Analysis of Bedform Instability with 1-D Two-phase Morphodynamical Models

The paper explores the possibility of predicting the occurrence of antidunes in gradually-varied flows through non-equilibrium morphological models natively derived, under the long-wave approximation, for fast geomorphic transients. Starting from a recent two-phase gradually-varied flow model, an improved version, which partially accounts for the bottom curvature effects, is proposed and analyzed. The normal mode analysis carried out on the linearized gradually-varied flow model shows the existence of unstable conditions at moderate Froude numbers characterized by bed perturbations migrating in the upstream direction. However, a proper wavelength selection may be obtained only when the bottom curvature is accounted for. Direct numerical simulations in linear regime of the improved model indicate the existence of unstable dominant wavelengths, which comply with experimental evidences. Full non-linear simulations confirm the ability of the improved two-phase model in predicting the antidunes formation.