Layered Convective Flows of Vertically Swirling Incompressible Fluid Affected by Tangential Stresses

Using the construction of several particular exact solutions, the article investigates the overdetermined system of equations of thermal convection of a vertically swirling viscous fluid in the Boussinesq approximation. The vertical component of vorticity in a non-rotating fluid is generated by an inhomogeneous velocity field at the lower boundary of the infinite horizontal fluid layer. The main causes of convection in the problem under consideration are linear heat sources and the field of shear stresses. The main attention is paid to the study of the properties of the flow velocity field and the dependence of the structure of this field on the magnitude of the vertical swirl.