Spatially averaged open-channel flow over rough bed

In this paper it is suggested that the double-averaged (in temporal and in spatial domains) momentum equations should be used as a natural basis for t he hydraulics of rough-bed open-channel flows, especially with small relati ve submergence. The relationships for the vertical distribution of the tota l stress for the simplest case of 2D, steady, uniform. spatially averaged f low over a rough bed with flat free surface are derived. These relationship s explicitly include the form-induced stresses and form drag as components of the total stress. Using this approach, we define three types of rough-be d flows: (1) Flow with high relative submergence; (2) how with small relati ve submergence; and (3) flow over a partially inundated rough bed. The rela tionships for the double-averaged velocity distribution and hydraulic resis tance for all three flow types are derived and compared with measurements w here possible. The double-averaged turbulent and form-induced intensities a nd stresses for the case of regular spherical-segment-type roughness show t he dominant role of the double-averaged turbulence stresses and form drag i n momentum transfer in the near-bed region.