Development of robust, physically-based numerical models for transport processes and geomorphodynamics changes

Bed changes in rivers may occur under several morphodynamics and hydrodynamics conditions. The modeling of this type of phenomena can be performed coupling the Shallow Water Equations (SWE) for the hydrodynamic part and the Exner equation for the morphodynamic part. The Exner equation states that the time variation of the sediment layer is due to the sediment transport discharge through the boundaries of the volume. Considering that sediment transport discharge are computed by means of sediment capacity formulae based on 1D experimental steady flows, the assessment of these empirical relations under unsteady 1D and 2D situations must be studied. In order to ensure the reliability of the numerical experimentation, the numerical scheme must handle correctly the coupling between the 2D SWE and the Exner equation under any condition. If possible, it is convenient to express the formulation of different empirical laws under a general framework. In consequence, a finite-volume numerical scheme that includes these two main features has been chosen as a benchmark for comparing the 1D and 2D results obtained when using several well known sediment transport formulae: Meyer-Peter and M\"uller, Ashida and Michiue, Engelund and Fredsoe, Fernandez Luque and Van Beek, Parker, Smart, Nielsen, Wong and Camenen and Larson. In addition, a new interpretation of the Smart empirical law is presented in order to cope with bed load transport over irregular beds of changing slope. Detailed results for this new modified empirical law together with the ones obtained with Meyer-Peter and M\"uller (which is the sediment capacity formula more used in hydraulic engineering) are provided for every test case analyzed. Furthermore, the Root Mean Square Error (RMSE) associated to every formula at each experimental condition is calculated with the purpose of evaluating quantitatively the overall behavior of each one. The results point out that the new interpretation of the Smart formula reaches the most accurate results in all cases, but in a genuinely 2D flow, that is, a situation involving more than one flow direction, the differences among sediment transport formulae are not as noticeable as in the 1D studied situations. Once the forecasting capacity of each sediment transport formula has been studied, another concern is the computational cost. The coupling between the SWE and the Exner equation by means of an augmented Jacobian matrix involves a high number of algebraic operations for computing the eigenvalues and the eigenvectors. Therefore, the computational cost is increased significantly, limiting the applicability of the numerical scheme to realistic situations where large domains are involved. In order to improve the computational efficiency, the coupling technique is modified, not decreasing the number of waves involved in the Riemann Problem but simplifying their definitions. The approach proposed in this thesis is a new strategy to combine concepts from hyperbolic conservation laws and conservative finite volume schemes. With the aim to control numerical stability in the most efficient form possible, a numerical eigenvalue is defined to control the discrete Exner equation in the explicit scheme. This bed wave celerity helps mainly to ensure conservation and to control automatically the numerical stability of the explicit scheme. The effects of the numerical coupling strategy proposed in this thesis are tested against exact solutions and 1D and 2D experimental data. The results emerging from this analysis show that efficiency and accuracy can be obtained when choosing an adequate sediment transport law and the stability condition is augmented by including a new celerity associated to the bed changes. On the other hand, in environmental and civil engineering applications, geomorphological changes are not only present in rivers but also in steep areas where massive mobilizations of poorly sorted material can occur. This sliding material is usually composed by a mixture of sand and water. For simplifying the phenomenon, dry granular flows have been considered as a starting point for the understanding of the physics involved within the landslides. The hypothesis of Saint-Venant equations are considered valid for modeling these land movements. Taking advantage of this approach, in this thesis approximate augmented Riemann solvers are formulated providing appropriate numerical schemes for mathematical models of granular flow on irregular steep slopes. Fluxes and source terms are discretized to ensure steady state configurations including correct modeling of start/stop flow conditions, both in a global and a local system of coordinates. The weak solutions presented involve the effect of bed slope in pressure distribution and frictional effects by means of the adequate gravity acceleration components. The numerical solvers proposed are first tested against 1D cases with exact solution and then are compared with 2D experimental data in order to check the suitability of the mathematical models described in this thesis. Comparisons between results provided when using global and local system of coordinates are presented. Both the global and the local system of coordinates can be used to predict faithfully the overall behavior of the landslides. The performance of the numerical scheme has been studied using novel experimental situations. These laboratory works include bidimensional configurations, the inclusion of obstacles in the flow path and a variable slope in the domain. Hence, a further step in mimicking realistic situations is obtained, since the behavior of the granular flow is affected by the presence of natural elements such as boulders or trees. Three situations have been considered. The first experiment is based on a single obstacle, the second one is performed against multiple obstacles and the third one study the influence of a dike when an overtopping situation takes place. Due to the impact of the flow against the obstacles, fast moving shocks appear, and a variety of secondary waves emerge. Comparisons between computed and experimental data are presented for the three cases. The computed results show that the numerical tool previously developed is able to predict faithfully the overall behavior of this type of complex dense granular flow

