Dans cette thèse, nous étudions l’effet de la turbulence en rotation sur l’instabilité dynamo. Nous étudions les différentes limites de la turbulence en rotation numériquement et théoriquement. D’abord, nous avons considéré l’effet dynamo engendré par les écoulements quasi-bidimensionnel (un écoulement avec trois composantes de vitesse qui dépendent de deux directions), qui modélise la limite de rotation très rapide. Nous avons étudié l’amplitude de saturation du champ magnétique en fonction du nombre de Prandt magnétique pour ce type d’écoulement. Un modèle théorique est développé et comparé avec les résultats numériques. Nous avons aussi regardé l’effet d’une vitesse bruitée sur le taux de croissance des différents moments du champ magnétique. Nous avons étudié l’écoulement 3D en rotation globale pour différents régimes du paramètre de contrôle. Pour l’écoulement hydrodynamique, nous avons étudié la transition vers une cascade inverse et les différents types de saturation de la cascade inverse. Nous avons regardé l’instabilité dynamo de ces écoulements. Nous avons montré que la rotation modifie le mode le plus instable et dans certains cas peut réduire le seuil de l’instabilité dynamo. / In this thesis, we study the effect of rotating turbulent flows on the dynamo instability. We study the different limits of rotating turbulence using numerical simulations and theoretical tools. We first look at the dynamo instability driven by quasi-twodimensional flows (flows with three components varying along two directions), which models the limit of very fast rotation. We look at the saturation amplitude of the magnetic field as a function of the magnetic Prandtl number for such flows. A theoretical model for the dynamo instability is later developed and compared with the numerical results. We also study the effect of a fluctuating velocity field on the growth rate of different moments of the magnetic field. The three dimensional rotating flow is then studied for different range of parameters. For the hydrodynamic problem, we study the transition to an inverse cascade and the different saturation mechanism of the inverse cascade. Later the dynamoinstability driven by such flows is investigated. We show that the effect of rotation modifies the most unstable mode and in some cases can reduce the dynamo threshold.

This thesis is an account of various phenomena caused by the interaction of the motion of electrically conducting fluids with magnetic fields. Such phenomena, the study of which is usually known as Magnetohydrodynamics (MHD), occur on a galactic, planetary or laboratory length scale; however in this thesis we concentrate on those phenomena which can be reproduced in the laboratory. In chapter 2 we study the laminar flow of uniformly conducting, incompressible fluids in rectangular ducts under the action of transverse magnetic fields. We begin by proving that when the duct has a constant cross-section the solution is unique and then analyse theoretically some of the curious effects on the flow of the duct's walls being electrically conducting. We find close agreement between the results of these theories and the experiments of Alty (1966) and Baylis (1966). We then analyse the flow in ducts with varying cross-sections. In chapter 3 we analyse some of the curious flows and current streamline patterns produced by placing electrodes on the non-conducting walls of a container, filled with a conducting fluid, and passing electric currents between the electrodes in the presence of a strong magnetic field. In chapter 4 we analyse some of the theoretical limitations on the use of Pitot tubes and electric potential (e.p.) probes in MHD flows, and provide some estimates of the errors to be expected. In chapter 5 we analyse the stability of parallel flows in parallel magnetic fields and also some aspects of the stability of the flows analysed in chapters 2 and 3. In chapters 6, 7 and 8 we describe our experimental apparatus, the experiments to investigate directly some of the flows analysed theoretically in chapters 2 and 3 by means of Pitot and e.p. probes, and experiments to measure the MHD errors inherent in the use of these probes. We concluded that the curious phenomena predicted actually exist. We also learnt much about the use of Pitot and e.p. probes, especially as some of the experimental results were as predicted in chapter 4.

