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This thesis concerns the investigation of the meandering phenomena, focusing on the hydrodynamic (Part I) and on the morphodynamic (Part II) of meandering rivers. In the first part of this work, sharp curved single-bend open channel flow with a flat bed, representative of the early phase of bed erosion, is investigated by the use of Large Eddy Simulation (LES). The three-dimensional (3D) numerical simulation can provide flow field information that are difficult to obtain in the laboratory or in a real river. The focus is to provide insight into the physics of sharp meandering bends, highlighting the main flow and secondary flow characteristics and the role of turbulence. The latter plays an important role in many processes that are key in natural rivers, such as the phenomena of spreading and mixing of suspended matter, of sediment transport and scour processes. Turbulence affects the strength of the curvature-induced secondary flow in the core of the flow domain, a typical feature of curved open-channel flow. It rules the intensity of the bed shear stresses and the friction losses along the bend. It is especially important in the flow regions near the banks, affecting the stability of the channel banks. At the inner bank, the model predicts, rather accurately, the boundary layer detachment and the formation of an internal shear layer. Furthermore, the model adequately reproduces the outer-bank cell of secondary flow and the local increase of turbulent kinetic energy. In this work, two curved channels are investigated with the intent to underline the influence of the water depth on the flow features. Finally, the effects of the super-elevation of the free surface on the meandering hydrodynamics are analyzed using a Detached Eddy Simulation (DES) model available in the free software OpenFOAM. In the second part of this work, a mathematical model for meandering rivers with spatial width variations is developed. The mathematical modeling of the long-term evolution of meandering rivers needs an efficient computation of the flow field. Therefore, the development of a mathematical model based on the complete response of a meandering river to spatially varying channel axis curvature and width is necessary. For this purpose, we elaborate a morphodynamic model able to predict the spatial distribution of the flow field and the equilibrium bed configuration of an alluvial river characterized by arbitrary distributions of both the channel axis curvature and the channel width. Owing to analytical character of the model, it provides a computationally efficient tool that can be easily incorporated in long-term river planform evolution models. Furthermore, it can be used to rapidly evaluate the morphological tendencies of an alluvial river in response to variations in planform geometry or hydrodynamic forcing. The model is tested by comparison with the bed topography observed in a typical reach of the Po River, showing that in presence of wide, mildly curved and long bend and weak width variations, the river topography is described with a good accuracy.

This paper investigates the spatial evolution of a disturbance in an open-channel flow of a power-law fluid at non-uniform accelerated and decelerated initial profiles, up to the occurrence of roll-waves in mild and steep slope channels. Both theoretical and numerical analyses are applied to the depth-averaged continuity and momentum conservation equations, deduced from the von Kármán's integral method. For the theoretical investigation, the nonlinear near-front expansion technique was applied. Then, the full nonlinear problem in its conservative formulation was numerically solved. Independently of the rheology of the flowing medium, non-uniform initial conditions strongly influence the perturbation celerity, the disturbance evolution and the roll-wave development. For mild slope channels, an initially decelerated profile of shear-thinning fluids has a stabilizing effect, while the opposite is found for accelerated profiles. For shear-thickening fluids, only the stabilizing effect caused by a decelerated profile is observed. In steep slope channels, independently of the fluid rheology, decelerated initial conditions promote roll-wave occurrence, while accelerated conditions inhibit the perturbation growth. Although experimental verifications are needed, the present results have to be properly accounted for in defining roll-wave prediction methods and in assigning appropriate boundary conditions to enhance or to reduce their formation.

The present work investigates the effect of the flow profile induced by an inlet condition on the roll-wave evolution in turbulent clear-water flows. The study employs theoretical and numerical analyses. Firstly, the influence of the inlet condition on the spatial evolution of a single perturbation in a hypercritical flow is examined through the expansion near a wavefront analysis. The results show that an accelerated unperturbed profile reduces the disturbance spatial growth. A decelerated profile causes an increase. The effect of the flow profile on the spatial evolution of roll-wave trains is then numerically investigated solving the Saint Venant equations with a second-order Runge-Kutta Total Variation Diminishing (TVD) Finite Volume scheme. The numerical simulations comply with the analytical results for the initial and transition phases of the roll-wave development. The unperturbed profile influences even the roll-waves statistical characteristics in the final stage, with a more evident effect in case of accelerated profiles. The influence of the flow profile should be therefore accounted for in the formulation of predictive criteria for roll-waves appearance based on the estimation of the disturbance spatial growth rate.