Nonlinear processes, such as passive scalar fluctuations driven by the turbulent wind field, exhibit extreme variability over a wide range of space-time scales and intensifies. As a resuit, of the complexity of those fields, the theoretical treatment of turbulence is a long-standing challenge of fluid mechanics. An empirical study of stochastic fluctuations in atmospheric aerosol concentration using state of the art lidar data is the subject of this thesis. The statistics of the fluctuations in the scalar field are closely related to those of the turbulent Avind field. Initially, a detailed review of the treatments of such turbulent atmospheric fields that is commonly found in the littérature is given. The main strands of research relevant to a statistical understanding of atmospheric dynamics are (1) isotropic hydrodynamic turbulence in 2D and 3D (with extensions), (2) buoyancy driven flows (3) gravity wave theories, (4) closures, (5) direct numerical simulations. It is argued that all current approaches treat the anisotropy of the dynamics and the characteristic intermittency inappropriately. Already existing - albeit limited - empirical evidence is then used to motivate the relevance of Generalized Scale Invariance and the Unified Scaling Model (e.g. [Schertzer and Lovejoy, 1983, 1984, 1985]) Avhich models turbulent atmospheric fields as anisotropic multifractal cascade processes. This model implies the anisotropic multiscaling of the fields over the entire range of spatial scales and that variability increases algebraically downscale leading to a highly intermittent field.

We introduce and study new lattice gas models of hydrodynamics to simulate thermal fluids in non-equilibrium. The new approach consists in modifying the conventional Lattice Gas Cellular Automata method for fluids by removing the constraints of the Fermi exclusion principle and by introducing internal potential energy levels for the particles. These modifications allow the effective employment of Monte-Carlo dynamics for the evolution of the models, so that the temperature is defined in a natural way, and the introduction of interactions becomes straightforward. / Because the transport properties of fluids determine their behavior in non-equilibrium, we study in detail the effect of our modifications on transport coefficients. We derive expressions for these coefficients in two ways: from Chapman-Enskog expansions and from linear response theory. Because of the potential energy, the transport properties are more similar to those of real fluids than are conventional LGCA models with kinetic energy only: the bulk viscosity is non-zero and thermal diffusion is well defined over a range of densities and temperatures. / We construct several models to illustrate the advantages and implications of our approach. One model is used to study the local temperature distribution in a simulation of Rayleigh Benard convection. Another is used to introduce interactions between particles and to simulate the 1st order phase separation of a fluid into the regions of low and high density. This latter model is also used to study the dynamics of interfaces between the phases. We observe the effects of inertia at the interface and demonstrate that the mean square width of an initially flat interface scales as t3/2 for late times t.

Motivation: we investigate scaling anisotropy in cloud images. Even if these images look much the same in all directions, we can observe anisotropic structure at different scales. Scaling anisotropy measurement method: we propose a simple method to visualize and measure basic exponents of scaling anisotropy in all directions, assuming weak anisotropy. MODIS satellite images are used to measure scaling anisotropy on cloud fields. Main results: a smooth variation of the structure function exponent with the geographic direction has been observed and the behaviour of the function corresponds to what is mathematically expected. There is also a clear difference between the exponents in the North-South and East-West directions. The variation in the value of the exponent between the two axes is one quarter of the exponent, with a higher exponent in the East-West axis. / Motivation : l'anisotropie invariante d'échelle est mise en évidence dans des images de nuage. Même si ces images paraissent les mêmes dans toutes les directions, des structures anisotropes peuvent s'observer à différentes échelles. Méthode de mesure de l'anisotropie invariante d échelle : une méthode simple de visualisation et de mesure des exposants de base de l'anisotropie invariante d'échelle dans toutes les directions est proposée pour le cas d'anisotropie légère. Des images des satellites MODIS sont utilisées pour mesurer l'anisotropie invariante d'échelle sur des champs de nuages. Principaux résultats : une variation douce de l'exposant de la fonction de structure avec la direction géographique a été observée et le comportement de la fonction correspond à ce à quoi on s'attend, d'un point de vue mathématique. Il y a aussi une nette différence entre les exposants dans les directions nord-sud et est-ouest. La variation de la valeur de l'exposant entre les deux axes est du quart de leur valeur ; l'exposant le plus grand est celui de l'axe est-ouest. fr

Historically discrete multiplicative cascade models have been developed to mimic some of the characteristics of fully-developed turbulence. Some of these models have been found to be of much more general relevancy and have been used to simulate and analyse many different kinds of simple geophysical and other scaling fields. The desire to describe more complex processes has led to the invention of multivariate multiplicative cascade models. Of these the simple "complex cascade model" is considered in detail in this thesis. The background theory of Levy random variables and discrete scalar cascades is covered and a description of the various existing analysis techniques is provided. Two analysis techniques are described and tested on complex cascade simulations. The new "adjacent data points" (ADP) method is found to be superior to the traditional analysis technique. A discussion of the difficulties which may be encountered when analysing recorded complex data is included.

