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 the hydraulics of rough-bed open-channel flows, especially with small relative submergence. The relationships for the vertical distribution of the total stress for the simplest case of 2D, steady, uniform, spatially averaged flow over a rough bed with flat free surface are derived. These relationships explicitly include the form-induced stresses and form drag as components of the total stress. Using this approach, we define three types of rough-bed flows: (1) Flow with high relative submergence; (2) flow with small relative submergence; and (3) flow over a partially inundated rough bed. The relationships for the double-averaged velocity distribution and hydraulic resistance for all three flow types are derived and compared with measurements where possible. The double-averaged turbulent and form-induced intensities and stresses for the case of regular spherical-segment-type roughness show the dominant role of the double-averaged turbulence stresses and form drag in momentum transfer in the near-bed region.

[1] We introduce a new conceptual model for longitudinal and transverse diffusion of moving bed particles under weak bed load transport. For both rolling/sliding and saltating modes the model suggests that the particle motion is diffusive and comprises at least three ranges of temporal and spatial scales with different diffusion regimes: (1) the local range (ballistic diffusion), (2) the intermediate range (normal or anomalous diffusion), and (3) the global range (subdiffusion). The local range corresponds to ballistic particle trajectories between two successive collisions with the static bed particles. The intermediate range corresponds to particle trajectories between two successive periods of rest. These trajectories consist of many local trajectories and may include tens or hundreds of collisions with the bed. The global range of scales corresponds to particle trajectories consisting of many intermediate trajectories, just as intermediate trajectories consist of many local trajectories. Our data from the Balmoral Canal (the intermediate range) and Drake et al. 's [1988] data from the Duck Creek (the global range) provide strong support for this conceptual model and identify anomalous diffusion regimes for the intermediate range (superdiffusion) and the global range (subdiffusion).

No abstract