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.

No description available.

: Ce travail concerne l'écoulement inertiel en milieu poreux rencontré dans diversessituations telles que les écoulements autour des puits pour la récupération pétrolière, lesécoulements dans les réacteurs catalytiques, etc. En régime stationnaire, les différents modèlesmacroscopiques pour décrire ces écoulements inertiels (non-linéaires) demeurent encore sujetsà débat. Ces modèles consistent en une loi de Darcy corrigée de termes dont la dépendancevis à vis de la vitesse de filtration relève du régime d'écoulement. Dans ce travail, une attentionparticulière est portée tout d'abord à l'étude numérique (DNS), sur des structures modèles, de lalimite de stationnarité de l'écoulement monophasique newtonien qui correspond à la premièrebifurcation de Hopf, caractérisée par un nombre de Reynolds critique. La connaissance de cettelimite est cruciale puisqu'elle détermine le domaine de validité des modèles macroscopiquesstationnaires pertinents. Dans un deuxième temps, la dépendance de la déviation (inertielle) àla loi de Darcy par rapport aux propriétés de la structure poreuse (forme des grains, désordre)et à l'orientation de l'écoulement est étudiée dans le cas de structures 2D et 3D. Les propriétéseffectives de la structure à l'échelle macroscopique sont déterminées à partir de la résolutionnumérique des problèmes de fermeture associés au modèle macroscopique obtenu par prisede moyenne des équations de Navier-Stokes. Afin de déceler l'origine de cette déviation et sesdifférentes formes, l'évolution de la structure microscopique de l'écoulement en fonction dunombre de Reynolds est analysée. Plus particulièrement, le rôle des zones de recirculation, etles corrélations avec la courbure des lignes de courant multipliée par l’énergie cinétique localeet la variation de l’énergie cinétique le long de ces lignes sont étudiés. La dernière partie dutravail est consacrée à une étude numérique, toujours dans des situations modèles, de ladéviation à la loi de Darcy généralisée dans le cas de l'écoulement diphasique inertiel. / This work focuses on inertial flow in porous media encountered in differentindustrial situations such as flow around wells in oil recovery, flow in filters and in columns ofreactors for chemical engineering, etc. In stationary flow regime, the different macroscopicmodels describing inertial (non-linear) flow are still discussed. These models consist in theDarcy’s law with correction extra terms whose dependence upon the filtration velocity is afunction of the flow regime. In this work, a particular attention is attributed first to the numericalinvestigation (DNS), on model structures, of the limit of one phase Newtonian stationary flowwhich corresponds to the first Hopf bifurcation, characterized by a critical Reynolds number.The knowledge of this limit is crucial since it establishes the ranges of validity of the relevantmacroscopic stationary models. In a second step, the dependence of the deviation (inertial)from Darcy’s law on the properties of the porous structure (grains shape, disorder) and on theorientation of the flow is analyzed in 2D and 3D situations. The effective properties of thestructure and the flow at the macroscopic scale are obtained from the numerical resolution ofthe closure problems associated to the macroscopic model obtained from an up-scalingprocedure (volume averaging) of the Navier-Stokes equations. In order to identify the origin ofthe deviation and its different forms, the variation of the microscopic flow structure with theReynolds number is analyzed. More specifically, the role of the recirculation zones, and thecorrelations with flow streamlines curvature multiplied by the local kinetic energy and thevariation of the kinetic energy along these lines are studied. The last part of the work isdedicated to a numerical investigation of the deviation from the generalized Darcy’s law in thecase of two phase inertial flow.

