Numerical modelling of sediment transport, bed morphology and porous obstructions in shallow channels

Abstract

Many environmental free surface flows involve water and sediment transport. The net changes to the surface level of an erodible bed by sediment entrainment and deposition processes have a feedback effect on the local ow hydrodynamics. Bed morphological change is of great socio-economic and environmental importance in that it affects navigation, flood risk management, water quality, species diversity, and overall river sustainability. This thesis describes a mathematical model of the depth-averaged shallow water-sediment equations based on mass and momentum conservation laws. A 2D numerical model is then presented of the fully coupled, variable-density governing equations, which are solved using a Godunov-type HLLC scheme. Dependent variables are specially selected in the numerical model to handle the presence of the variable-density mixture in the mathematical formulation. The model includes suspended sediment, bedload transport, and bed morphological change. The numerical model is verified against benchmark analytical and semi-analytical solutions for complicated, clear water flows, bedload transport and suspended sediment transport. The well-balanced property of the governing equations is verified for a variable-density dam break flow over a bed step. Simulations of an idealised dam-break flow over an erodible bed, in excellent agreement with previously published results, validate the ability of the model to capture complex water-sediment interactions under rapidly-varying flow conditions and a mobile bed, and validate the eigenstructure of the system of variable-density governing equations. The model is then further validated against laboratory based data for complex 2D partial dam breaks over fixed and mobile beds, respectively. The simulations of 2D dam break flows over mobile beds highlight the sensitivity of the results to the choice of closure relationships for sediment transport. To investigate this further, a parameter study is carried out using a variety of commonly used empirical formulae for suspended sediment transport. The numerical model is also used to inform a theoretical model that predicts the flow through and around a porous obstruction in a shallow channel. This problem is relevant to several practical applications, including flow through aquatic vegetation and the performance of arrays of tidal turbines in a finite-width tidal channel. The theoretical model is used to reinterpret the core flow velocities in laboratory-based data for an array of emergent cylinders in a shallow channel. Comparison with experimental data indicates the maximum obstacle resistance for which the theoretical model is valid. In a final application, the theoretical model examines the optimum arrangement of tidal turbines to generate power in a tidal channel, confirming that natural bed resistance increases the power extraction potential for a partial tidal fence.