La formation des étoiles, processus fondamental en astrophysique, résiste toujours à la compréhension. En effet, de nombreux phénomènes interagissent durant les différentes étapes, et ce sur une large gamme d’échelles. Il est donc primordial de comprendre la dynamique du milieu interstellaire, dans lequel les étoiles se forment. En particulier, il est maintenant bien établi que la structure du milieu interstellaire est fortement impactée par des processus de rétroaction de la part des étoiles qui s’y forment. D’une part cette rétroaction limite le taux de formation de nouvelles étoiles, et d’autre part elle est l’un des contributeurs à la morphologie et la dynamique des galaxies : taille du disque, éjection de matière, etc. Ce travail de thèse propose d’étudier numériquement la dynamique du milieu interstellaire, de manière à mettre en évidence l’impact des processus de rétroaction. Le processus principal qui sera étudié est les supernovae, figurant parmi les évènements les plus énergétiques dans le milieu interstellaire. Après l’étude et la modélisation en détail de l’explosion d’une unique supernova dans nuage moléculaire, un modèle numérique incluant formation d’étoiles et rétroaction par supernovae sera présenté et mis en œuvre dans des simulations d’un disque galactique stratifié à l’échelle du kiloparsec. Une extension de ce modèle pour tenir compte du rayonnement ionisant sera proposée. Il est effectivement possible de réguler la formation d’étoiles à l’aide de modèles de rétroaction par les supernovae, mais les résultats précis dépendent de manière significative des détails du schéma mis en œuvre. En utilisant la variante apparaissant comme la plus réaliste, des simulations à haute résolution du milieu interstellaire sont présentées et étudiées. En particulier, il est possible de mettre en évidence des propriétés de la turbulence compressible et magnétisée à l’échelle galactique : variation des spectres de puissance en fonction de l’altitude, alignement spontané de la vitesse et du champ magnétique, effet antagoniste de la rétroaction sur cet alignement et formation de structures. / Star formation, a fundamental process in astrophysics, remains only partially understood. Several processes are known to interact during all the steps over a large range of scales. It is therefore of highest importance to understand the dynamics of the interstellar medium, in which stars form. In particular, it is now well-known that the structure of the interstellar medium is strongly affected by feedback processes emanating from the stars that form in it. On the one hand this feedback limits the rate of formation of new stars, and on the other hand it is one of the main contributors to the shape and dynamics of galaxies: thickness of the disk, matter outflows, etc. This work aims to study numerically the dynamics of the interstellar medium, in order to highlight the impact of stellar feedback processes. The main process that will be studied is supernovae, being among the most energetic events in the interstellar medium. After the study and detailed modeling of the explosion of a single supernova inside a molecular cloud, a numerical model including star formation and supernova feedback will be presented and used in kiloparsec-scale simulations of a stratified galactic disk. An extension of this model will be suggested in order to take into account the ionizing radiation. It is indeed possible to regulate star formation with supernova feedback models, although the precise results strongly depend on the detailed scheme that is implemented. Using the most realistic-looking variant, high-resolution simulations are presented and studied. In particular, it is possible to extract properties of compressible and magnetized turbulence at the galactic scale: variation of the power spectra as a function of altitude, spontaneous alignment between velocity and magnetic field, antagonistic effect of stellar feedback onto this alignment, and structure formation.

We investigate the Richtmyer-Meshkov instability (RMI) that occurs when an incident shock impulsively accelerates the interface between two different fluids. RMI is important in many technological applications such as Inertial Confinement Fusion (ICF) and astrophysical phenomena such as supernovae. We consider RMI in the presence of the magnetic field in converging geometry through both simulations and analytical means in the framework of ideal magnetohydrodynamics (MHD). In this thesis, we perform linear stability analyses via simulations in the cylindrical geometry, which is of relevance to ICF. In converging geometry, RMI is usually followed by the Rayleigh-Taylor instability (RTI). We show that the presence of a magnetic field suppresses the instabilities. We study the influence of the strength of the magnetic field, perturbation wavenumbers and other relevant parameters on the evolution of the RM and RT instabilities. First, we perform linear stability simulations for a single interface between two different fluids in which the magnetic field is normal to the direction of the average motion of the density interface. The suppression of the instabilities is most evident for large wavenumbers and relatively strong magnetic fields strengths. The mechanism of suppression is the transport of vorticity away from the density interface by two Alfv ́en fronts. Second, we examine the case of an azimuthal magnetic field at the density interface. The most evident suppression of the instability at the interface is for large wavenumbers and relatively strong magnetic fields strengths. After the shock interacts with the interface, the emerging vorticity breaks up into waves traveling parallel and anti-parallel to the magnetic field. The interference as these waves propagate with alternating phase causing the perturbation growth rate of the interface to oscillate in time. Finally, we propose incompressible models for MHD RMI in the presence of normal or azimuthal magnetic field. The linearized equations are solved numerically using inverse Laplace transform. The incompressible models show that the magnetic field suppresses the RMI, and the mechanism of this suppression depends on the orientation of the initially applied magnetic field. The incompressible model agrees reasonably well with compressible linear simulations.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23011号 / 理博第4688号 / 新制||理||1672(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 浅井 歩, 教授 嶺重 慎, 教授 一本 潔 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Theoretical part of this thesis is dedicated to the theoretical basis of electric conduction phenomena in fluids and method of calculation of magnetohydrodynamic phenomena. In the experimental part, computational modules have been developed to complement and augment the use of commercial simulation programs for simulation in the field of magnetohydrodynamics. On practical examples of mass spectrometer simulation, Einzel lens, electron movement and electric circuit breaker, the functionality of the computational models and the correctness of the obtained results were documented. Created computational modules can be used to design and optimize products using magnetohydrodynamic phenomena.

