Numerical modelling of river processes: flow and river bed deformation

The morphology of alluvial river channels is a consequence of complex interaction among a number of constituent physical processes, such as flow, sediment transport and river bed deformation. This is, an alluvial river channel is formed from its own sediment. From time to time, alluvial river channels are subject to disturbances in their immediate environment caused by natural or artificial effects, namely variable inflow, sediment supply, and various human activities such as channel regulation or reservoir construction. Flows are primary driving forces governing the behaviour of alluvial river morphology. An increase in flow magnitude may initiate bed surface movements and bank erosion, once the force exerted by the flood event has passed some threshold for movement or erosion. The timing and frequency of flood may also have profound effects on a population; a flood can cause catastrophic damage to civil infrastructure located on or nearby the river. The wish to improve the safety situation and to foresee the impact of the ever growing human interference with the environment, has created a need for reliable predictions of complex situations found in nature. The socio-economical and political importance of alluvial systems has also increased this need. In early time, research methodologies of river processes were primarily based on field observation and laboratory scale modelling. Laboratory scale models and field measurements have been and are still essential for the understanding of complex river processes, and are used as design and verification tools, despite their high cost of construction, maintenance and operation. An alternative that has been growing in popularity and acceptance is river modelling. River modelling is the analysis and simulation of flow conditions based on the formulation and solution of mathematical relationships expressing hydraulic principles. In this thesis, we focused our efforts on two main activities associated with the application of river modelling to solve particular river hydraulics problems: (i) In Chapters 2 and 3, we perform numerical simulations based on the solution of the shallow water equations to predict flow resistance and eddy viscosity for vegetated floodplains, and we present a numerical reconstruction of the catastrophic flooding of Santa Fe City, Argentina. (ii) In Chapters 4 and 5, the derivation, design, and implementation of a discontinuous Galerkin method for the solution of the shallow water, sediment transport, and bed evolution equations is presented. Our numerical scheme shows ability to handle advection dominated flows, including problems with hydraulic and sediment jumps or bores. Additionally, its inherent mass and momentum conservation properties make it suitable for coupling flow and sediment transport. We have developed a mathematical-numerical tool that enables us to reproduce, and eventually, to predict morphological changes produced in alluvial systems, in response to highly varying flow regimes.