EXPERIMENTAL RESULTS ON SEDIMENT ENTRAINMENT BY GRAVITY CURRENTS

Gravity currents are geophysical flows responsible of the distal transport of high volumes of sediments. In particular, turbidity currents, a form of gravity currents where sediments in suspension confer the buoyancy that ignites the flow, are the main mechanism for distal sediment transport within lakes and reservoirs. In maritime environment, submarine clay-rich gravity currents can impact and may endanger human made infrastructures such as submarine cables and platforms. It is thus important to understand the dynamics of sediment transport associated to gravity currents. In the present research, it is intended to experimentally investigate the mechanisms of entrainment, transport and deposition of fine sediments caused by the passage of a saline gravity current. Conservative saline currents, with varied initial density, are let to flow over an erodible bed sector where fine sediments, with three different grain sizes, are at rest. A detailed description of the gravity current dynamics is reported using 3D instantaneous velocities measurements over a certain profile. Video records obtained synoptically and laterally through a transparent wall, provide a visualization of the entrainment and resuspension processes which is further related to the flow hydrodynamics. The critical threshold conditions for initiating sediment motion is frequently related to the balance of boundary shear stress and the submerged weight of the particle. However boundary shear stress is just one of several impelling forces and the particle submerged weight is just one of several inertial forces. Here the attention is first focused on the complete description of the flow velocity, in term of instantaneous and mean flow. A deep analysis of the hydrodynamic of one gravity current reproduced in laboratory is here presented and its role in sediments’ entrainment discussed

LABORATORY EXPERIMENTS OF PULSED SUBAQEOUS SEDIMENT DENSITY FLOWS: INTERNAL STRATIFICATION AND LAYERING

This paper reports on an experimental study which focuses on reproducing small scale sediment density flows in a laboratory flume. The observations are aimed at improving the parametrization of the relations that govern the transition between different phases of the flows. Dense mixtures of plastic sediment of variable grain size (thermoplastic polyurethane) and water were fed into the water-filled flume by gravity from a supply tank. Different grain-size and slope combinations were examined and the resulting velocity fields were obtained using UVP (Ultrasonic Velocity Profile) at various points along the channel. The flow was imaged through the transparent sidewall to track the velocity of the flow head for each test case. Image analysis also allowed a qualitative characterization of the vertical density stratification and water entrainment during runout. The runout distance and flow thickness are used to highlight the differences in the dynamic behavior of the flow for each test case. Data gathered from the experiments will be exploited in the further development of predictive numerical models for slide-induced debris flows transitioning to turbidity currents

Transport of suspended sediments under the influence of bank macro-roughness

River restoration works often include measures to promote morphological diversity and enhance habitat suitability. One of these measures is the creation of macro-roughness elements, such as lateral cavities and embayments, in the banks of channelized rivers. However, in flows that are heavily charged with fine sediments in suspension, such as glacier-fed streams and very low-gradient reaches of large catchment rivers, these lateral cavities may trap these sediments. Consequently, the morphological changes may be affected, and the functionality of the restoration interventions may be compromised. Herein, we analyse the influence of these macro-roughness elements on the transport of fine sediments in the main channel. Laboratory tests with uniform flow charged with sediments in a channel with banks equipped with large-scale rectangular roughness elements were carried out. The laboratory experiments covered a wide range of rectangular cavity geometrical configurations and shallowness ratios. The influence of key parameters such as flow shallowness, geometric ratios of the cavities and initial sediment concentration was tested. Surface particle image velocimetry, sediment samples and temporal turbidity records were collected during the experiments. The amount of sediments captured by the cavities, the temporal evolution of the concentration of sediments in suspension and the flow hydrodynamics are cross-analysed and discussed. It is shown that the trapping efficiency of the macro-roughness elements is a clear function of the channel geometry and the shallowness of the flow