A galaxy's angular momentum is known to be correlated with its morphology: at a given mass, spiral galaxies have higher angular momenta than elliptical galaxies. A galaxy's angular momentum is also largely set by its formation history: in particular, how much gas and the kinematic state of the gas that both accretes onto it and is expelled in galactic outflows from AGN and supernovae. All gas inflowing to and outflowing from the galaxy interacts with gas in the region surrounding the galaxy called the circumgalactic medium (CGM), which means at a fundamental level, the CGM controls the angular momentum of the galaxy. Therefore, to really understand the origins of galactic angular momentum, it is necessary to understand the angular momentum of the CGM itself. In this dissertation, I present a series of projects aimed at studying angular momentum in the CGM using the Illustris and IllustrisTNG cosmological hydrodynamical simulations suites. In an appendix, I also present a project on searching a survey of neutral hydrogen for previously undetected ultra-faint dwarf galaxies in and around the Milky Way's CGM. First, to understand how present-day galaxies acquire their observed angular momentum, I analyze the evolution of the angular momentum of Lagrangian gas mass elements as they accrete onto dark matter halos, condense into Milky Way-scale galaxies, and join the z=0 stellar phase of those galaxies. I find that physical feedback from the galaxy is essential in order to produce reasonable values of galactic angular momentum, and that most of the effects of this feedback occur in the CGM, necessitating studying the angular momentum of the CGM itself. Following on from this result, I then characterize the angular momentum distribution and structure within the CGM of simulated galaxies over a much larger range of halo masses and redshifts, with the goal of determining if there are common angular momentum properties in CGM populations. I indeed find that the angular momentum of the CGM is larger and better aligned around disk galaxies that themselves have high angular momentum. I also identify rotating structures of cold gas that are generally present around galactic disks. This clear connection of the CGM to the galaxy motivated a detailed comparison to observations of cold CGM gas. I perform this comparison in the following chapter where I use the highest-resolution simulation from the IllustrisTNG suite of cosmological magneto-hydrodynamical simulations to generate synthetic observations of cold CGM gas around star-forming galaxies in order to study kinematics and compare them to line-of-sight observations of cold gas near comparable galaxies. With this direct comparison to observations of the CGM, I show that IllustrisTNG produces rotating CGM gas consistent with observations to a high degree. In the penultimate chapter I present unpublished work where I begin to examine angular momentum evolution in the CGM on much finer timescales than can be resolved with the cosmological simulations I have used thus far. Preliminary results suggest that gas can experience large changes in angular momentum very quickly, and that these changes may be connected to corresponding changes in the temperature of the gas. Finally, I conclude by summarizing my main results and briefly discussing what questions still remain unanswered and my plans and strategies for pursuing these questions in my future work.

Untersuchung konvektiver Transportprozesse innerhalb einer auf der Lorentz-Kraft basierenden Strömung während der elektrolytischen Abscheidung.

NR 20140805

Thesis (Ph.D. (Applied Mathematics)) -- University of Limpopo, 2020 / The flow of electrically conducting fluids in the presence of a magnetic field has wide applications in science, engineering and technology. Examples of the applications include industrial processes such as the cooling of reactors, extrusion of plastics, purification of crude oil, medical applications, aerodynamics and many more. The induced magnetic field usually act as a flow control mechanism, especially under intense heat. In this study a couple stress fluid in a channel will be used as the working fluid. Channel flow and heat transfer characteristics of couple stress fluids find applications in processes such as the extrusion of polymer fluids, solidification of liquid crystals, cooling of metallic plates in a bath, tribology of thrust bearings and lubrication of engine rod bearings. One major characteristic that distinguishes the couple stress fluid from other non-Newtonian fluids is the inclusion of size-dependent microstructure that is of mechanical significance. As such, the couple stress constitutive model is capable of describing the couple stresses, the effect of body couples and the nonsymmetric tensors manifested in several real fluids of technological importance. A fully developed laminar magnetohydrodynamic (MHD) flow of an incompressible couple stress fluid through a vertical channel due to a steady-periodic temperature on the channel plates is investigated. Specifically, the effects of couple stresses and internal heat generation on MHD natural convection flow with steady-periodic heat input, the impact of magnetic field induction on the buoyancy-induced oscillatory flow of couple stress fluid with varying heating and a mixed convective two dimensional flow of unsteady MHD couple stress fluid through a channel field with porous medium are studied. Analytical methods and the semi-analytic Adomian decomposition method will be used to solve the resulting non-linear differential equations governing the flow systems. Useful results for velocity, temperature, skin friction and Nusselt number are obtained and discussed quantitatively. The effects of the various flow governing parameters on the flow field are investigated.