Analysis of bedform instability with 1-D two-phase morphodynamical models

•Bed-forms may appear on the bottom surface during fast geomorphic transients.•A two-phase gradually-varied flow model accounting for bottom curvature is proposed.•The prediction of antidune formation is investigated in the linear regime.•Unstable bed perturbations are found owing to the sediment dy...

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Bibliographic Details
Published in:Advances in water resources 2018-10, Vol.120, p.50-64
Main Authors: Greco, Massimo, Iervolino, Michele, Vacca, Andrea
Format: Article
Language:English
Subjects:
Antidunes
Approximation
Bedforms
Bottom curvature
Computer simulation
Curvature
Geomorphology
Gradually-varied flow
Instability
Linearization
Mathematical models
Numerical simulations
Sedimentary structures
Stability
Stability analysis
Two-phase model
Varied flow
Water flow
Water measurement
Water resources
Wavelength
Wavelengths
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Summary:•Bed-forms may appear on the bottom surface during fast geomorphic transients.•A two-phase gradually-varied flow model accounting for bottom curvature is proposed.•The prediction of antidune formation is investigated in the linear regime.•Unstable bed perturbations are found owing to the sediment dynamics description.•The bottom curvature correction is mandatory for proper antidune length selection. 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.
ISSN:0309-1708
1872-9657
DOI:10.1016/j.advwatres.2017.07.002