Modelling Sediment Transport and Morphodynamics of Gravel‐Bed Rivers

Abstract

Mathematical models of morphodynamics compute bed level changes and changes in bed sediment composition as a result of open channel hydraulics and sediment transport. They have found widespread application in river engineering and fluvial geomorphology. This chapter reviews some aspects of the present state of knowledge regarding morphodynamic models of gravel-bed rivers: non-uniform sediment (Section 9.2), analytical solutions (Section 9.3), bank erosion and accretion (Section 9.4), vegetation dynamics (Section 9.5), and validation (Section 9.6). For these aspects, the chapter also identifies trends and challenges ahead. The concluding section (Section 9.7) presents the challenges in the framework of Syvitski et al., (2009), who identify upscaling, process coupling, model coupling, data systems, high-performance computing, and model testing as the challenges for the morphodynamic modelling community in general. The first and most obvious trend is the continuing development of knowledge and computer technology, leading to models of greater detail that, at the same time, can be run feasibly for longer river reaches and longer periods of time. The dimensionality of models increases, from 1-D to 2-D depth-averaged for reach-scale models and from 2-D width-averaged or depth-averaged to 3-D for models on a local scale. Morphodynamic models mostly compute the flow using a Reynolds-averaged momentum equation, but excursions into large-eddy simulation have been made. Direct numerical simulation has come within reach for the motion of sediment, but customary models remain based on empirical transport relations and a volumetric sediment balance or Exner equation. Sediment non-uniformity is an essential feature of gravel-bed rivers. Section 9.2 reviews the classical approach to modelling non-uniform sediment, and indicates areas for improvement. Deeper insights into improvements have been obtained from analytical solutions that are reviewed in Section 9.3. A second trend for gravel-bed rivers lies in the area of application. One’s first image of a gravel-bed river might be a braided river with gravel bars, in a natural environment and preferably wadeable to carry out field work for research. However, the focus of research and modelling moves increasingly to larger gravel-bed rivers in more populated and urban areas, where every inch is optimized to meet demands for safety against flooding, navigation, hydropower, aggregate mining, water supply, and the like, often at the cost of ecological values. The management of these rivers is almost industrial, putting high demands on accuracy in design, implementation, and monitoring. The bed of the river Rhine, for instance, is routinely corrected by gravel nourishment (Figure 9.1) and is inspected by using a diving bell several metres under water, which can be conveniently reached by descending a staircase (Figure 9.2). Similar high demands are put on projects to counter the adverse effects on ecology in these rivers, even though river restoration is often limited here to cosmetic embellishment, gardening or, as Parker (2004) puts it, “disneylandification”, rather than truly letting nature take its course. The high demands on accurately predicting the morphological effects of interventions also imply high demands on model reliability and, hence, model validation. Section 9.6 advocates setting international standards for model validation in fluvial morphodynamics. A third trend is that morphodynamic models are becoming a standard element in decision-making for river projects where many stakeholders are involved. This makes the communication of model results a major issue, as most stakeholders will not have a background in fluvial morphodynamics. Moreover, stakeholders will