A numerical model to predict the formation processes of dunes and antidunes in open channel flows was developed. Flows and bed shear stresses over dunes were evaluated by a depth averaged model considering the effect of vertical acceleration, so-called Boussinesq type equation. Irrotational condition of vertical velocity distributions far from a dune bed and the acceleration/de-acceleration effect near a bed were considered in the depth averaged model to evaluate the bed shear stresses correctly. It was shown that the initiation and development processes of dunes can be simulated incorporating a non-equilibrium sediment transport model proposed by Nakagawa & Tsujimoto in the water surface profile analysis with a Boussinesq type equation. Calculated results on the temporal development processes and shape characteristics of dunes were compared with previous theoretical and experimental studies. It was indicated that the calculated wave length caused by initial instability is coincident with the resonant relation of open channel flows over a wavy bed, and the wave length and height of dunes in the equilibrium state are dependent on the step length, though further investigations are needed to clarify the increase of flow resistance during the development processes of dunes.
展开▼