The studies which are presented here are computer simulations of fluid phenomena based on 2D lattice gas models of the kind first described by Frisch et al. (1986). The primary advantage of using these models is that they are easily implemented on massively parallel computers and as a result are extremely fast. / The first of these studies is of a model of phase separation in binary fluids. The growth laws of the fluid domains are examined and are shown to compare favourably to theoretical predictions of San Miguel et al. (1985). This appears to be a first verification of these results. The second study is of the critical behavior of a system of binary fluids. The model is shown to have a phase transition and the critical temperature is determined with an accuracy of 1%. Several critical exponents are also determined and evidence is provided that the model falls into the 2D Ising model universality class. A new model of fluid convection is also presented though no concrete results are yet available for this model.

A current literature review revealed that unsteady shock reflection is an active research field in terms of the number of still unanswered questions in this area. One of the unresolved aspects of unsteady shock reflection is the relationship between the catch-up and sonic points. In a recent experiment, Skews and Kleine found that the catch-up point is reached at a higher wall angle than the theoretical sonic point predicted by the steady-state two-shock theory. This thesis attempts to shed some light on these matters via numerical flowfield analysis of unsteady shock reflections. Two-dimensional computations are performed using a locally adaptive unstructured unsteady Euler/Navier-Stokes code. At the first stage, a general guideline for numerical modeling of shock wave front structure using the Navier-Stokes equations on adaptive unstructured grid is presented. Obtained results can be directly used for selection of grid resolution required to study shock reflection problems in a viscous flowfields. Then, various techniques for determination of the location of the sonic/catch-up points in unsteady shock reflection based on numerical flowfield analysis are introduced. The results obtained with these techniques regarding the sonic/catch-up points locations are not in agreement with the experimental results of Skews and Kleine. The causes of this disagreement between the experiments and the present CFD study are studied by imitating the experimental technique used for catch-up point determination. It is shown that the reason for this disagreement is that the shock thickness captured in experimental images exceeds the shock physical thickness by a few orders of magnitude, which leads to detection of the catch-up point at higher wall angles. Three flow models are studied to investigate the location of the sonic/catch-up points on a circular cylinder. The first model is based on the Euler (inviscid, non-heat-conducting) equations and an ideal reflecting surface (impermeable wall boundary condition). The computational experiment for this case shows that the sonic and catch-up points are actually the same points, which approach to the theoretical sonic point with grid refinement. The other two models are intend to study the effect of viscosity on the sonic/catch-up points. At first, the ideal reflecting surface (slip boundary condition) is considered. It is shown that for this case the sonic and catch-up points are again the same points, but the viscous effects (finite shock thickness) cause the sonic/catch-up point to be delayed (to occur at lower wall angles) as compared to the two-shock theory predictions. The final model employs the non-slip reflecting surface. Since in this model the flow velocity at the wall is zero, the sonic point cannot be obtained on the reflection surface; however, the catch-up point can be defined and analyzed. The results of the simulations show that even larger delay for the catch-up point is obtained for the viscous case with the non-slip reflecting surface (in the presence of the boundary layer) as compared to the viscous case with the ideal reflecting surface. / De nos jours, la réflexion instationnaire de choc est un domaine de recherche en plein essor dans lequel subsistent de nombreuses questions qui demeurent sans réponses. Un des aspects non résolus de la réflexion instationnaire de choc est la relation entre le rattrapage et les points soniques. Dans une expérience récente, Skews et Kleine ont constaté que le point de rattrapage est atteint à un angle de paroi plus élevé que le point sonique théorique prédit par la théorie de l'état stationnaire de deux-chocs. Cette thèse tente de faire la lumière sur ces questions via lanalyse numérique d´ecoulement des réflexions instationnaires de choc. Les calculs 2D sont effectués en utilisant un code localement adaptif non structuré pour la résolution numérique des équations d'Euler/Navier-Stokes instationnaire. A la première étape, un cadre général est présenté pour la modélisation numérique de la structure de l'onde de choc en utilisant les équations de Navier-Stokes sur un maillage adaptatif non structuré. Les résultats ainsi obtenus sont directement utilisés afin de choisir une grille de résolution nécessaire lorsque l'on étudie les problèmes de réflexion de choc dans un écoulement visqueux. Par la suite, diverses techniques basées sur l'analyse numérique d'écoulement sont introduites pour localiser le point sonique/rattrapage dans la réflexion instationnaire de choc. En vue de la localisation du point sonique/rattrapage les résultats obtenus avec ces techniques ne sont pas en accord avec les résultats expérimentaux de Skews et Kleine. Les raisons de ce désaccord entre les résultats expérimentaux et les études CFD actuelles sont étudiées en imitant la technique expérimentale utilisée pour la détermination du point de rattrapage. Il est démontré que la raison de ce désaccord réside dans le fait que l'épaisseur de choc sur les images expérimentales dépasse l'épaisseur physique de choc de quelques ordres de grandeur, ce qui entraîne une prédiction du point de rattrapage à des angles de paroi supérieur. Trois modèles d'écoulement sont étudiés afin de localiser le point sonique/rattrapage sur un cylindre circulaire. Le premier modèle est basé sur les équations d'Euler (non visqueux, non conducteur de chaleur) et les équations d'une surface réfléchissante idéale (conditions aux limites de paroi imperméable). L'expérience numérique sur ce cas montre que les points soniques et rattrapages sont identiques, convergeant vers le point sonique théorique après le raffinement de maillage. Les deux autres modèles sont destinés à étudier l'effet de la viscosité sur le point soniques / rattrapage. Dans un premier temps, la surface réfléchissante idéale (condition de glissement) est considérée. Il est démontré que pour ce cas, les points sonique et rattrapage sont encore les mêmes, mais les effets visqueux (l'épaisseur finie de choc) provoquent le point sonique/rattrapage d'être retardé (de se produire à des angles paroi inférieure) par rapport aux prédictions de la théorie de deux-chocs. Le modèle final utilise la surface réfléchissante réelle (condition non-glissement). Etant donné que la vitesse d'écoulement à la paroi est nulle dans ce modèle, le point sonique ne peut être obtenu sur la surface de réflexion. Cependant, le point de rattrapage peut être déterminé et analysé. Les résultats des simulations montrent quun retard encore plus grand est obtenu pour le point de rattrapage pour le cas visqueux avec la surface réfléchissante réelle (en présence de la couche limite) par rapport au cas visqueux avec la surface réfléchissante idéale.

