Exact Solutions for Stationary and Unsteady Layered Convection of a Viscous Incompressible Fluid with the Specified Velocities at the Bottom

The layered convective flow of a viscous incompressible fluid is considered with the specified velocities at the bottom of an infinite layer. A new exact stationary and nonstationary solution of the Oberbeck-Boussinesq system is presented. The account of fluid velocity at the bottom is characterized by the presence of two stagnant points, this being indicative of the nonmonotonic kinetic energy profile with two local extrema. (paper)