This Thesis is concerned with three particular aspects of extended cosmic strings and domain walls in cosmology: their dynamics, gravitation and interaction with a black hole. In Chapter 3, we study the dynamics of an abelian-Higgs cosmic string. We find its equations of motion from an effective action and compare, for three test trajectories, the resulting motion with that observed in the Nambu-Gotō approximation. We also present a general argument showing that the corrected motion of any string is generically antirigid. We pursue the investigation of the dynamics of topological defects in Chapter 5, where we find (from integrability conditions rather than an effective action) the effective equations governing the motion of a gravitating curved domain wall. In Chapter 4 we investigate the spacetime of a gravitating domain wall in a theory with a general potential V(ɸ). We show that, depending on the gravitational coupling e of the scalar ɸ, all nontrivial solutions fall into two categories interpretable as describing respectively domain wall and false vacuum-de Sitter solutions. Wall solutions cannot exist beyond a value (^4)(_3)ɛmax, and vacuum-de Sitter solutions are unstable to decaying into wall solutions below ɛmax at ɛmax we observe a phase transition between the two types of solution. We finally specialize for the Goldstone and sine-Gordon potentials. In Chapter 6 we consider a Nielsen-Olesen vortex whose axis passes through the centre of an extremal Reissner-Nordstr0m black hole. We examine in particular the existence of piercing and expelled solutions (where the string respectively does and does not penetrate the black hole's horizon) and determine that while thin strings penetrate the horizon — and therefore can be genuinely called hair — thick strings are expelled; the two kinds of solution are separated by a phase transition.

Lors des phases de vol à basse vitesse et à forte incidence, les effets d’installation motrice sontpilotés par une dynamique tourbillonnaire complexe, instationnaire et en interaction pariétaleforte. Il en résulte en particulier, à la jonction du mât réacteur et de la voilure, l’apparition d’untourbillon de type trombe qui est advecté proche de l’extrados de la voilure. Son interaction avecla couche limite d’extrados a tendance à dégrader les performances aérodynamiques de l’aile etpeut favoriser son décrochage prématuré. Dans ces conditions de vol, l’écoulement autour del’installation motrice est alors régi par la concomitance de décollements locaux, d’interactionstourbillon / couche limite et tourbillon / tourbillon, ainsi que le développement d’instabilitéstelles que l’éclatement tourbillonnaire, le tout en présence d’un gradient de pression défavorableimposé par la voilure.Les travaux menés au cours de cette thèse visent dans un premier temps, par une recherchebibliographique ciblée, à identifier et à analyser les mécanismes tourbillonnaires imposés par laprésence d’une installation motrice proche de voilure afin d’améliorer la compréhension de leurimpact sur les performances aérodynamiques de l’avion. Une attention particulière est portéesur l’analyse des phénomènes d’interaction tourbillon / couche limite qui se produisent sur l’extradosde la voilure.En se basant sur les formes tri-dimensionnelles complexes d’un avion de transport commercial,une simplification géométrique du système Nacelle/Mât/Voilure est proposée. Dans certainesconditions d’angle d’incidence et de dérapage, cette géométrie de référence permet de reproduireune dynamique tourbillonnaire analogue à celle rencontrée sur un avion. Plus spécifiquement,l’accent est porté sur la capacité de cette géométrie à générer un tourbillon de type trombe.Sur cette base, les travaux menés au cours de cette thèse s’intéressent ensuite à caractériserl’influence de modifications locales de la forme du mât sur cette dynamique tourbillonnaire,et notamment sur le tourbillon de type trombe naissant à la jonction mât/voilure. Afin de répondreà ces objectifs, deux approches complémentaires de la mécanique des fluides sont mises enœuvre : d’une part, une approche numérique menée à travers des calculs chimères stationnaireset instationnaires de types RANS et URANS; d’autre part une approche expérimentale conduitepar le biais d’essais en soufflerie mettant en œuvre des visualisations par enduit pariétal ainsique de la PIV bi-composante et stéréoscopique. Une cartographie exhaustive de l’écoulement estainsi obtenue autour de la géométrie de référence et des différents effets de forme. Combiné àun algorithme de suivi des structures cohérentes, les phénomènes tourbillonnaires en interactionpariétale forte sont alors précisément caractérisés. En l’absence de dérapage, l’écoulement autourde la géométrie de référence en incidence est symétrique. Deux structures tourbillonnairescontra-rotatives, générées de part et d’autres des flancs du mât simplifié sont advectés sur l’extradosde la voilure. Cette topologie d’écoulement, partiellement connue de la littérature, a enpartie permis de valider les méthodes expérimentales et numériques mises en place ici. La miseen dérapage de la géométrie en incidence complique l’écoulement et permet de restituer uneorganisation tourbillonnaire analogue à celle rencontrée sur un avion réel, avec en particulier lagénération d’un tourbillon trombe. Le bon accord des résultats expérimentaux et numériques, etla complémentarité des méthodes ont ainsi apporté des éléments de réponse sur les mécanismesà l’origine des décollements locaux d’extrados, qui favorise le décrochage prématuré de la voilure. / At low speed/high angle of attack flight conditions, the presence of the powerplant installationunder the wing initiates a complex and unsteady vortical flow field at the nacelle/pylon/wingjunctions. In particular, it results the occurrence of a tornado-like vortex on the pylon crestwhich is advected close to the upper wing. The interaction of this vortical flow with the upperwing boundary layer causes a drop of aircraft performances