Direct numerical simulations are carried out for incompressible viscous turbulent flows over a porous wall with reduced spanwise permeability. This paper is intended to examine how the anisotropy of a porous wall affects the turbulence characteristics and modifies the skin-friction drag and to demonstrate numerically how sensitive the turbulent drag is to the porous layer thickness in channel flows. Simulations are carried out at a friction Reynolds number of 180, which is based on the averaged friction velocity at the interface between the porous medium and the clear fluid domain. The thickness of the porous layer ranges from 0.9 to 54 viscous units. For each fixed permeability, the drag is observed to decrease for flow over the porous layer with a smaller thickness hp, while a drag increase occurs for a larger hp. The division between two regimes (drag-reducing and drag-increasing) highlights a critical roughness height hc*, which depends linearly on the spanwise permeability Reynolds number as hc* similar to Re-kz. A larger value of hc* suggests an increasing degree of drag reduction can be achieved in a relative wider range of the porous layer thickness. For the porous medium configurations considered, the maximum drag reduction rate obtained is about 20.3% at h(p)* = 9 (hc* = 18.3, Re-kz = 0.18).
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