The Karman’s problem concerning permeable disk rotation described in Brinkman equations

Abstract

The problem of the Karman of a stationary suspended particles in a viscous incompressible fluid in half-space under the evenly rotating in the own plane permeable and porous infinite radius disk is considered. It is assumed that the skeleton of the disk and its associated permeability significantly less than permeability unrelated suspended particles in a viscous incompressible liquid. In addition it is assumed that the motion of a viscous fluid in the disk and environment obey the Darcy -Brinkmann law (Navier-Stokes equations with linear speed of the resistance forces without convective components), and the suspension is described by Brinkmann equations (full Navier-Stokes equations without the resistance forces). The Brinkmann equations are used because they describe the flow of viscous incompressible fluid with partially blocked space, averaged by volume-porous mass.