and can promote a premature stallmechanism. In this flight conditions, the flow field around the engine installation is led by theconcomitance of local boundary layer separations, vortex-wall and vortex-vortex interactions,instabilities like vortex breakdown as well as a strong adverse pressure gradient imposed by thewing.First, thanks to a targeted bibliographic research the present thesis work aims at identifyand analyse the vortical flow field imposed by the presence of the engine installation close tothe wing, in order to have a more comprehensive knowledge of the complex physics. So, it isinitially proposed to simplify the nacelle/pylon/wing configuration of a real transport aircraftby isolating some fundamental mechanisms responsible for this vortical physics, highly designsensitive.In certain conditions of angle of attack and side-slip angle, this simplified geometry isable to recover this particular vortex dynamics interacting with the upper wing boundary layer.Second, based on this previous work, the influence of different local changes of pylon designas well as the influence of the swept wing on the vortex dynamics, and more particularly on thetornado-like vortex are characterised.In order to fulfil these objectives, this thesis work relies on Reynolds Averaged Navier Stokes(RANS) and unsteady Reynolds Averaged Navier Stokes (URANS) computations, oil flow visualizationsand stereoscopic Particle Image Velocimetry (3C-PIV) measurements. An exhaustivecartography of the flow field is then obtained around the simplified geometry and the differentdesign effects. The vortex dynamics thus produced is described in terms of vortex core position,intensity, size, tangential velocity and fluctuating intensity thanks to a vortex trackingapproach. Without side-slip angle, the flow field around the simplified geometry at incidence issymmetric and is characterized by the separation and the longitudinal rolling-up of the cylinderboundary layer into two main counter-rotating vortices distributed on both sides of the cylinder.This vortical topology, partially known in the literature, enables to validate numerical andexperimental methods used here. With a certain side-slip angle, the analysis of the simplifiedgeometry brought to light a more complex vortex dynamics, close to a real aircraft in high-liftflight conditions. This analysis, obtained from the computations and the PIV measurements,highlights the influence of the tornado-like vortex initiated at the pylon/wing junction on theseparation process of the boundary layer near the upper wing leading-edge, which can lead tothe premature stall mechanism.

O fenômeno de vibração induzida por vórtices em travessas de pré-distribuidores de turbinas hidráulicas tem sido estudado nos últimos anos e várias soluções têm sido adotadas para minimizar interferências na estrutura que podem causar fratura por fadiga. O princípio básico das modificações é alterar o perfil da travessa de modo que as frequências de emissão de vórtices não coincidam com as frequências naturais da estrutura. Este trabalho tem como objetivo avaliar através de uma série de simulações computacionais um perfil mais adequado para um pré-distribuidor de turbina Francis. Essas simulações envolvem o cálculo do escoamento ao redor da travessa e da vibração induzida por vórtices nele presentes, bem como uma técnica que combina as análises dinâmicas com uma otimização paramétrica. Para isso, foi utilizado um código comercial de CFD, ANSYS Fluent e o cálculo da resposta estrutural e seu acoplamento com as equações do escoamento foi feito através de uma UDF (User Defined Function). Para validar a metodologia, a resposta estrutural de um corpo prismático sobre base elástica foi calculada e comparada a dados previamente publicados na literatura. Por fim, um código desenvolvido controla a análise fluido-estrutural e passa as variáveis para o otimizador Mode Frontier, que trabalha para encontrar a estrutura mais eficiente variando-se os parâmetros pré-determinados da geometria da peça. A metodologia desenvolvida tem a vantagem de ajudar no projeto de tais componentes sem depender excessivamente de métodos experimentais ou regras empíricas. Dessa forma, torna possível modificar perfis existentes ou desenvolver perfis novos baseado nos melhores critérios de manufatura. / Vortex induced vibration phenomena in hydraulic turbines stay vanes have been studied in the last years and several solutions have been adopted in order to minimize interferences that can cause fatigue in the structure. The basic principle of all modifications is to change the stay vane profile so the natural vortex shedding frequency is different from the natural frequencies of the structure. This work presents a detailed computational simulation of a Francis turbine stay vane whose main objective is to find out a more suitable profile these components should assume. These simulations involve the calculation of the flow around the vanes and the associated vortex induced vibration in the structure in addition to a technique that combines the dynamic analysis with a parametric optimization In order to do that, a commercial CFD code, ANSYS Fluent, was adopted and the calculation of the structural response and its coupling with the flow equations was done with User Defined Functions. Validation of the methodology was made by comparing the structural response of an elastically-mounted prismatic body immersed in uniform flow with previously published data. Finally, a developed code controls the FSI analysis and provides information about the vibrations to the Mode Frontier optimizer, responsible to address the problem and determine the set of parameters that lead to the most efficient structure. The methodology developed has the advantage of helping the design of such components without depending excessively on experimental methods or empirical rules. Also, it allows either modifying existing profiles or choosing the best shape for new ones based on the best manufacturing criteria.

