Synthetic events for flood risk calculation by using a nested Copula structure

Risk analysis requires considering the entire frequency domain of flood consequences. Synthetic events were generated for the entire river system of the Scheldt estuary. This estuary contains multiple navigable waterways and is situated in Belgium and the Netherlands. Extreme water levels are influenced by rainfall-runoff discharges, tiding, storm surges, and wind speed and direction. For the generation of hydraulic boundary conditions for flood risk assessment, these influences and their mutual dependencies and correlations are taken into account by means of a nested extreme value copula structure. The variation in time is taken into account by standardized profiles, computed by normalizing all recorded extreme events and fitting a probability distribution to the variation of the standardized events, yielding 5 profile classes through another stratification. Eventually this resulted in a total of 1920 sets of synthetic events. All events were run through the hydrodynamic model of the river system. The frequency distribution of the resulting water levels are calculated by accumulation of the corresponding probabilities of occurrence of the synthetic events at each location. The methodology has the advantage that it determines a statistical distribution of consequences, rather than assigning frequencies to hydrodynamic boundary conditions

Validation of a non-linear reduced hydrodynamic model for curved open-channel flow

River morphodynamics and sediment transportRiver morphology and morphodynamic

Large-eddy simulation of a mildly curved open-channel flow

After validation with experimental data, large-eddy simulation (LES) is used to study in detail the open-channel flow through a curved flume. Based on the LES results, the present paper addresses four issues. Firstly, features of the complex bicellular pattern of the secondary flow, occurring in curved open-channel flows, and its origin are investigated. Secondly, the turbulence characteristics of the flow are studied in detail, incorporating the anisotropy of the turbulence stresses, as well as the distribution of the kinetic energy and the turbulent kinetic energy. Moreover, the implications of the pattern of the production of turbulent kinetic energy is discussed within this context. Thirdly, the distribution of the wall shear stresses at the bottom and sidewalls is computed. Fourthly, the effects of changes in the subgrid-scale model and the boundary conditions are investigated. It turns out that the counter-rotating secondary flow cell near the outer bank is a result of the complex interaction between the spatial distribution of turbulence stresses and centrifugal effects. Moreover, it is found that this outer bank cell forms a region of a local increase of turbulent kinetic energy and of its production. Furthermore, it is shown that the bed shear stresses are amplified in the bend. The distribution of the wall shear stresses is deformed throughout the bend due to curvature. Finally, it is shown that changes in the subgrid-scale model, as well as changes in the boundary conditions, have no strong effect on the result

Scalar dispersion in strongly curved open-channel flows

River hydrodynamicsTurbulent open channel flow and transport phenomen

Processes governing the flow redistribution in sharp river bends

Insight is provided in hydrodynamic processes governing the velocity redistribution in sharp river bends based on simulations of three recent experiments by means of Blanckaert and de Vriend's (2003, 2010) reduced-order nonlinear model without curvature restrictions. This model successfully simulated the flow redistribution and the secondary flow in all three experiments. The results indicate that the flow redistribution is primarily governed by topographic steering, curvature variations and secondary flow, in a broad range of different configurations, including mildly to sharply curved bends, narrow to shallow bends, smooth to rough bends, bends with additional complexities such as horizontal recirculation zones or patches of riverbed vegetation. The relative importance of these three dominant processes is case dependent, and controlled by the parameters Cf −1H/B, R/B and streamwise curvature variations. The first parameter characterizes a river reach, whereas the second and third parameters are characteristics of individual bends. Major differences exist between the hydrodynamic processes in mildly and sharply curved bends. First, velocity redistribution induced by curvature variations is negligible in mildly curved bends, but the dominant process in sharp bends. This result is relevant, because most meander models are based on the assumption of weak-curvature variations. Second, nonlinear hydrodynamic interactions play a dominant role in sharp bends, where mild-curvature models overpredict the secondary flow and in some cases even falsely identify it as the dominant process governing the velocity redistribution, which leads to unsatisfactory flow predictions. The reduction in secondary flow strength provoked by the nonlinear hydrodynamic interactions is accompanied by a reduction in the transverse bed slope, which reduces the effect of topographic steerin

Quasi-3D modelling of bed shear stresses at high curvature

Single thread meandering rivers exhibit complex planformpatterns in their floodplains, resulting from a complex interaction between flow, bed and bank morphology. The flow through meander bends may be characterized by primary flow in streamwise direction and secondary flow in transverse direction. The secondary flow plays an important role in the redistribution of streamwise momentum and also affects the bed shear stress, which is important for the shaping of the bed topography. Presently, most depth-averaged morphodynamic models adopt a secondary flow parameterization, based on mild curvature assumptions. This yields a linear relation between curvature and secondary flow strength. However, in strongly curved river bends, the secondary flow strength weakens considerably, due to the non-linear interaction of the streamwise and transverse velocity profiles. This interaction does not only affect the redistribution of streamwise momentum, but it is also important for the direction and magnitude of the bed shear stresses. A non-linear quasi-3D hydrodynamic model (i.e. depth averaged plus 3D parameterizations) is presented and used to simulate two sharply curved flume experiments over a horizontal and fully developed bed. The hydrodynamics results are compared to measurements, a three-dimensional hydrodynamic model, a three-dimensional hydrodynamic model with few layers, a linear hydrodynamic model based on mild curvature assumptions, and a depth-averaged model without secondary flow. The non-linear quasi-3D model results show a qualitatively good agreement with measurements and the three dimensional model. The linear quasi-3D model overestimates the angle between the bed shear stress and the depth averaged velocity direction through the bend. Furthermore the linear model fails to capture the increase of bed shear stress magnitude correctly. The depth-averaged model without secondary flow shows no increase of bed shear stress magnitude and no angle between the bed shear stress and the depth averaged velocity direction. Over the horizontal bed the 3D model with a small number of vertical layers underestimates the bed shear stress angle as well as the increase of bed shear stress magnitude. Over the fully developed bed the 3D model with a small number of vertical layers shows an underestimation of the increase of bed shear stress, but shows good agreement for the bed shear stress angle

Validation of a non-linear reduced hydrodynamic model for curved open-channel flow

The flow through meander bends is inherently three dimensional and may be characterized by primary flow in streamwise direction and secondary flow in transverse direction. Although, three dimensional simulations of meander bends are feasible for laboratory scale experiments, temporal and spatial scales of naturally occurring meandering rivers are much larger than those found in laboratory experiments. Therefore, computationally less expensive (reduced) flow models are necessary. Reduced hydrodynamic models are depth-integrated models and therefore require a closure model to resolve the effect of secondary flow. At present, most reduced flow models are linear as they neglect the feedback between the primary and secondary flow, which limits their validity to mild curvature. A non-linear reduced flow model, including this feedback, is compared to experimental data from the laboratory and the field which are both sharply and moderately curved. The model predictions compare well to the global flow structure in the high curvature Kinoshita flume and the moderate curvature Tollense River bend (with extra complicating factors of vegetation and horizontal recirculation zones). A linear model is also used to model the selected cases, showing good agreement for moderate curvature but not for sharp curvature. An analysis of the driving mechanisms reveals the reason for the difference in the model predictions