Le couplage important entre les différentes échelles d’un écoulement est une des caractéristiques prin-cipales des turbulences. Cela est exprimé mathématiquement par les termes non linéaires présents dans les équations d’équilibre de l’écoulement, dominants en dynamique turbulente. En magnétohy-drodynamique (MHD), la force de Lorentz influe sur l’équation de conservation de l’impulsion et le nombre de termes non linéaires passe à quatre au lieu d’un seul pour un fluide non conducteur. L’objectif principal de cette thèse est d’analyser le transport d’énergie inter-échelles en utilisant une simulation numérique directe d’un écoulement turbulent MHD. Les propriétés de localité du transport de l’énergie entre les échelles pour un écoulement anisotropique ou isotropique, généré par la présence d’un champ magnétique constant, sont renforcées. Un objectif secondaire est d’établir un cadre de travail pour l’étude du transport de particules test chargées dans un champ électromagnétique turbu-lent, i.e. généré par le mouvement d’un fluide conducteur, qui possède des structures à plusieurs ordres de grandeur. La structure de la thèse est présentée ci-dessous. Dans la première partie, composée des deux premiers chapitres, l’auteur présente les notions de turbu-lences, aussi bien hydrodynamiques que MHD. Ces deux chapitres sont des synthèses. La deuxième partie est la principale source de nouveaux résultats. Le chapitre 3 présente les méthodes numériques pour la résolution des équations, les méthodes pseudo-spectrales. Un nouveau type de force est introduit, imposant un niveau de dissipation pour tous les invariants. Dans le chapitre 4, il est effectué une analyse du transfert d'énergie entre ordres de grandeur pour les turbulences MHD. Pour explorer ces transferts d'énergie, le domaine spectral est décomposé en une série de coques de même nombre d'onde. Le transfert moyen d'énergie entre ces coques est analysé. Les transferts d'énergie s'avèrent être surtout locaux en ordre de grandeur, alors qu'une contribution non locale existe due à la force. En présence d'un champ magnétique, l'écoulement développe une direction préférentielle, une anisotropie, où une idée nouvelle de décomposition de l'espace spectral en structures annulaires est présentée. Utilisant cette décomposition annulaire on trouve que le transfert entre anneaux est local, surtout dans les anneaux de direction perpendiculaire au champ magnétique. Pour les turbulences isotropiques, dans le chapitre 5, la localité des flux d'énergie est explorée par le biais de fonctions de localité. Dans le cas de la turbulence MHD, nous avons un comportement non local plus prononcé. La dernière partie, les chapitres 6 et 7, présente le formalisme de suivi des trajectoires de particules chargées évoluant dans un champ électromagnétique turbulent. L'influence de la méthode d'interpola-tion du solveur de particules est étudiée avant la présentation des concepts liés au transport de particu-les et aux régimes de diffusion. L'adiabatisme du mouvement des particules chargées est discuté et le transport de particules chargées dans un champ magnétique turbulent est montré en exemple.

The main idea behind the work presented in this thesis is to investigate if it is possible to find a mechanism that leads to surface magnetic field concentrations and could operate under solar conditions without postulating the presence of magnetic flux tubes rising from the bottom of the convection zone, a commonly used yet physically problematic approach. In this context we study the ‘negative effective magnetic pressure effect’: it was pointed out in earlier work (Kleeorin et al., 1989) that the presence of a weak magnetic field can lead to a reduction of the mean turbulent pressure on large length scales. This reduction is now indeed clearly observed in simulations. As magnetic fluctuations experience an unstable feedback through this effect, it leads, in a stratified medium, to the formation of magnetic structures, first observed numerically in the fifth paper of this thesis. While our setup is relatively simple, one wonders if this instability, as a mechanism able to concentrate magnetic fields in the near surface layers, may play a role in the formation of sunspots, starting from a weak dynamo-generated field throughout the convection zone rather than from strong flux tubes stored at the bottom. A generalization of the studied case is ongoing. / <p>At the time of the the doctoral defence the following paper was unpublished and had a status as follows: Paper nr 7: Submitted</p>

