Surface mining of oil sands in northern Alberta requires stripping of saline-sodic shale overburden, which is typically placed in large upland overburden dumps. Due to the chemical nature of this shale, engineered soil covers must be constructed over the shale to support the growth of forest vegetation. A research site on South Bison Hill (SBH), a shale overburden dump at the Syncrude Canada Ltd. Mildred Lake Mine, has been used by researchers over the past decade to study the performance of a reclamation cover. This study was undertaken to improve the understanding of salt and moisture dynamics in the cover-shale system. In particular, the objective of this study was to develop an estimate of the net percolation rate through the cover soil and into the shale overburden. Stable isotope (ä2H and ä18O) measurements obtained from the pore water of soil samples were used to develop stable isotope profiles at various sampling locations along the slope and plateau of the SBH. Simulated profiles were then generated using 2D, finite element numerical modelling software and compared to the measured profiles. Model parameters were obtained from testing and the work of previous researchers. The model results revealed that the net percolation is greatest (32-50 mm/yr) for the plateau and mid-slope bench sample locations. Net percolation rates for sample locations on the slope were lower at 0-12 mm/yr. The results from the stable isotope modelling were utilized in a SO42- transport model to ascertain if calculated net percolation rates could explain measured salinity profiles. This modelling exercise revealed that calculated SO42- profiles are highly dependent on the assumed SO42- production rates in the shale, which is primarily attributed to pyrite oxidation. The model results showed the isotope-based net percolation rates could explain the measured SO42-profiles for a reasonable range SO42- production rates. The SO42- production rates calculated in the model were greatest for the plateau and mid-slope bench locations and lesser for the sloped locations. The model also showed that the mass of SO42- removed by interflow was minimal compared to the mass generated by pyrite oxidation and that net percolation is the dominant flushing mechanism at net percolation rates of 8 mm/yr or more.

In many engineering applications involving mixing of highly viscous fluids or mixing at micro-scales, efficient mixing must be accomplished in the absence of turbulence. Similarly in geophysical flows large-scale, deterministic flow structures can account for a considerable portion of global transport and mixing. For these types of problems, concepts from non-linear dynamical systems and the theory of chaotic advection provide the tools for understanding, quantifying, and optimizing transport and mixing processes. In this thesis chaotic advection is studied numerically in three, steady, experimentally realizable, three-dimensional flows: 1) steady vortex breakdown flow in a cylindrical container with bottom rotating lid, 2) flow in a cylindrical container with exactly counter rotating lids, and 3) flow in a new model stirred-tank with counter-rotating disks. For all cases the three-dimensional Navier-Stokes equations are solved numerically and the Lagrangian properties of the computed velocity fields are analyzed using a variety of computational and theoretical tools. For the flow in the interior of vortex breakdown bubbles it is shown that even though from the Eulerian viewpoint the simulated flow fields are steady and nearly axisymmetric the Lagrangian dynamics could be chaotic. Silnikovs mechanism is shown to play a critical role in breaking up the invariance of the bubble and giving rise to chaotic dynamics. The computations for the steady flow in a cylindrical container with two exactly counter-rotating lids confirm for the first time the findings of recent linear stability studies. Above a threshold Reynolds number the equatorial shear layer becomes unstable to azimuthal modes and an intricate web of radial (cats eyes) and axial, azimuthally-inclined vortices emerge in the flow paving the way for extremely complex chaotic dynamics. Using these fundamental insights, a new stirring tank device with exactly counter-rotating disks is proposed. Results show for the first time that counter rotation of the middle disk in a three-disk stirred tank can create a flow with large chaotic regions. The results of this thesis serve to demonstrate that fundamental studies of chaotic mixing are both important from a theoretical standpoint and can potentially lead to valuable technological breakthroughs.

