Hydraulic roughness over simple subaqueous dunes

Detailed studies of flow over subaqueous dunes in laboratory flumes were used to suggest a virtual near-bed layer of twice the dune height in which the mean velocity is accelerated towards the crest by contraction. The mean flow velocity in this layer above the crest, transformed into friction velocity by means of the surface skin roughness, is shown to give values consistent with measured values. The resulting dimensionless shear stress due to skin friction is depth-independent, in contrast to that derived by means of often cited traditional methods. As a result of the relationship between dune height and the thickness of the near-bed layer, an expression for the expansion loss behind dunes was formulated and used to relate form resistance directly to dune height.