INFLUENCE OF LATERAL RECTANGULAR EMBAYMENTS ON THE TRANSPORT OF SUSPENDED SEDIMENTS IN A FLUME

Systematic experimental investigations have been performed under uniform flow conditions in a channel whose banks are equipped with large scale rectangular roughness elements. The practical motivation of this project is to see how restoration of banks, such as lateral cavities, has an influence on the transport of fine sediments. The implementation of lateral cavities may affect the sediment and morphological equilibrium of the river since these may trap sediments. This work aims to study the influence of the lateral cavities on the transport of fine sediments in the main channel. A set of laboratory experiments are done which covers a wide range of rectangular cavity configurations and includes aspect ratios (lateral cavity depth divided by cavity length) between 0.2 and 0.8. Key parameters such as the flow discharge and the initial sediment concentration are tested. Surface PIV, sediment samples and turbidity temporal records are collected during the experiments. The trapping efficiency of the cavities and the associated flow patterns are calculated and discussed. The resulting conclusions provide useful information for the future design of river restoration projects

Feinsedimentdynamik in revitalisierten Flüssen

Im Rahmen von Flussrevitalisierungen werden oftmals seitliche Aufweitungen geschaffen, in denen sich Feinsedimente ablagern können. Insbesondere in Flüssen, die von Schwall und Sunk betroffen sind, stellt sich die Frage, wie der Ablagerungsprozess von Feinsedimenten in solch lokalen Aufweitungen verläuft. Werden die Ablagerungen bei Hochwasser- oder Schwallabfluss wieder ausgewaschen oder verlanden die Aufweitungen? Die durchgeführten systematischen Experimente geben Hinweise, welche Geometrien der Aufweitungen die Sohlenstrukturen nachhaltig erhalten können

NUMERICAL SIMULATION OF SEDIMENT ENTRAINMENT BY LOCK-EXCHANGE GRAVITY CURRENTS

Gravity currents are flows driven by buoyancy differences between two contacting fluids caused by differences in temperature, salinity, or by the presence of suspended particles. Such flows can reach high velocities near the bed, especially on the area behind the front of the current. As a result, rapid morphological changes may take place in river and estuarine beds due to the passage of these flows. Essential to determine the erosion induced by the current, are the spatial and temporal distributions of the bed shear stress. However, these are troublesome to measure in laboratory or in the field. To bridge this difficulty, the eddy-solving numerical simulations may be used. This study presents here the three-dimensional numerical simulations of lock-exchange salinity currents flowing over a mobile bed. It is aimed at the characterization of the sediment entrainment capacity of the current. The large eddy simulation technique is employed for analyzing the evolution and the structure of the current. For the sediment simulation, an Euler-Euler methodology based on a single phase approach is used. The main features of the current are compared with experimental data obtained in the laboratory. Velocity fields and bed shear stress distributions for different initial current densities are analyzed and linked to entrainment scenarios. The influence of small variations in particle size of the mobile bed is also discussed

Numerical discretization and assessment of bed load discharge closure equations for transient flow over erodible bed in 1D and 2D situations. Discretización numérica y aplicabilidad de fórmulas de cierre en flujos transitorios sobre lecho erosionable en configuraciones 1D y 2D