The effect of finite Reynolds numbers on chaotic advection is investigated for two dimensional lid-driven cavity flows that exhibit topological chaos in the creeping flow regime. The emphasis in this endeavor is to study how the inertial effects present due to small, but non-zero, Reynolds number influence the efficacy of mixing. A spectral method code based on the Fourier-Chebyshev method for two-dimensional flows is developed to solve the Navier-Stokes and species transport equations. The high sensitivity to initial conditions and the exponentional growth of errors in chaotic flows necessitate an accurate solution of the flow variables, which is provided by the exponentially convergent spectral methods. Using the spectral coefficients of the basis functions as solved through the conservation equations, exponentially accurate values of velocity everywhere in the flow domain are obtained as required for the Lagrangian particle tracking. Techniques such as Poincare maps, the stirring index based on the box counting method, and the tracking of passive scalars in the flow are used to analyze the topological chaos and quantify the mixing efficiency.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1972. / Typescript. eContent provider-neutral record in process. Description based on print version record.

Cord-forming fungi form extensive networks that continuously adapt to maintain an efficient transport system, and we can photograph their growth, digitize the network structure, and measure the movement of radio-tracers. Mycelial networks are more accessible than the transport networks of other multicellular organisms, but there are many open questions concerning the coordination of growth and transport within fungal networks. As osmotically driven water uptake is often distal from the growing margin, and aqueous fluids are effectively incompressible, we propose that growth induces mass flows across the mycelium, towards the growing regions. We imaged the temporal evolution of networks formed by Phanerochaete velutina, and at each stage calculated the unique set of currents that account for the observed changes in cord volume, while minimizing the work required to overcome viscous drag. Predicted speeds were in reasonable agreement with experimental data, and cords that were predicted to carry large currents were significantly more likely to increase in size than cords with small currents. We have also developed an efficient method for calculating the exact quantity of resource in each part of an arbitrary network, where the resource is lost or delivered out of the network at a given rate, while being subject to advection and diffusion. This method enabled us to model the spatial distribution of resource that emerges as a fungal network grows over time, and we found good empirical agreement between our model and experimental data gathered using radio-labelled tracers. Our results suggest that in well insulated fungal networks, growth-induced mass flow is sufficient to account for long distance transport. We conclude that active transport mechanisms may only be required at the very end of the transport pathway, near the growing tips. We also developed a simple model of glucose delivery through vascular networks, which indicates that increasing the number of blood vessels in a region can actually decrease the total rate of glucose delivery.

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Yes / Traditional Lattice-Boltzmann modelling of advection–diffusion flow is affected by numerical instability if the advective term becomes dominant over the diffusive (i.e., high-Péclet flow). To overcome the problem, two 3D one-way coupled models are proposed. In a traditional model, a Lattice-Boltzmann Navier–Stokes solver is coupled to a Lattice-Boltzmann advection–diffusion model. In a novel model, the Lattice-Boltzmann Navier–Stokes solver is coupled to an explicit finite-difference algorithm for advection–diffusion. The finite-difference algorithm also includes a novel approach to mitigate the numerical diffusivity connected with the upwind differentiation scheme.

