Schematic of the effect of a perturbation in bed elevation in a mixed sediment case (Source: Figure 1, Chavarrias et al. 2018).
Our aim is to provide modelers of river morphodynamics with the mathematical tools to detect the occurrence of ill-posedness in their results and understand how the observed unrealistic model behavior changes. Ill-posedness not only produces physically unrealistic results but may also cause the failure of numerical simulations. By considering a two-fraction sediment mixture instead of the typical one-size distribution that is used (see right Figure), we obtain analytical expressions for the mathematical characterization of the model.
Findings and implications to practice
The numerical solution of an ill-posed problem may be reliable if perturbations do not have space and/or time to grow or if the consequences of the perturbations are negligible compared to the accuracy of the problem data. However, the reliability of the solution becomes subjective. This implies that it is up to the modeler to decide whether a solution is representative of the physical phenomenon under consideration. The set of equations that we propose help to better represent the physical process to get a unique solution without perturbations.
As an example, the right figure shows the model results for the longitudinal profile of a river bed. The river bed of the ill-posed simulation coarsens unrealistically whereas the well-posed solution remains unaltered (Source: Figure 6, Chavarrias et al. 2019).
Publication open access
Chavarrias Borras, V., Stecca, G., & Blom, A. (2018). Ill-posedness in modeling mixed sediment river morphodynamics. Advances in Water Resources, 114, 219-235. DOI: https://doi.org/10.1016/j.advwatres.2018.02.011
Related journal publications
- Blom, A., Chavarrias Borras, V., Ferguson, R. I., & Viparelli, E. (2017). Advance, retreat, and halt of abrupt gravel-sand transitions in alluvial rivers. Geophysical Research Letters, 44, https://doi.org/10.1002/2017GL074231.
- Blom, A., Viparelli, E. and Chavarrias Borras, V. (2016), The graded alluvial river: Profile concavity and downstream fining, Geophys. Res. Lett., 43, doi:https://doi.org/10.1002/2016GL068898.
- Orrú, C., Blom, A., Chavarrias Borras, V., Ferrara, V. and Stecca, G. (2016), A new technique for measuring the bed surface texture during flow and application to a degradational sandgravel laboratory experiment, Water Resour. Res., 52, doi:https://doi.org/10.1002/2016WR018938.
- Orrú, C., Chavarrias Borras, V., Uijttewaal, W.S.J., and Blom, A. (2014) Image analysis for measuring the size stratification in sand–gravel laboratory experiments, Earth Surf. Dynam., 2, 217-232, doi:https://www.earth-surf-dynam.net/2/217/2014/esurf-2-217-2014.pdf.
Last modified: 03/06/2019