Made available in DSpace on 2016-08-18T18:19:31Z (GMT). No. of bitstreams: 1 Dissertacao Carlisson.pdf: 4828932 bytes, checksum: 305583106a3e64ae56a6815426ff10bc (MD5) Previous issue date: 2012-02-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work addresses the effects of spontaneous Lorentz symmetry breaking on the vortex solutions of the abelian Maxwell-Higgs (AMH) model. Our model is composed by the usual AMH model where the kinetic part of the gauge field is supplemented by a non-birrefringente CPT-even term contained in the electrodynamic sector of the Standard Model extension (SME) of Colladay & Kostelecky. The work is developed in the following way: In the chapter 1, we start by doing a review about topological defects in (1+1)-dimensional scalar field theories. Based on the criterion of energy finiteness, it has been established appropriated boundary conditions for the fields. By following the well-known Bogomol nyi s method and by minimizing the system energy, we have obtained the BPS equations (first order equations) which solves the Euler-Lagrange second order equations. By last, we study the more simples topological defect, named kink, which is obtained from a λϕ4 scalar field theory. The kink solution connects two different minimum energy potencial states or vacuum s states. The second chapter is devoted to the study of stationary BPS v´ortices in field theories where abelian gauge fields are coupled to the Higgs field. The first field theory to be studied is the Maxwell Higgs model in a |ϕ|4-type potencial. Next, we study the BPS vortex solutions in a model with a pure Chern-Simons term coupled to the Higgs field (CSH), subject to a |ϕ|6-type potencial. The third and last model to be analyzed is the Maxwell-Chern-Simons-Higgs model (MCSH). To obtain charged BPS vortex in MCSH model, it is necessary to introduce a dynamical and neutral scalar field N coupled to the Higgs field in a modified |ϕ|4 which depends explicitly of the field N. In the third and four chapters, we present the original contributions of the present monograph. We study the Maxwell-Higgs model in the presence of Lorentz-violating CPT-even terms belonging to the nonbirefringent electrodynamics of the SME. The nonbirefringent SME term is composed by both parity-even and parity-odd sectors. The third chapter we shows that the parity-even LIV coefficients admit only uncharged BPS and non-BPS v´ortices in the usual |ϕ|4-potencial. Our analysis shows that the parity-even LIV parameter controls the radial thickness of the profile of the defect, which can become narrower or wider (approaching to the standard behavior of a compacton-type defect). In chapter 4, we show that the LIV parity-odd parameters allow the existence of BPS-type charged vortices if we include a neutral scalar field Ψ in the original model, the situation is similar to what occurs in the MCSH model . We use a |ϕ|4-potencial which explicitly depends in the field Ψ and its derivative. / Esta dissertação aborda os efeitos da quebra espontânea da covariância de Lorentz na obtenção das soluções estacionárias de vórtices BPS e não-BPS no contexto da eletrodinâmica de Maxwell-Higgs abeliana suplementada pelo setor de gauge CPT-par e não-birrefringente do Modelo Padrão Estendido (MPE) de Colladay & Kostelecky. O trabalho inicia fazendo uma revisão sobre defeitos topológicos em modelos de campos escalares em (1+1)−dimensões. A partir do critério de finitude da energia estacionária, estabelecemos condições de contorno sobre os campos e suas derivadas. Apresentamos, também o bem conhecido método de Bogomol nyi, usado para obter as equações BPS que minimizam a energia do sistema. Por fim, apresentamos o defeito tipo Kink com o potencial tipo ϕ4, que conecta estados assintóticos de mínima energia (vácuos) diferentes. No segundo capítulo, seguindo o procedimento de Bogomol nyi, obtemos as soluções de vórtices BPS estacionárias em modelos abelianos acoplados ao campo de Higgs. Iniciamos com o modelo Maxwell-Higgs submetido a um potencial tipo |ϕ|4, usando o ansatz rotacionalmente simétrico a fim de obter as equações de vórtices BPS, e impondo condições sobre os campos na origem/no infinito. Em seguida, estudamos as soluções de vórtices BPS no modelo Chern-Simons puro acoplado ao campo de Higgs (CSH), sujeito a um potencial do tipo |ϕ|6. Apresentamos uma importante relação de acoplamento entre o setor elétrico e o setor magnético, e obtemos as equações BPS e a energia mínima do modelo, via o método de Bogomol nyi. Ainda neste capítulo, estudamos vórtices BPS no modelo Maxwell-Chern-Simons-Higgs (MCSH). Para isto, argumentamos a necessidade de introduzir no modelo um campo escalar neutro N dinâmico submetidos a um potencial do tipo |ϕ|4 dependente do campo N. As condições sobre N também foram obtidas. No terceiro capítulo, apresentamos a primeira contribuição original deste trabalho. Consideramos o modelo Maxwell-Higgs na presença de termos CPT-pares que violam a covariância de Lorentz, pertencentes ao MPE. Iniciamos usando uma parametrização que retém apenas o setor não-birrefringente do modelo. Escrevemos as equações de movimento e aplicamos a prescrição usual para soluções rotacionalmente simétricas, obtendo soluções de vórtices descarregados BPS e não-BPS para um potencial do tipo |ϕ|4. Nestas, o parâmetro de violação de Lorentz (paridade-par) desempenha papel importante, permitindo controlar a espessura do perfil do defeito, que pode tornar-se mais estreito (aproximando-se do padrão compacton ) ou mais largo. No capítulo 4, mostramos que os parâmetros da quebra de Lorentz de paridade-ímpar possibilitam a obtenção de vórtices carregados sempre que seja inserido no modelo um campo escalar neutro Ψ na lagrangiana, similarmente ao que ocorre no modelo MCSH. Usamos um potencial tipo |ϕ|4 dependente do campo Ψ e de sua derivada.

