Plane-Parallel Advective Flow in a Horizontal Layer of Incompressible Permeable Fluid

In this paper a new exact solution of the Navier – Stokes equations in the Boussinesq approximation describing advective flow in a horizontal liquid layer with free boundaries, where the vertical velocity component is a constant value, is obtained. The temperature is linear along the boundaries of the layer. Solutions of this kind are used to close three-dimensional equations averaged across the layer in the derivation of two-dimensional models of nonisothermal large-scale flows in a thin layer of liquid or incompressible gas. The properties of advective flow at different values of Reynolds number and Prandtl number are investigated.