Abstract
In this paper we analyze the Hirano active layer model used in mixed sediment river morphodynamics concerning its ill-posedness. Ill-posedness causes the solution to be unstable to short-wave perturbations. This implies that the solution presents spurious oscillations, the amplitude of which depends on the domain discretization. Ill-posedness not only produces physically unrealistic results but may also cause failure of numerical simulations. By considering a two-fraction sediment mixture we obtain analytical expressions for the mathematical characterization of the model. Using these we show that the ill-posed domain is larger than what was found in previous analyses, not only comprising cases of bed degradation into a substrate finer than the active layer but also in aggradational cases. Furthermore, by analyzing a three-fraction model we observe ill-posedness under conditions of bed degradation into a coarse substrate. We observe that oscillations in the numerical solution of ill-posed simulations grow until the model becomes well-posed, as the spurious mixing of the active layer sediment and substrate sediment acts as a regularization mechanism. Finally we conduct an eigenstructure analysis of a simplified vertically continuous model for mixed sediment for which we show that ill-posedness occurs in a wider range of conditions than the active layer model.
Highlights
The mixed character of the sediment is a property necessary to explain physical phenomena such as downstream fining (Sternberg, 1875; Blom et al, 2016), the gravel sand transition zone (Yatsu, 1955; Blom et al, 2017), the formation of bedload sheets (Seminara et al, 1996), or bed surface armoring (Parker and Klingeman, 1982). Hirano (1971) was the first to develop a mass conservation model for mixed-size sediment
We have assessed the well-posedness of the equations used to model mixed sediment river morphodynamics
In particular we have studied the system formed by the flow equations (SaintVenant, 1871) together with the active layer model (Hirano, 1971) and a simplified vertically continuous model (Viparelli et al, 2017)
Summary
The mixed character of the sediment is a property necessary to explain physical phenomena such as downstream fining (Sternberg, 1875; Blom et al, 2016), the gravel sand transition zone (Yatsu, 1955; Blom et al, 2017), the formation of bedload sheets (Seminara et al, 1996), or bed surface armoring (Parker and Klingeman, 1982). Hirano (1971) was the first to develop a mass conservation model for mixed-size sediment. Sieben (1994) identified a region of parameters where, for a sediment mixture consisting of two grain size classes under bed degradation into a substrate finer than the active layer, the model is unconditionally ill-posed This occurs when the “sorting celerity” equals the “bed celerity”. The opposite happens for coarse sediment fractions, which experience a larger exposure to the flow than in a unisize case In their analysis Stecca et al (2014) showed that the model can become illposed under degradational conditions if and only if the substrate is finer than a reference grain size distribution which is related to the grain size distribution of the bedload, instead of the active layer (as in Ribberink’s (1987) analysis).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
