  We study the effect of surface texture on an overlying turbulent flow for
textures made of an alternating slip/no-slip pattern, a common model for
superhydrophobic surfaces, but also a particularly simple form of texture. For
texture sizes $L^+ \gtrsim 25$, the texture effectively imposes homogeneous
slip boundary conditions on the overlying, background turbulence, but this is
not its sole effect. The effective conditions only produce an origin offset on
the background turbulence, which remains otherwise smooth-wall-like. For actual
textures, however, for $L^+ \gtrsim 25$ the flow progressively departs from
this smooth-wall-like regime, resulting in additional shear Reynolds stress and
increased drag, in a non-homogeneous fashion not reproduced by the effective
boundary conditions. We focus on the underlying physical mechanism of this
phenomenon. We argue that it is caused by the non-linear interaction of the
texture-coherent flow, directly induced by the surface topology, and the
background turbulence, as it acts directly on the latter and alters it, not at
the boundary where effective conditions are imposed, but within the flow
itself. The interaction acts as a forcing on the governing equations of the
background turbulence, and takes the form of cross-advective terms between the
latter and the texture-coherent flow. We show this with simulations with the
texture removed and additional, forcing terms in the Navier-Stokes equations,
in addition to the effective boundary conditions. The forcing captures the
effect of the non-linear interaction on the background turbulence without the
need to resolve the texture. When the forcing is derived accounting for the
background turbulence amplitude-modulating the texture-coherent flow, it
captures the changes in the flow up to $L^+ \approx 70$--$100$, including the
roughness function and also the changes in the flow statistics and structure.
