Print Email Facebook Twitter Ill posedness in modelling two-dimensional morphodynamic problems Title Ill posedness in modelling two-dimensional morphodynamic problems: Effects of bed slope and secondary flow Author Chavarrias Borras, V. (TU Delft Rivers, Ports, Waterways and Dredging Engineering) Schielen, R.M.J. (University of Twente; Rijkswaterstaat) Ottevanger, Willem (Deltares) Blom, A. (TU Delft Rivers, Ports, Waterways and Dredging Engineering) Date 2019 Abstract A two-dimensional model describing river morphodynamic processes under mixed-size sediment conditions is analysed with respect to its well posedness. Well posedness guarantees the existence of a unique solution continuously depending on the problem data. When a model becomes ill posed, infinitesimal perturbations to a solution grow infinitely fast. Apart from the fact that this behaviour cannot represent a physical process, numerical simulations of an ill-posed model continue to change as the grid is refined. For this reason, ill-posed models cannot be used as predictive tools. One source of ill posedness is due to the simplified description of the processes related to vertical mixing of sediment. The current analysis reveals the existence of two additional mechanisms that lead to model ill posedness: secondary flow due to the flow curvature and the effect of gravity on the sediment transport direction. When parametrising secondary flow, accounting for diffusion in the transport of secondary flow intensity is a requirement for obtaining a well-posed model. When considering the theoretical amount of diffusion, the model predicts instability of perturbations that are incompatible with the shallow water assumption. The effect of gravity on the sediment transport direction is a necessary mechanism to yield a well-posed model, but not all closure relations to account for this mechanism are valid under mixed-size sediment conditions. Numerical simulations of idealised situations confirm the results of the stability analysis and highlight the consequences of ill posedness. Subject nonlinear instabilityriver dynamicssediment transport To reference this document use: http://resolver.tudelft.nl/uuid:59f3342f-f53b-4e27-95d9-9851da65e6c9 DOI https://doi.org/10.1017/jfm.2019.166 Embargo date 2019-10-11 ISSN 0022-1120 Source Journal of Fluid Mechanics, 868, 461-500 Bibliographical note Accepted Author Manuscript Part of collection Institutional Repository Document type journal article Rights © 2019 V. Chavarrias Borras, R.M.J. Schielen, Willem Ottevanger, A. Blom Files PDF Chavarrias19_2.pdf 10.34 MB Close viewer /islandora/object/uuid:59f3342f-f53b-4e27-95d9-9851da65e6c9/datastream/OBJ/view