  We present modeling of an incompressible viscous flow through a fracture
adjacent to a porous medium. We consider a fast stationary flow, predominantly
tangential to the porous medium. Slow flow in such setting can be described by
the Beavers-Joseph-Saffman slip. For fast flows, a nonlinear filtration law in
the porous medium and a non- linear interface law are expected. In this paper
we rigorously derive a quadratic effective slip interface law which holds for a
range of Reynolds numbers and fracture widths. The porous medium flow is
described by the Darcys law. The result shows that the interface slip law can
be nonlinear, independently of the regime for the bulk flow. Since most of the
interface and boundary slip laws are obtained via upscaling of complex systems,
the result indicates that studying the inviscid limits for the Navier-Stokes
equations with linear slip law at the boundary should be rethought.