<p> This dissertation presents a new high-order front tracking method for two-phase hyperbolic systems of conservation laws separated by a contact discontinuity. A review of existing methods for moving and/or irregular boundaries shows the significance of accurate geometry data and flux calculation near the interface to achieve a high order method. A general method for hyperbolic systems of conservation laws is presented along with the implementations of numerical methods for simulations of gas dynamics in 2-D using the Euler equations. Convergence tests show the new method is second order accurate for smooth solutions and first order in presence of shocks. Also the new method is used for simulation of Richtmyer-Meshkov instability, in which results are in agreement with both theoretical and experimental approaches.</p>

Nanopores with diameters ranging from 30 nm to 50 nm were drilled in siliconnitride membranes using a transmission electron microscope (TEM) electronbeam. High pressures of cold helium gas were applied to one side of themembranes to achieve flow through the nanopores. Mass flows for pressuregradients up to 1000 psi were measured with the goal of achieving transonicflow. Measured mass flows were compared to theoretical choked flow valuesand the flow speeds were deduced analytically. The ultimate goal of this workwas to determine whether or not TEM drilled nanopores can act as de Lavalnozzles and accelerate fluid to, or close to the speed of sound. While the siliconnitride nanopores do present some technical difficulties, we estimated that inour nanopores, Unruh temperatures on the order of 7 10^-3 K were reached,leading to phonons being emitted at a rate in the range of 10^5 to 10^6 Hz. / Des nanopores de diamètres situés entre 30 et 50 nm ont été perçés dans desmembranes de nitrure de silicium (amorphe) à l'aide d'un microscope électroniqueen transmission (MET). De hautes pressions de gaz d'hélium froidont été appliquées d'un côté de la membrane permettant l'écoulement du fluideà travers le nanopore. Le débit de masse a été mesuré pour des differencesde pressions allant jusqu'à 1000 psi, l'objectif étant d'atteindre un écoulementtransonique. Les mesures ont été comparées à un modèle théorique et lesvitesses d'écoulement ont été déduit analytiquement. Le but de ce projet estde déterminer si les nanopores perçés à l'aide du MET peuvent agir commedes tuyères de Laval et accélerer le fluide à des vitesses proches de celle duson. Bien que les nanopores utilisés présentent des difficultés techniques, il aété estimé qu'il permettraient d'observer une température de Unruh de l'ordrede 7 10^-3 K, et les phonons seraient émis à une fréquence de l'ordre de 10^5à 10^6 Hz.

