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ABSTRACT
This paper introduces an 1D numerical code RubarBE for hydraulic and mobile-bed simulations. The code's ability to reproduce the downstream fining of a gravel–sand mixture in response to bed aggradation is tested against laboratory experiments. Unlike in most numerical models, grain size distribution in each sediment layer is not represented using a multi-class model, but using the median diameter and a sorting coefficient σ. The comparison of numerical results with experimental data shows that the adaptation length
, classically used for non-equilibrium sediment transport, is an essential parameter of the model to accurately reproduce the evolution of the deposit front. Empirical laws for adjustments of
and σ are proposed to reproduce sediment sorting through two grain-size related adaptation lengths (
,
). They are scaled by the length of the reach in morphological equilibrium, which is a useful result for field applications.
Acknowledgements
We would like to thank Prof. Nikora and Prof. Uchida, as well as the two other anonymous reviewers, for their significant input to improve the quality of this paper.
Notation
Latin and Greek variables
| Ab | = | cross-sectional area of the bed above a reference datum |
| B | = | width of the river |
| cf | = | volume concentration of fine sediments |
| CF | = | time-averaged front velocity |
| d50 | = | median diameter |
| dx | = | grain diameter at which x percent of the distribution in mass lies below |
| F | = | Froude number |
| h | = | water depth |
| Hd | = | height of the deposit at the injection point |
| HF | = | front height |
| Htail | = | height of the tailgate |
| L | = | length of the reach in morphological equilibrium |
| La | = | non-equilibrium adaptation length |
| Ld | = | adaptation length related to the median diameter evolution |
| Lσ | = | adaptation length related to the sorting coefficient evolution |
| M | = | sediment mass |
| qsb | = | volumetric bedload transport per unit width |
| Q0 | = | water discharge |
| Qs | = | volumetric sediment transport |
| Qs* | = | equilibrium sediment transport or sediment transport capacity |
| Qs0 | = | sediment input |
| t | = | time |
| Tf | = | final time of the runs |
| u* | = | shear velocity |
| U | = | depth-averaged velocity of the flow |
| rd | = | ratio between fine and coarse sediment diameters |
| Sb | = | slope of the bed |
| V | = | volume of the deposit |
| Ws | = | settling velocity |
| x | = | longitudinal direction |
| x0 | = | position of the sediment input |
| xF | = | position of the front |
| zw,tail | = | water level at the tailgate |
| αd | = | constant for Sternberg equation for d |
| ασ | = | constant for Sternberg equation for σ |
| αL | = | constant for adaptation length equations |
| δAL | = | active layer thickness |
| φ | = | porosity |
| ρs | = | sediment density |
| σ | = | sorting coefficient |
| θ | = | Shields parameter |
| θcr | = | critical Shields parameter for the inception of movement |
Subscripts and exponents
| dn | = | upstream cell |
| up | = | downstream cell |
| dep | = | deposit |
| ero | = | erosion |
| tra | = | transit |
| f | = | fine |
| c | = | coarse |
| adj | = | adjusted |
| F | = | front |