A extensão dos fenômenos quânticos em escala macroscópica é responsável por toda uma classe de efeitos como a supercondutividade, superfluidez, e condensação de Bose-Einstein, as quais desempenham um papel central na física ao longo do século passado. A produção dos primeiros condensados de Bose-Einstein tornou possível a realização de experimentos envolvendo fenômenos quânticos macroscópicos com um nível sem precedentes de controle dos parâmetros externos. As correntes persistentes em condensados estão intimamente relacionados com a nucleação de vórtices quantificados, que são defeitos topológicos como resposta à transferência de quanta de momento angular. Um método convencional para geração de tais defeitos consiste em confinar a nuvem atômica condensada em uma armadilha com rotação. Acontece que, para velocidades angulares acima de um valor crítico, estados de vórtice se tornam energeticamente favoráveis, induzindo assim a criação de vórtices quânticos. Realizações experimentais de condensados de átomos de metais alcalinos confinados por potenciais dependentes do tempo permitiram a observação não só de redes de vórtices, mas também de turbulência quântica. Uma vez que a turbulência quântica é caracterizada pela presença de um emaranhado de vórtices quânticos interagindo entre si, uma correta compreensão da dinâmica, formação e estabilidade de vórtices tem se mostrado de grande importância sendo objeto de muitos trabalhos teóricos. Em particular, o papel das excitações acústicas geradas pelo decaimento de vórtices de multipla carga no desenvolvimento de turbulência ainda é uma questão em aberto. Este trabalho tem como objetivo fornecer um conjunto de ferramentas que ajude a identificar a presença, como também a carga de vórtices em nuvens (não turbulentas) observadas utilizando imagens de tempo-de-voo. Temos feito um estudo detalhado de condensados contendo vórtices carga múltipla colocados no seu centro, onde a dinâmica do tempo-de-voo é apenas de nossos pontos de interesse. Devido ao controle que este sistema fornece experimentalmente, os modos coletivos tornam-se uma descrição importante, uma vez que podem ser excitadas usando métodos experimentais bem estabelecido tal como a modulação do comprimento de espalhamento de ondas-s, e que também pode ser responsável pelo decaimento do vórtice. Para tais fins, temos utilizado o método variacional (semi-analítico), e o cálculo totalmente numérico da equação de Gross-Pitaevskii. Assim, descrevemos os modos coletivos que acoplam a dinâmica do vórtice com as oscilações das componentes externas do condensado, bem como os efeitos em tempo-de-voo. O momento angular atua aumentando a energia cinética em torno do núcleo de vórtice, que implica em um aumento mais rápido da direção perpendicular a este. Esta situação desloca as freqüências de oscilações coletivas de um estado livre de vórtice, e gera modos coletivos mais ricos devido ao acoplamento. Agora, existem quatro modos possíveis, sendo dois tipos de modo monopolar e dois tipos de modos de quadrupolo. A diferença dentre tais modos é a fase de oscilação do vórtice. Quando se considera flutuações sem simetria polar, seus modos coletivos resultam no decaimento do vórtice. A fim de controlar e prevenir estes processos propusemos três mecanismos dinâmicos, tais como a modulação de comprimento de espalhamento, a modulação das frequências da armadilha harmônica e modulação da amplitude do potencial de Laguerre-Gauss. O último tem provado ser mais eficaz. / The extension of quantum phenomena into macroscopic scales is responsible for a whole class of effects such as superconductivity, superfluidity, and Bose-Einstein condensation, which played central roles in physics throughout the last century. The production of the first Bose-Einstein condensates made possible the realization of experiments involving macroscopic quantum phenomena with an unprecedented level of control of the external parameters. The persistent currents in condensates are intimately related to the nucleation of quantized vortices, which are topological defects as response to transference of quanta of angular momentum. A conventional method for generation of such defects consists in confining the condensed atomic cloud into a rotating trap. It turns out that, for angular velocities higher than a critical value, vortex states become energetically