<p> Laser pulses propagating through plasma undergo spectral broadening through local energy exchange with driven plasma waves. During propagation, a high power laser pulse drives large amplitude plasma waves, depleting the pulse energy. At the same time, the large amplitude plasma wave provides a dynamic dielectric response that leads to spectral shifting. The loss of laser pulse energy and the approximate conservation of laser pulse action imply that spectral red-shifts accompany the depletion. Here we examine the spectral shift and broadening, energy depletion, and action conservation of nonlinear laser pulses using the modified paraxial solver in WAKE. For pulses causing complete cavitation, large wavenumber shifts and action decay are observed at the distance where 40&ndash;50% of the pulse energy is depleted, consistent with theoretical prediction. </p><p> A tenuous plasma, enveloped, full wave solver was further implemented and compared to the modified paraxial solver through studying the University of Maryland laser-plasma system. The full wave solver has the advantage of better predicting the dispersion relation and eliminating the problematic divergence in the dispersion of the modified paraxial solver as wavenumber approaches zero, which is important especially when considering long wavelength generation. </p><p> Numerical analysis of the two propagation algorithms has been conducted via monitoring conservation laws. For large spectral shifts, numerical damping and convection of radiation out of the simulation domain result in action decay. Implementing a higher order evaluation of numerical derivatives and smaller spatial step have reduced numerical damping. </p><p> Spectral red-shifting of high power laser pulses propagating through underdensed plasma channel can be a source of ultrashort mid-infrared (MIR) radiation. Parametric dependence of MIR generation on laser pulse power, initial pulse duration, and plasma density is investigated through characteristic wavenubmer estimates and simulations.</p>

<p> As of 2013, the Carbon Dioxide Information Analysis Center (CDIAC) estimates that the world emits approximately 36 trillion metric tons of Carbon Dioxide (CO₂) into the atmosphere every year. These large emissions have been correlated to global warming trends that have many consequences across the globe, including glacial retraction, ocean acidification and increased severity of weather events. With green technologies still in the infancy stage, it can be expected that CO₂ emissions will stay this way for along time to come. Approximately 41% of the emissions are due to electricity production, which pump out condensed forms of CO₂. This danger to our world is why research towards new and innovative ways of controlling CO₂ emissions from these large sources is necessary. </p><p> As of now, research is focused on two primary methods of CO₂ reduction from condensed CO₂ emission sources (like fossil fuel power plants): Carbon Capture and Sequestration (CCS) and Carbon Capture and Utilization (CCU). CCS is the process of collecting CO₂ using absorbers or chemicals, extracting the gas from those absorbers and finally pumping the gas into reservoirs. CCU on the other hand, is the process of reacting CO₂ to form value added chemicals, which can then be recycled or stored chemically. </p><p> A Dielectric Barrier discharge (DBD) is a pulsed, low temperature, non-thermal, atmospheric pressure plasma which creates high energy electrons suitable for dissociating CO₂ into its components (CO and O) as one step in the CCU process. Here I discuss the viability of using a DBD for CO₂ dissociation on an industrial scale as well as the fundamental physics and chemistry of a DBD for CO₂ dissociation. This work involved modeling the DBD discharge and chemistry, which showed that there are specific chemical pathways and plasma parameters that can be adjusted to improve the CO₂ reaction efficiencies and rates. Experimental studies using the Versatile Atmospheric dielectric barrier Discharge ExpeRiment (VADER) demonstrated how different factors, like voltage, frequency and the addition of a photocatalyst, change the efficiency of CO₂ dissociation in VADER and the plasma chemistry involved.</p>