Nonuniform convective Couette flow

Abstract

An exact solution describing the convective flow of a vortical viscous incompressible fluid is derived. The solution of the Oberbeck–Boussinesq equation possesses a characteristic feature in describing a fluid in motion, namely, it holds true when not only viscous but also inertia forces are taken into account. Taking the inertia forces into account leads to the appearance of stagnation points in a fluid layer and counterflows, as well as the existence of layer thicknesses at which the tangent stresses vanish on the lower boundary. It is shown that the vortices in the fluid are generated due to the nonlinear effects leading to the occurrence of counterflows and flow velocity amplification, compared with those given by the boundary conditions. The solution of the spectral problem for the polynomials describing the tangent stress distribution makes it possible to explain the absence of the skin friction on the solid surface and in an arbitrary section of an infinite layer.