favorable, thus inducing the creation of quantized vortices. Experimental realizations of condensed alkali-metal atoms confined by more general time-dependent potentials allowed the observation not only of vortex lattices but also of quantum turbulence. Since quantum turbulence is characterized by the presence of a self-interacting tangle of quantized vortices, the correct understanding of dynamics, formation, and stability of vortices has shown to be of paramount importance being the subject of many theoretical works. In particular, the role of acoustic excitations generated by decaying multi-charged vortices in the development of turbulence is still an open question. This work aims to provide a set of tools that helps to identify the presence as well as the charge of vortices in non-turbulent clouds observed using time-of-flight pictures. We have done a detailed study of condensates containing multi-charged vortices placed at its center where time-of-flight dynamics is only one point of our interest. Due to the control that this system provides experimentally, the collective modes become an important description since they can be excited using well stablished experimental methods as such as modulation of the s-wave scattering length, and they can also be responsible to vortex decaying. For such purposes we have used the semi-analytical variational method, and the fully numerical calculation of Gross-Pitaevskii equation. Thus we have describes the collective modes that couples dynamics of vortex with the oscillation of external components of condensed atomic cloud as well as the effects in time-of-flight. The angular momentum acts increasing the kinetic energy around the vortex core, which results in a faster expansion of perpendicular direction to it. This situation shifts the frequencies of collective oscillations of a vortex-free state, and generates richer collective modes due the coupling. Now there are four possible modes, being two types of monopole mode and two types of quadrupole modes. The difference among these types is the phase of vortex oscillation. When one considers fluctuations without polar symmetry, their collective modes result in the vortex decaying. In order to control and prevent these processes we have proposed three dynamical mechanisms such as modulation of s-wave scattering length, modulation of frequencies of harmonic trap, and modulation of the amplitude of Laguerre-Gauss potential. The last one has proven to be more effective.

Neste trabalho descrevemos a produção e estudo de excitações topológicas em um condensado de Bose-Einstein em átomos de Rubídio-87. O condensado é produzido através de resfriamento evaporativo forçado por rádio-freqüência em uma armadilha puramente magnética do tipo QUIC. A armadilha magnética é carregada por um sistema de duplo-MOT. A temperatura de transição é de cerca de 150nK. Condensados puros com 1 - 2 × 10^5 átomos de Rb-87 são observados. Realizamos uma caracterização da amostra em relação às suas características fundamentais. Fração condensada, expansão anisotrópica, distribuição espacial e efeitos de temperatura finita são descritos. Com o objetivo de observar excitações coerentes do condensado entre os estados da armadilha, adicionamos um campo magnético do tipo quadrupolo esférico oscilante no tempo. Observamos, no entanto, a transferência de momento angular para a amostra com a formação de vórtices e arranjos de vórtices. Definimos regiões de amplitude que geram números de vórtices crescentes. Observamos a formação de estruturas de três vórtices não convencionais donde supusemos a possibilidade de excitação conjunta de vórtices e anti-vórtices. Observamos evidência de turbulência quântica, um estado onde os arranjos dos vórtices não são regulares nem as linhas de vórtices têm um eixo de rotação comum. / In this work we describe the production and investigation of topological excitations in a Bose-Einstein condensate in Rubidium-87 atoms. The condensate is produced through forced evaporative cooling by radio-frequency in a QUIC-type purely magnetic trap. The magnetic trap is loaded from a double-MOT system. Transition temperature is about 150nK. Pure condensates containing 1-2×105 87Rb atoms are observed. We performed the characterization of the sample in relation to its fundamental aspects. Condensed fraction, anisotropic expansion, spacial distribution and finite temperature effects are described. Aiming to observe coherent topological excitations of the condensate between two states of the trap, we added a spherical quadrupole magnetic fields oscillating in time. We observe, instead, angular momentum tranference to the sample and the formation of vortices and arrays of vortices. We define amplitude regions where an increasing number of vortices are observed. We observe the formation of non-usual three-vortex structures from which we infer the existence of vortices and anti-vortices together in the sample. We observe evidence of quantum turbulence, a state where non-regular vortex arrays appear as well as vortex lines have no preferred direction to form.

