Exact Solutions for Isobaric Inhomogeneous Couette Flows of a ‎Vertically Swirling Fluid

The paper generalizes the partial class of exact solutions to the Navier–Stokes equations. The proposed exact solution describes an inhomogeneous three-dimensional shear flow in a layer of a viscous incompressible fluid. The solution is studied for the case of the motion of a steady-state isobaric fluid. One of the longitudinal velocity components is represented by an arbitrary-degree polynomial. The other longitudinal velocity vector component is described by the Couette profile. For a particular case (the quadratic dependence of the velocity field on two coordinates), profiles of the obtained exact solution are constructed, which illustrate the existence of counterflows in the fluid layer. The components of the vorticity vector and the tangential stresses are analyzed for this exact solution.