A gravel-sand bifurcation: a simple model and the stability of the equilibrium states

Ralph M.J. Schielen, Astrid Blom

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Abstract

A river bifurcation, can be found in, for instance, a river delta, in braided or anabranching reaches, and in manmade side channels in restored river reaches. Depending on the partitioning of water and sediment over the bifurcating branches, the bifurcation develops toward (a) a stable state with two downstream branches or (b) a state in which the water discharge in one of the branches continues to increase at the expense of the other branch (Wang et al., 1995). This may lead to excessive deposition in the latter branch that eventually silts up. For navigation, flood safety, and river restoration purposes, it is important to assess and develop tools to predict such long-term behavior of the bifurcation. A first and highly schematized one-dimensional model describing (the development towards) the equilibrium states of two bifurcating branches was developed by Wang et al (1995). The use of a one-dimensional model implies the need for a nodal point relation that describes the partitioning of sediment over the bifurcating branches. Wang et al (1995) introduce a nodal point relation as a function of the partitioning of the water discharge. They simplify their nodal point relation to the following form: s*=q*k , where s* denotes the ratio of the sediment discharges per unit width in the bifurcating branches, q* denotes the ratio of the water discharges per unit width in the bifurcating branches, and k is a constant. The Wang et al. (1995) model is limited to conditions with unisize sediment and application of the Engelund & Hansen (1967) sediment transport relation. They assume the same constant base level for the two bifurcating branches, and constant water and sediment discharges in the upstream channel. A mathematical stability analysis is conducted to predict the stability of the equilibrium states. Depending on the exponent k they find a stable equilibrium state with two downstream branches or a stable state with one branch only (i.e. the other branch has silted up). Here we extend the Wang et al. (1995) model to conditions with gravel and sand and study the stability of the equilibrium states.
Original languageEnglish
Pages94-94
Number of pages1
Publication statusPublished - 2017
EventRCEM2017 Back to Italy: 10th Symposium on river coastal and estuarine morphodynamics - Trento-Padova, Italy
Duration: 15 Sep 201722 Sep 2017

Conference

ConferenceRCEM2017 Back to Italy
CountryItaly
CityTrento-Padova
Period15/09/1722/09/17

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