Los flujos transitorios sobre lecho rígido son normalmente modelados usando un conjunto de ecuaciones que incluyen las de conservación de masa y cantidad de movimiento. Para el caso de lecho deformable, la física del problema necesita ser descrita de forma matemática a través de diferentes modelos. La primera parte de este trabajo se centra en clarificar las distintas hipótesis asumidas por dichos modelos matemáticos. Como consecuencia de este estudio se deriva la inclusión de una variable en la formulación del problema que incluye la variación de fondo. En la mayoría de los casos a la hora de modelar el flujo de agua sobre fondo erosionable se suele desacoplar la parte hidrodinámica de la parte morfodinámica. Las soluciones obtenidas con los modelos desacoplados han demostrado ser inadequados para la resolución de flujos transitorios con variaciones rápidas de régimen de flujo, puesto que se generan inestabilidades. En consecuencia, es necesario emplear una formulación acoplada capaz de manejar un rango amplio de situaciones hidrodinámicas y morfodinámicas diferentes. Un sistema completo y acoplado de ecuaciones diferenciales parciales que incluía las ecuaciones de aguas poco profundas y una ecuación de conservación de masa para el sedimento fue desarrollado en un trabajo previo. Partiendo de este trabajo anterior se han implementado diferentes formulaciones de cierre para calcular el transporte de sedimento. Puesto que dichas formulaciones fueran derivadas de ensayos de laboratorio en situaciones 1D y para situaciones en equilibrio, se impone la necesidad de valorar su efectividad en situaciones transitorias para configuaciones 1D y 2D. Además de realizar la comparativa entre estas correlaciones empíricas se ha propuesto una nueva discretización para una de ellas, obteniéndose de esta manera unos resultados numéricos más precisos en comparación con los datos experimentales. Las conclusiones extraídas de este trabajo han permitido comprender mejor la dinámica del transporte de sedimento en flujos de agua y serán utilizadas en un futuro próximo para dotar de mayor complejidad al modelo matemático

Assessment of the performance of numerical modeling in reproducing a replenishment of sediments in a water-worked channel

The artificial replenishment of sediment is used as a method to re-establish sediment continuity down- stream of a dam. However, the impact of this technique on the hydraulics conditions, and resulting bed morphology, is yet to be understood. Several numerical tools have been developed during last years for modeling sediment transport and morphology evolution which can be used for this application. These models range from 1D to 3D approaches: the first being over simplistic for the simulation of such a complex geometry; the latter requires often a prohibitive computational effort. However, 2D models are computationally efficient and in these cases may already provide sufficiently accurate predictions of the morphology evolution caused by the sediment replenishment in a river. Here, the 2D shallow water equa- tions in combination with the Exner equation are solved by means of a weak-coupled strategy. The clas- sical friction approach considered for reproducing the bed channel roughness has been modified to take into account the morphological effect of replenishment which provokes a channel bed fining. Computa- tional outcomes are compared with four sets of experimental data obtained from several replenishment configurations studied in the laboratory. The experiments differ in terms of placement volume and con- figuration. A set of analysis parameters is proposed for the experimental-numerical comparison, with particular attention to the spreading, covered surface and travel distance of placed replenishment grains. The numerical tool is reliable in reproducing the overall tendency shown by the experimental data. The effect of fining roughness is better reproduced with the approach herein proposed. However, it is also highlighted that the sediment clusters found in the experiment are not well numerically reproduced in the regions of the channel with a limited number of sediment grains

The origin of fine sediment determines the observations of suspended sediment fluxes under unsteady flow conditions

Field observations in a wide range of environments have shown that sediment availability is a major control on the suspended sediment observations in streams. Here we examine, via laboratory experiments, how the amount of proximal in-channel fine sediment storage relative to the upstream fine sediment distal supply influences the observations of suspended sediment concentrations in streams. Experiments under idealized conditions in a laboratory flume with different ratios of proximal and distal sediment supplies were conducted under a varying flow regime. In addition, the role of the sediment particle size of the supplied sediment on suspended sediment observations was explored. The combinations of proximal and distal sediment supply result in multiple responses of the channel bed and sediment quantity within the channel bed, and the responses adjust through aggradation and degradation. The signature of sediment concentration observed at the upstream section of the channel, given by the distal supply, differs from the downstream observations of the total conveyed sediment(distal and proximal), as shown by an in-phase analysis of sediment concentration-discharge plots.Furthermore, we show that nonuniform sediment mixtures may result in a change in the direction of the hysteresis observed between sediment concentration and discharge (i.e., from a clockwise hysteresis toa counterclockwise hysteresis). We also demonstrate that the ratio between sediment distal supply and proximal sediment availability modulates the magnitude of the aggradation/degradation processes in the channel reach and thus the joint observations of sediment concentration and discharge