La technique micro météorologique de covariance de turbulences est utilisée pour estimer les échanges de CO2 entre les écosystèmes et latmosphère. Des centaines de sites instrumentés, répartis dans le monde entier, lutilisent désormais pour étudier une grande variété décosystèmes. Cette technique est cependant entachée dune erreur systématique lorsquelle est appliquée sur des couverts hauts comme des forêts, en conditions atmosphériques stables, cest-à-dire essentiellement pendant les nuits peu venteuses et sans couverture nuageuse. Pendant ces périodes, en effet, le transport turbulent serait concurrencé par un autre mécanisme de transport qui est ladvection. Dans ce travail, la présence dadvection a été testée sur le site expérimental forestier de Vielsalm (Belgique) et son importance a été évaluée. A cette fin, un dispositif expérimental permettant des mesures de vitesse de vent, de concentration de CO2 et de température de lair à lintérieur de la forêt a été installé. Il a permis la mise en évidence, pendant les périodes stables, découlements gravitationnels se réalisant près du sol suite au refroidissement des surfaces et à la présence dune faible pente. Il a été montré que ces écoulements étaient responsables du transport advectif de CO2. Une analyse dincertitude a été menée à laide de campagnes de mesures spécifiques. Elle a conclu à la faisabilité des mesures de gradients verticaux et surtout horizontaux de CO2 sur le site mais a montré que le plus grand facteur dincertitude portait sur les estimations de la composante verticale de la vitesse au-dessus de et dans la forêt. Malgré ces incertitudes, une analyse fine des épisodes gravitationnels a permis de mettre en évidence un mécanisme cohérent liant les écoulements dair et le champ des concentrations de CO2 et permettant de mieux comprendre comment le CO2 pouvait être transporté latéralement et verticalement par les écoulements gravitationnels. Finalement, la faisabilité dune correction basée sur lestimation des termes advectifs a été évaluée. Il a été montré que les incertitudes portant sur ladvection étaient trop importantes pour permettre daméliorer sensiblement le bilan nocturne des flux de CO2 au moyen de cette méthode. Celle-ci savère toutefois intéressante pour mieux comprendre les processus de transport à loeuvre dans un couvert forestier./The micrometeorological technique of eddy-covariance is used for the estimation of the CO2 exchange between the ecosystems and the atmosphere. Hundreds of instrumented sites, spread all over the world, use it henceforth to study a great variety of ecosystems. This technique is however affected by a systematic error when applied above tall canopies like forests, in stable atmospheric conditions, i.e. primarily during non windy nights without cloud cover. Indeed, during these periods the turbulent transport would be competed with by another transport mechanism which is called advection. In this work, the presence of advection has been tested on the experimental forested site of Vielsalm (Belgium) and its importance has been evaluated. For this purpose, an experimental set-up allowing the measurements of wind velocity, CO2 concentration and temperature of the air inside the forest has been installed. It has allowed the description, for the stable periods, of gravitational flows being carried out close to the ground due to the cooling of surfaces and the presence of a weak slope. These flows were shown to be responsible for advective CO2 transport. An uncertainty analysis has been carried out using dedicated measurement campaigns. It has conclude with the feasibility of measurements of vertical and especially horizontal CO2 gradients on the site but has shown that the greatest factor of uncertainty related to the estimate of the vertical velocity component above and in the forest. In spite of these uncertainties, a fine analysis of the gravitational episodes has made it possible to highlight a coherent mechanism linking the flow field and the CO2 concentration field and making it possible to better understand how CO2 could be transported laterally and vertically by the gravitational flows. Finally, the feasibility of a correction based on the estimate of the advective terms has been evaluated. It has been shown that uncertainties relating to advection were too important to make it possible to appreciably improve the night assessment of CO2 fluxes by means of this method. This one proves however interesting for better understanding the processes of transport at work in a forest cover.