L’étude des vortex trouve sa justification dans le rôle que ces derniers jouent dans la turbulence quantique. L’équation de Gross-Pitaevskii ne peut pas nous permettre de modéliser convenablement l’Hélium superfluide, mais on peut l’utiliser pour obtenir le paramètre d'ordre d’un superfluide modèle, ayant le maximum de propriétés en commun avec l’Hélium, notamment une courbe de dispersion identique, par la modification du terme d’interactions.En supposant que le minimum roton influence l’essentiel de la physique, on détermine la forme du paramètre d’ordre loin de la perturbation créée par le vortex rectilinéaire axisymétrique par deux approches différentes - il apparaît alors que seuls deux paramètres sont nécessaires pour caractériser entièrement le profil.Le modèle proposé par Pomeau-Rica, qui offre la possibilité d’étudier le superfluide près de la cristallisation, met en lumière l’impact de la profondeur du minimum roton sur l’amplitude des oscillations. Par comparaison avec les résultats obtenus ab initio par Reatto, les résultats donnés par le modèle de Berloff-Roberts exhibent un déphasage marqué, qui semble être une conséquence non-physique de la forme du spectre d’excitation. Les calculs énergétiques laissent à penser que les oscillations portent une faible fraction de l’énergie du vortex, l'énergie cinétique dominant.Le calcul du paramètre d’ordre est effectué pour un anneau de grande taille par rapport à la distance interatomique, à vitesse nulle et à vitesse non-nulle. La détermination des énergies potentielle et cinétique permet d’accéder à la vitesse maximale atteinte par l’anneau en fonction de son rayon et de la comparer à la vitesse critique de Landau. / Vortices study's justification lays in the fact that those former play an important part in quantum turbulence. The Gross-Pitaevskii equation can't be a proper model for superfluid helium, but we can still use it to determine the order parameter of a theoretical superfluid, which has then the maximum amount of properties in common with liquid helium, and in particular, the same dispersion relation, thus gained by modifying the interaction terms.We then make the assumption that all the physical properties of the superfluid are triggered by the existence of the roton minimum, which allows us to calculate the order parameter far from the perturbation created by an axisymmetric rectilinear vortex, using two different methods. At that point, it appears that only two parameters are needed to fully characterize vortex profil.Pomeau-Rica's model offers the possibility to study the superfluid near crystallization and reveals the influence of the roton minimum's shape and depth on oscillations' amplitude. Results are subsequently compared to those given by Reatto's ab initio calculations. In Berloff-Roberts' model, profil displays a strong phase shift, which seems to be a non-physical consequence of the dispersion relation's shape at high frequencies. Energies reckoning leads us to think that oscillations carry a small fraction of the total vortex' energy, meaning that the kinetic energy is dominant.The order parameter for a vortex ring, whose radius is much larger than the interatomic distance, is calculated at zero and nonzero speed. Potential and kinetic energies are estimated and help us obtain the maximal speed reached by such a ring, depending on its radius and finally discussed this speed in regard to the Landau critical speed.

