Flow with convective acceleration through a porous medium

TLDR: In this article, the authors considered the flow streaming into a porous and permeable medium with arbitrary but smooth wall surface and considered the Euler equation (in the pure fluid region) and generalized Darcy's law in which the convective acceleration is taken into account.

Abstract: The flow streaming into a porous and permeable medium with arbitrary but smooth wall surface is considered on the basis of the Euler equation (in the pure fluid region) and a generalized Darcy's law in which the convective acceleration is taken into account. The asymptotic behavior of the flow for small permeability of the medium is investigated. It is shown that the flow in the porous medium is irrotational except in the boundary layer next to the surface. The velocity distribution in the boundary layer is given in a universal form. Proper boundary conditions connecting the potential flow in the pure fluid region and the potential flow in the porous medium are obtained when the boundary layer is neglected.