La modélisation et la simulation de la croissance racinaire des plantes en relation avec l'eau et le transfert de nutriments dans le sol constituent un défi majeur permettant des applications dans diverses thématiques de recherche. Les modèles de croissance racinaire ont été classés en SM (Structural Models), FSM (Functional Structural Models) et DBM (Density Based Models). Les modèles basés sur des représentations explicites de la structure du système racinaire simulent des systèmes de manière réaliste. Les modèles basés sur des densités agrègent le développement racinaire et décrivent l'évolution de densités racinaires dans l'espace et le temps. Le principal avantage de ce type de modèles basés sur des formulations continues est le temps de calcul qui est indépendant du nombre de racines, ce qui est particulièrement utile pour des applications à l'échelle d'une population de plantes. De plus, l'utilisation de modèles continus facilite le couplage avec d'autres modèles fonctionnels et physiques qui sont aussi basés sur des équations continues, tels que le transport de nutriments et d'eau dans le sol.Le but de la thèse est de proposer un modèle continu générique (i.e. applicable à une large diversité d'architectures racinaires) et minimal (i.e. avec le moins de paramètres possible), basé sur une équation aux dérivées partielles. Ce modèle est présenté en 3D et considère le nombre d'apex par unité de volume comme étant la variable de sortie. L'équation est composée de trois principaux phénomènes physiques, à savoir l'advection, la diffusion et la réaction, qui agrègent différents processus racinaires de développement et d'architecture, e.g. la croissance primaire, la ramification et la mortalité. Un schéma numérique basé sur la méthode de splitting d'opérateurs est proposée afin de résoudre l'équation en séparant les trois opérateurs physiques. C'est une méthode puissante et numériquement consistante qui permet de choisir des schémas numériques appropriés pour chaque opérateur. Des données observées avec leur variabilité, qui sont codées en utilisant les modèles architecturaux, sont permettent la calibration du modèle continu. Le modèle continu est donc utilisé afin de simuler l'évolution spatio-temporelle de la densité moyenne du nombre d'apex pour des systèmes racinaires dont leurs développements diffèrent. L'évaluation de cette approche de modélisation est traitée sur : 1- des racines horizontales d'eucalyptus, chacune contrôlée par un apex principal ; 2- des systèmes centralisés, e.g. les systèmes du maïs, et 3- des systèmes décentralisés, e.g. les systèmes de chiendent. Les résultats de la méthode de calibration sont satisfaisants et ont permis de définir et simuler diverses stratégies de croissance racinaire. / Modelling and simulating plant root growth in connection with soil water and nutrient transfer is an important challenge that finds applications in many fields of research. Root growth models have been classified into SM (Structural Models), FSM (Functional Structural Models) and DBM (Density Based Models). Models based on explicit representations of root system structures simulate realistic patterns. Density based models aggregate root development and describe the evolution of root densities in space and time. The main advantage of this kind of models based on continuous formulation is that the computational time is independent of the number of roots, which is especially useful for applications at the plant stand scale. Moreover, the use of continuous models facilitates coupling with other functional and physical models that are also based on continuous equations such as water and nutrient transport.The aim of the thesis is to propose a minimal (i.e. involving a minimum number of parameters) and generic (i.e. applicable to a wide range of root architectures) continuous model based on a partial differential equation. This model is presented in a 3D form and considers the number of apices per unit volume of soil as output variable. The equation includes three main physical phenomena, namely advection, diffusion andreaction, which aggregate different aspects of root architectural and developmental rules, e.g. primary growth, branching and mortality. A numerical scheme based on an operator splitting method is proposed to solve the equation by separating the three different processes. It is a powerful and consistent numerical method that allows the use of appropriate numerical scheme for each operator. Observed data with their variability, which are encoded using architectural models, are used to calibrate the continuous model. The continuous model is then used to simulate the spatio-temporal evolution of the mean density of apex number for root systems with different developmental rules. The evaluation of this modelling approach is carried out on : 1- horizontal roots of eucalyptus that are controlled by a main apex ; 2- centralizedsystems, e.g. maize root systems, and 3- decentralized root systems, e.g. couch grass root systems.The results of the calibration method were satisfactory and allowed us to define and simulate different root growth strategies.

We study a number of non-equilibrium models of interest to both active matter and biological physicists. Using microscopic agent-based simulation as well as numerical integration of stochastic PDEs, we uncover the non-trivial behaviour exhibited when active transport, or an advection field, is added to out of equilibrium systems. When gravity is included in the celebrated Fisher-Kolmogoro Petrovsky Piscouno (F-KPP) equation, to model sedimentation of active bacteria in a container, we observe a discontinuous phase transition between a `sedimentation' and a `growth' phase, which should in principle be observable in real systems. With the addition of multiplicative noise, the resulting model contains, as its limits, both the bacterial sedimentation previously described and the fluctuating hydrodynamic description of Directed Percolation (DP), an important and well-studied non-equilibrium system whose physics incorporate many universal features which are typical of systems with absorbing states. We map out the phase diagram describing all the systems in between these two limiting cases, finding that adding an advection term, however small, immediately lifts the resulting system out of the DP universality class. Furthermore, we find two distinct low-density phases separated by a dynamical phase transition reminiscent of a spinodal transition. Finally, we attempt to improve the current diffusion-limited model for the growth of filopodia, which are intriguing networks of actin fibres used by moving cells to sense their environment. By the addition of directed transport of actin monomers to the fibre tip complex by myosin molecular motors, we show that, under appropriate conditions, the resulting dynamics may be more efficient that transport by diffusion alone, which would result in filopodial lengths better corresponding to experimental observation.