Boundary-layer flow in a porous domain above a flat plate

This paper is concerned with the structure and properties of boundary-layer flow in a porous domain above a flat plate. The flow is generated by an incoming uniform stream at the vertical boundary of the porous domain and is maintained by an external pressure forcing. Herein we provide the parametrization of the interphasial drag in terms of a Darcy–Forchheimer law, derive the momentum boundary-layer equation and elaborate on the profile of the free-stream velocity. The boundary-layer equation is then solved numerically via the local similarity method and via two local nonsimilarity methods at different levels of truncation. The accuracy of these methods is compared via a series of numerical tests. For the problem in hand, the free-stream velocity decreases monotonically to a terminal far-field value. Once this value is reached, the velocity profile no longer evolves in the streamwise direction. The computations further reveal that, for sufficiently small external forcing, the boundary-layer thickness initially increases, reaches a peak and then decreases towards its terminal value. This unusual overshoot is attributed to the large variation of the rate of decrease of the free-stream velocity. On the other hand, our computations predict that the wall stress always decreases monotonically in the streamwise direction.