In canonical boundary layer transition, a uniform laminar flow perturbed by 2-d T-S waves develops downstream into 3-d waves, which eventually break down with turbulent spots appearing. Previous experimental studies have established that this kind of development is absent, is by-passed, in transition induced by free-stream turbulence or surface roughness. However a common, characteristic feature of the late, three-dimensional stage is the prevalence of streamwise vorticity and streaks. Isolated and multiple streamwise vortices are present in both, canonical transition and bypass transition. This thesis de-scribes an experimental study of the late stages of boundary layer transition after a single or a pair of streamwise vortices have formed. The present work can be considered both as a study of transition induced by surface roughness and as a study of the late stages of transition in general. The experiments were made on a zero-pressure-gradient boundary layer in a low speed wind tunnel. Various hill configurations, mounted on a flat plate, were used to create isolated and multiple streamwise vortices. Particle image velocimetry (PIV) and hot-wire anemometry used for measurements. Numerical simulations of the initial laminar stage were carried out to understand the vortex formation at the edge of the hills. Computations have shown that the streamwise vorticity induced by the spanwise asymmetry of the hill rolls up into a single streamwise vortex. The streamwise vortex causes high speed fluid to be brought close to the wall and low speed fluid to move away. In turn, streamwise velocity profiles acquire inflections in both the spanwise and wall-normal directions. Previous studies have concluded that the inviscid instability of inflectional profiles are essential, or at least common, precursors to transition. Another view of the structure of bypass transition induced involves a secondary instability of streaks that can be sinuous or varicose. These two types follow from instabilities of the inflectional spanwise and wall-normal profiles of the streamwise velocity, respectively. However the present study confirms that the occurrence of inflections is not sufficient for transition. The first series of experiments were with smooth Gaussian shaped hills that spanned one-half of the tunnel. Two hill shapes were taken, steep and shallow. Isolated streamwise vortices formed by the side of the hill. Hill heights were less than that of the incoming boundary layer, and they were mounted within the subcritical part of the boundary layer. At low free stream speeds, streaks formed, with inflectional wall-normal and spanwise velocity profiles, but without effecting transition. The necessary conditions for inviscid instability Rayleigh’s inflexion-point theorem and Fjortoft’s theorem are satisfied for these low-speed non-transitional cases. Transition observed at higher speeds show two kinds of development. With the steep hill, the streamwise vortex is not too close to the plate and it exhibits oscillations over some distance before flow breaks down to turbulence; streamwise velocity signals exhibited the passage of a wave packet which intensified before break-down to turbulence. This dominant mode persists far downstream from the hill even while the flow breaks down and frequency content grows over a range of scales. With the shallow hill, the breakdown develops continuously without such a precursor stage; there was a broad range of frequencies present immediately downstream of the hill. For the steep hill the maximum fluctuation is observed on the upwash side of the vortex. With the shallow hill, the fluctuation level is maximum at the location between low and high speed streak. Features of breakdown to transition caused by these single streamwise vortices are found to be similar to those in transition by other causes such as surface roughness, freestream turbulence etc. With the steep hill, the growth of fluctuations(urms, the peak levels of streamwise velocity component fluctuations) is remarkably similar to that in the K-type transition. Unlike in freestream induced transition, the initial growth of u2 rms,max with downstream distance was not linear. Profiles of urms/urms,max vs. y/δ∗where δ∗,is the displacement thickness is partially matching with the optimal disturbances, for the steep hill case. The phase velocity matches as in previous measurements of roughness induced transition. The flow exhibits the breakup of a shear layer near the outer edge of the boundary layer into successive vortices. This breakdown pattern resembles to those in the recent numerical simulations. The passing frequency of these vortices scales with freestream velocity, similar to that in single-roughness induced transition. Quadrant analysis of streamwise and wall-normal velocity fluctuations show large ejection events in the outer layer. The difference in the route to transition between the steep and shallow hills was considered to the relative proximity of the initial streamwise vortex to the flat plate and its interaction with the wall. To examine this conjecture, two configurations were prepared to produce two types of counter-rotating streamwise vortices. One is a hill that span the tunnel except for a short gap, and the other, its complement, is a short span hill. The short-gap hill produce a pair of vortices with the common flow directed away from the wall. This resulted in a separation bubble that formed a short distance downstream and breakdown to turbulence. The short-span hill configuration seems to have a stabilizing effect. With the short gap hill, transition occurs for lower freestream speeds than with the isolated vortices considered before. Also, the breakdown location is further downstream when the gap is larger. The initial velocity profiles look similar for transitional and non-transitional flow cases, and are inflectional, which clearly indicates that inflectional instabilities are not effective here. A separation index was computed to identify unsteadiness of the separated flow region. The separation is itself steady, where as the reattachment is unsteady. Fluctuations grow near this reattachment zone. The unsteadiness of the reattachment coexists with the appearance of strong fluctuations and transition. It is likely that the this last stage of breakdown results when the shear layer, lifted up by the separation bubble, breaks down near the edge of the boundary layer and the consequent unsteadiness is in the reattachment also. Coherent cat’s-eye-like patterns were observed in a longitudinal, plane normal to the wall. With isolated vortices sinuous oscillations and with stream-wise vortex pairs varicose oscillations were observed in wall-parallel planes. In both cases passing frequency of these vortices scales with freestream velocity. Λ-type vortices were identified in spanwise plane with counter-rotating legs. These experiments have identified some possible roles of streamwise vortices in the last stages of boundary layer transition. Vortices may undergo their own instability in the background shear layer, evident as oscillations, if they are not too close to the wall. Otherwise the breakdown is without such a stage. Wall interaction of these vortices seems to be a necessary last stage. Inflectional instability is not indicated. Wall interaction that results in separation results in break-down in the unsteady reattachment zone. Breakdown coexists with the reattachment and not at separation, even though it may be the separating shear layer that breaks down.

