  Direct numerical simulations of turbulent channels with rough walls are
conducted in the transitionally rough regime. The effect that roughness
produces on the overlying turbulence is studied using a modified triple
decomposition of the flow. This decomposition separates the roughness-induced
contribution from the background turbulence, with the latter essentially free
of any texture footprint. For small roughness, the background turbulence is not
significantly altered, but merely displaced closer to the roughness crests,
with the change in drag being proportional to this displacement. As the
roughness size increases, the background turbulence begins to be modified,
notably by the increase of energy for short, wide wavelengths, which is
consistent with the appearance of a shear-flow instability of the mean flow. A
laminar model is presented to estimate the roughness-coherent contribution, as
well as the displacement height and the velocity at the roughness crests. Based
on the effects observed in the background turbulence, the roughness function is
decomposed into different terms to analyse different contributions to the
change in drag, laying the foundations for a predictive model.