In this thesis we study the NS-alpha model of flow turbulence. In this model the closure arises through a modified nonlinearity. For the NS-alpha model currently used in published numerical studies, the parameter representing turbulent fluctuations, alpha, is a scalar and is assumed to be a constant. This corresponds to homogeneous, isotropic fluctuations. In this thesis we investigate the NS-alpha model for the more practical situation where fluctuations may be inhomogeneous and anisotropic. We begin by reviewing the derivation of the governing equations using Hamilton's principle. This is followed by the formulation of a subgrid model, where the dependent variable is the smoothed velocity. The isotropic and anisotropic subgrid models are then tested on a recirculating cavity flow and a fully turbulent channel flow. Initial tests used a simple definition of the model parameter based on the grid size. Two specific problems with the model in these test cases were isolated and addressed. For the cavity flow we found abrupt changes in the model parameter at the solid boundary led to numerical oscillations. To overcome this problem an alternative definition was proposed and found to produce improved turbulence statistics. For the channel flow, interaction between the model and the velocity streaks near the wall led to high skin friction. A damping factor through the streak-affected region removed this problem.

In this thesis we study the NS-alpha model of flow turbulence. In this model the closure arises through a modified nonlinearity. For the NS-alpha model currently used in published numerical studies, the parameter representing turbulent fluctuations, alpha, is a scalar and is assumed to be a constant. This corresponds to homogeneous, isotropic fluctuations. In this thesis we investigate the NS-alpha model for the more practical situation where fluctuations may be inhomogeneous and anisotropic. We begin by reviewing the derivation of the governing equations using Hamilton's principle. This is followed by the formulation of a subgrid model, where the dependent variable is the smoothed velocity. The isotropic and anisotropic subgrid models are then tested on a recirculating cavity flow and a fully turbulent channel flow. Initial tests used a simple definition of the model parameter based on the grid size. Two specific problems with the model in these test cases were isolated and addressed. For the cavity flow we found abrupt changes in the model parameter at the solid boundary led to numerical oscillations. To overcome this problem an alternative definition was proposed and found to produce improved turbulence statistics. For the channel flow, interaction between the model and the velocity streaks near the wall led to high skin friction. A damping factor through the streak-affected region removed this problem.

The present research investigates the details of mixture preparation and combustion in a two-stroke, small-scale research engine with a numerical methodology based on large eddy simulation (LES) technique. A major motivation to study such small-scale engines is their potential use in applications requiring portable power sources with high power density. The investigated research engine has a rectangular planform with a thickness very close to quenching limits of typical hydrocarbon fuels. As such, the combustor has a high aspect ratio (defined as the ratio of surface area to volume) that makes it different than the conventional engines which typically have small aspect ratios to avoid intense heat losses from the combustor in the bulk flame propagation period. In most other aspects, this engine involves all the main characteristics of traditional reciprocating engines. A previous experimental work has identified some major design problems and demonstrated the feasibility of cyclic combustion in the high aspect ratio combustor. Because of the difficulty of carrying out experimental studies in such small devices, resolving all flow structures and completely characterizing the flame propagation have been an enormously challenging task. The numerical methodology developed in this work attempts to complement these previous studies by providing a complete evolution of flow variables. Results of the present study demonstrated strengths of the proposed methodology in revealing physical processes occurring in a typical operation of the high aspect ratio combustor. For example, in the scavenging phase, the dominant flow structure is a tumble vortex that forms due to the high velocity reactant jet (premixed) interacting with the walls of the combustor. LES gives the complete evolution of this flow structure, from its beginning to its eventual decay after the scavenging period is over. In addition, LES is able to predict the interaction between the bulk flow at top dead center (TDC) and the turbulent flame propagation. The success of this depends on the ability of the model in predicting turbulent flow structure including its length and velocity scales.

Th. doct.--Paris 6, 2004. / Bibliogr. p. 131-140. Résumé en français et en anglais. L'ouvrage porte par erreur : ISSN 0078-3780.

Afhandling--Naturvidenskabelige Fakultet--Københavns universitet, 2004. / Résumé en danois. Bibliogr. p. 319-338.

Thesis (Ph. D.)--University of Alberta, 2009. / Title from PDF file main screen (viewed on Nov. 27, 2009). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Department of Physics, University of Alberta." Includes bibliographical references.

Thèse de doctorat : Physique : Lyon, École normale supérieure (sciences) : 2003. / Bibliogr. p. [243]-248.

Reproduction de : Thèse de doctorat : Dynamique des fluides : Toulouse, INPT : 2005. Reproduction de : Thèse de doctorat : Dynamique des fluides : Tunis, ENIT : 2005. / Thèse soutenue en co-tutelle. Titre provenant de l'écran-titre. Bibliogr. 121 réf.