Moment Model of Nonuniform Channel‐Bend Flow. II: Erodible Beds

The hybrid integral‐differential moment and momentum model of fixed‐boundary channel‐bend flows developed in the companion paper is extended to erodible‐bed flows. The $\theta$ unit sediment discharge is formulated as a power of local depth‐averaged $\theta$ velocity; and the $r$ unit sediment discharge as proportional to the ratio of the excess of the $r$ bed shear stress, over the radial component of the submerged weight of the sediment bed layer, to the $\theta$ bed shear stress. Bed topography is computed from two‐dimensional (2D) sediment continuity. The resulting two coupled sets of simultaneous equations are solved numerically. The model yields accurate predictions of the velocities (primary and secondary), and 2D bed topography. The average radial bed slope, primary velocity‐profile exponent, and secondary rotational and translational velocities exhibit much larger variations along the channel than in fixed‐boundary bends. The increased variation and oscillatory behavior of these quantities are elucidated from moment‐of‐momentum conservation and interaction of bed topography and flow.