Viscous fluid flow induced by translational-oscillatory motion of a plane layer of porous medium

Background. The study of fluid motion through porous media is of significant interest for investigation of natural phenomena and technological processes. In the paper we consider the motion of viscous fluid that contacts a plane layer of porous medium. The porous medium layer is executing harmonic translational-oscillatory motion in direction parallel to the non-penetrable plane constraining this layer from below and moving at velocity of the layer. Materials and methods. To describe fluid flow in porous medium we used a time-dependent Brinkman equation, for fluid flow outside porous medium - Navier-Stokes equations. When formulating the boundary conditions we took into account a no-slip condition on the non-penetrable surface that bounds the porous medium. At the interface of porous medium and free fluid we took the condition of continuity of fluid velocity and the jump of tangential stresses was assumed proportional to the relative fluid velocity at the interface (in the special case these stresses can be continuous). Results. The motion of viscous fluid inside and outside the layer of porous medium has been determined. The exact solutions have been obtained for the unsteady Brinkman equations inside the porous layer and for the Navier-Stokes equations outside. Conclusions. The existence of intrinsic transverse waves was deduced. In such waves the velocity is perpendicular to the direction of their propagation. Inside and outside the porous layer there are plane surfaces, on which the velocity equals zero. In gaps between those surfaces liquid flows at velocities of pairwise opposite directions.