Sediment Inertia as Cause of River Antidunes

The formation of antidunes on riverbeds is explained in terms of sediment inertial effects. Due to inertia, bed sediment in transport cannot respond immediately to flow changes. To quantify the effect, a simple equation for sediment momentum balance is derived. A stability analysis indicates that riverbeds are unstable for a specific range of Froude numbers and that the instability leads exclusively to antidune formation. The instability, which is scaled by a dimensionless number representing the ratio of sediment inertia to friction, is a result of a spatial lag of bed load behind bed stress. An analytical relation for spatial lag is obtained, and the lag is estimated for some experimental data. The limits of antidune formation are compared with data.