscous incompressible fluid in a steady case is considered. It was shown that the received problem is, firstly, overdetermined and, secondly, a nonlinear (due to the presence of members of a convective derivative in a heat conduction equation). Also it was shown that the solution class choice can eliminate the override, and the specification of a boundary conditions can reduce the problem to the study of a thermal capillary convection (convection Benard–Marangoni). Then conditions of the counterflow appearance are defined, and their possible amount is investigated. In addition, the analysis of the nonvortex region in the test flow is made. And it was shown that under certain combinations of system parameters the vortex can change the direction.