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-11T14:24:18Z No. of bitstreams: 1 arquivototal.pdf: 2910617 bytes, checksum: 78d320ecf6eab76dd1627257ec1aa34d (MD5) / Made available in DSpace on 2017-09-11T14:24:18Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2910617 bytes, checksum: 78d320ecf6eab76dd1627257ec1aa34d (MD5) Previous issue date: 2017-03-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Electromagnetic fields acting on particles have been extensively studied in different areas of physics. In quantum mechanics for example, effects such as Aharonov-Bohm, Landau levels and Hall conductivity, have always motivated new papers including analogous inertial models. Inertial effects play an important role in classical mechanics, but have been largely ignored in quantum mechanics. However, the analogy between inertial forces on mass particles and electromagnetic forces on charged particles is not new. Another factor that may influence the classical and quantum behavior of particles is geometry. An element related to geometry that has been extensively studied in several areas is the topological defect. Topological defects represent an interface between areas such as cosmology, gravitation, and condensed matter. Such defects in condensed matter can be developed through the classical theory of elasticity. However, due to the interdisciplinarity of this theme, approaches from gravitation can also describe them. Based on this analogy, the medium formed by a topological defect is characterized by a metric tensor. From this approach, several problems can be discussed by analyzing the influence of the topological defect in the solution of the problem. In this work, it will be discussed how magnetic field, rotation and topological defects, especially the disclination, influence in the Landau Levels and the Hall conductivity for a noninteracting planar two-dimensional electron gas. First we will discuss the influence of each of these elements and then the influence of all of them simultaneously. / A atuação de campos eletromagnéticos em partículas têm sido extensivamente estudada em diferentes áreas da física. Em mecânica quântica por exemplo, efeitos como Aharonov-Bohm, níveis de Landau e condutividade Hall, têm sempre motivado novos trabalhos inclusive para modelos análogos inerciais. Os efeitos inerciais desempenham um papel importante na mecânica clássica, mas tem sido largamente ignorados em mecânica quântica. No entanto, a analogia entre forças inerciais sobre partículas de massa e forças eletromagnéticas sobre partículas carregadas não é nova. Um outro fator que pode influenciar no comportamento clássico e quântico de partículas é a geometria. Um elemento relacionado a geometria e que tem sido bastante estudado em diversas áreas, é o defeito topológico. Os defeitos topológicos representam uma interface entre áreas como cosmologia, gravitação e matéria condensada. Tais defeitos em matéria condensada podem ser desenvolvidos através da teoria clássica da elasticidade. Contudo, devido a interdisciplinaridade desse tema, abordagens provenientes da gravitação podem também descrevê-los. Com base nessa analogia, caracteriza-se o meio formado por um defeito topológico mediante um tensor métrico. A partir dessa abordagem, diversos problemas podem ser discutidos analisando a influência do defeito topológico na solução do problema. Nesse trabalho, será discutido como campo magnético, rotação e defeitos topológicos, em especial a desclinação, influenciam os níveis de Landau e a condutividade Hall para um gás de elétrons bidimensional planar não interagente. Primeiramente discutiremos a influência de cada um desses elementos e em seguida a influência de todos simultaneamente. Será mostrado como a rotação quebra a degenerescência dos níveis de Landau aumentando consequentemente a condutividade Hall. Será mostrado também que acoplamento dos três elementos gera uma região para campos magnéticos fracos com sem estados ligados. Com um outro ponto de partida mostraremos também que a rotação pode ser utilizada para sintonizar a condutividade Hall.

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-13T11:51:46Z No. of bitstreams: 1 arquivototal.pdf: 831966 bytes, checksum: a9f68724ebd2fdd53f6f561f0f45d42c (MD5) / Made available in DSpace on 2017-09-13T11:51:46Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 831966 bytes, checksum: a9f68724ebd2fdd53f6f561f0f45d42c (MD5) Previous issue date: 2013-02-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Inertial effects, such as Coriolis’ and centrifuge forces play an interesting role on classical mechanics and currently has been largely used in quantum mechanics, including in analogies with the electromagnetic effects. However, these analogies between the inertial forces on the massives particules and the electromagnetic forces on charged particles is not new. They were explored by Aharonov and Carmi in 1970 and by Tsai and Nelson in 1988 in the context of a rotational quantum phase like an Aharonov-Bohm phase. Based in this analogy, Dattoli and Quattromini, introduced Coriolis’ analogue quantum states to Landau levels. In 1915, Barnett had already published a paper about magnetization due to rotation which recently had a renewed interest applyed to nanostructures. A rotational analogy of the classical Hall effect was proposed and rotational inertial forces were studied in spintronic. Energy spectra like Landau levels appear under the action of Coriolis forces when the centrifuge force acting on free electrons is compensated by a radial electric field. In this work, we will demonstrate effects caused by rotation and magnetic field in a spinning conductor disc. We will study both the electromagnetic and inertial interactions simultaneously. Some values to the relation between the magnetic field and the rotation will be chosen and this will result in Landau-like levels to a system with resultant force composed by Coriolis’ and magnetic forces. A similar behavior for the energy spectrum will be found without a magnetic force composing the resultant force. / Efeitos inerciais, tais como a força centrífuga e a de Coriolis, desempenham um papel importante na mecânica clássica e atualmente têm sido amplamente explorados na mecânica quântica, inclusive em analogias com efeitos eletromagnéticos. No entanto, essas analogias entre as forças inerciais sobre partículas massivas e as forças electromagnéticas sobre partículas carregadas não é nenhuma novidade. Elas foram exploradas por Aharonov e Carmi em 1970 e por Tsai e Neilson em 1988 no contexto de uma fase quântica rotacional similar à fase de Aharonov- Bohm. Baseados nessa mesma analogia, Dattoli e Quattromini introduziram estados quânticos de Coriolis análogos aos níveis de Landau. Em 1915, Barnett já havia publicado um artigo sobre magnetização devido à rotação o qual teve recentemente um interesse renovado aplicado a nanoestruturas. Um análogo rotacional do efeito Hall clássico foi proposto e os efeitos inerciais da rotação foram estudados em spintrônica. Espectros de energia tipo níveis de Landau aparecem sob a ação da força de Coriolis quando a força centrífuga agindo nos elétrons livres é compensada por um campo elétrico radial. Neste trabalho, vamos demonstrar efeitos devido à rotação e ao campo magnético em um disco condutor girante. Estudaremos as interações eletromagnéticas e inerciais simultaneamente. Alguns valores para a relação entre o campo magnético e a rotação serão escolhidos e resultarão em níveis tipo Landau para um sistema com força resultante composta pelas forças de Coriolis e magnética. Um mesmo comportamento para o espectro de energia será obtido sem força magnética compondo a força resultante.