A two-dimensional model describing river morphodynamic processes under mixed-size sediment conditions is analyzed with respect to its well-posedness. The figure below shows the results of a numerical simulation of idealized cases. For the left, the model gives a unique solution (well-posed) independent of the grid size whereas for the right the solution is not unique (ill-posed) and does not yield physically realistic results. The results present an oscillatory characteristic that changes with the grid size. One known source of ill-posedness is is the simplification of processes related to vertical mixing of sediment. We reveal the existence of two additional mechanisms under which the 2D system of equations does not provide a unique solution.
Findings and implications to practice
By analyzing the system of equations for 2D modeling of mix-sized sediment, we found that the parametrization accounting for secondary flow does not give a unique solution when the diffusion of sediment is not accounted for. In addition, the effect of the bed slope on the direction of the sediment transport is a necessary mechanism for the model is well posed. Yet, a different modeling strategy accounting for the conservation of the sediment in transport and an erosion–deposition formulation may yield a well-posed model without accounting for the effect of the bed slope.
Publication open access
Chavarrías, V., Schielen, R., Ottevanger, W., Blom, A., 2019. Ill posedness in modelling two-dimensional morphodynamic problems: effects of bed slope and secondary flow. J. Fluid Mech. 868, 461–500. https://doi.org/10.1017/jfm.2019.166
Ill-posedness in modeling mixed sediment river morphodynamics
Last modified: 03/06/2019