A nonlinear asymptotic model for the inertial flow at a fluid-porous interface

•An asymptotic analysis of the homogenized Navier-Stokes equations is developed in the thin transition porous layer between the pure fluid and the homogeneous porous medium.•An original nonlinear and multi-dimensional interface model is thus derived for the macroscale inertial flow over a permeable medium with arbitrary flow directions.•The present theory also enables us to analyze the dependence on porosity of the slip and friction coefficients included in the proposed jump interface conditions.•The coupled Navier-Stokes/Darcy-Forchheimer fluid-porous model supplemented with the present interface conditions is shown to be globally dissipative.•This is the first nonlinear and multi-dimensional model proposed in the literature for the inertial flow at a permeable interface with arbitrary flow directions. An original nonlinear multi-dimensional model for the inertial fluid flow through a fluid-porous interface is derived by asymptotic theory for arbitrary flow directions. The interfacial region between the pure fluid and the homogeneous porous region is viewed as a thin transition porous layer characterized by smoothly evolving heterogeneities. The asymptotic analysis applied to the homogenized Navier-Stokes equations in this thin heterogeneous porous layer leads to nonlinear momentum jump conditions at the equivalent dividing interface. These jump conditions involve slip and friction coefficients whose dependence on porosity are analyzed. Moreover, we show that the resulting Navier-Stokes/Darcy-Forchheimer macroscale coupled model is globally dissipative in the porosity range 0