The purpose of this thesis is to investigate and model how roughness increases drag in turbulent flows.

This work focuses on the transitionally rough regime, where roughness is large enough to have an impact on drag but the rough regime is not fully developed. By restricting ourselves to this regime, we can investigate the changes produced in the flow by roughness before the canonical smooth-wall turbulence is entirely altered. To study this regime, direct numerical simulations of turbulent flows over transitionally rough surfaces are conducted.

First, a modulated triple decomposition of the flow is proposed to study the effect that roughness produces on the overlying turbulence. This decomposition allows us to separate the roughness-coherent component from the background turbulence. Second, the roughness function is decomposed into different contributions to identify the sources of drag increase and propose the initial steps towards a predictive model. A simplified model for the roughness function is then presented. Finally, the modifications to turbulence that arise for larger roughness size, when scaled in viscous units, are also analysed; notably the increase in energy of short, wide eddies, which is consistent with the appearance of a shear flow instability. A complementary study is also presented, which models densely packed roughness elements as anisotropic permeable substrate. This analysis leads to the study of permeable substrates, with the focus, not on drag increase, but on their potential capability to reduce drag.