Ce travail de thèse porte sur les propriétés de stabilité des tourbillons hélicoïdaux, structures que l'on retrouve notamment dans le sillage des rotors d'hélicoptères et d'éoliennes.Dans une première partie, le développement spatio-temporel de l'instabilité d'appariement est caractérisé à l'aide d'un code numérique pseudo-spectral pour une allée infinie d'anneaux tourbillonnaires. On montre que ce modèle axisymétrique d'écoulement est en effet une bonne approximation du système hélicoïdal dans la limite des grands rayons et petits pas d’hélice. Dans ces conditions, et en utilisant un adimensionnement judicieux, on obtient également que le résultat théorique pour le taux de croissance spatio-temporel obtenu pour une double allée de tourbillons ponctuels s’avère être une bonne prédiction pour le cas hélicoïdal.Dans une seconde partie, on décrit comment un ou plusieurs tourbillons hélicoïdaux ont pu être générés de façon très peu perturbée à l’aide de modèles réduits de rotors dans le canal hydrodynamique du laboratoire. Grâce à l’introduction de perturbations d’amplitudes et de fréquences soigneusement contrôlées, le taux de croissance de l’instabilité d’appariement a pu être mesuré et comparé aux résultats théoriques. L’évolution non linéaire de ces perturbations ainsi que d’autres modes instables, à plus petites longueurs d’onde, ont également pu être observés expérimentalement pour la première fois.Enfin, ces résultats ont été appliqués au cas des rotors d’hélicoptères pour la prédiction du régime de Vortex Ring State (VRS) et à la transition vers la turbulence du sillage des éoliennes. / This thesis is devoted to the stability properties of helical vortices, which are of interest for applications such as helicopter and wind turbine wakes.In a first part, the spatio-temporal development of the pairing instability is characterised for an infinite array of vortex rings, using a pseudo-spectral numerical code. We show that this axisymmetric flow model is indeed a good approximation of the helical system in the limit of large helix radius and small pitch. Under these assumptions, and by using appropriate dimensionless variables, we also show that the theoretical result concerning the spatio-temporal growth rate for a double row of point vortices represents a good prediction for the helical case.In a second part, we describe how one or several helical vortices were generated in a carefully controlled way using small-scale rotor models in the water channel of the laboratory. Introducing perturbations with well-defined amplitudes and frequencies, the growth rate of the pairing instability could be measured experimentally and compared to theoretical predictions. The non-linear evolution of these perturbations, as well as other unstable modes of smaller wavelengths, were also observed experimentally for the first time.Finally, these results were applied to helicopter wakes for the prediction of the Vortex Ring State (VRS) regime and to the transition to turbulence in wind turbine wakes.

Les tourbillons océaniques de subsurface sont des structures dynamiques qui peuplent l'océan global. Ils sont souvent générés à partir de courants d'échanges entre les bassins d'évaporation semi-fermés (comme la Mer Méditerranée, la Mer Rouge et le Golfe Persique) et l'océan ouvert ou pendant des processus de convection profonde. Ces tourbillons peuvent maintenir une géométrie cohérente sur des échelles de temps pluriannuelles et sont capables, du fait de leur migration, de transporter des quantités significatives de chaleur, sel et nutriments. Les tourbillons de subsurface contribuent donc à la redistribution tridimensionnelle des traceurs océaniques à échelle globale, d'où l'intérêt de connaître leurs positions et déplacements.En général, les tourbillons sont capables de modifier localement la surface de la mer, en générant des anomalies qui permettent leur suivi à travers des observations satellitaires. Notre étude se base sur l'utilisation de modèles analytiques et numériques pour caractériser les signatures induites à la surface par les tourbillons de subsurface; en particulier les anomalies de l'élévation (SSH), de température (SST) et de salinité (SSS) de la surface océanique.D'abord, nous avons étudié les signatures de surface (en SSH) dans un cadre idéalisé. Leurs propriétés ont été mises en relation avec la structure tridimensionnelle des tourbillons, nous permettant de déterminer que seulement les tourbillons de subsurface de meso-échelle océanique sont détectables via les observations altimétriques actuelles. En outre, en utilisant un modèle réaliste, nous avons étudié les signatures de surface des tourbillons d'eau méditerranéenne (MEDDIES) en termes de SSH, SST et SSS. L'étude a mis en évidence des différences entre les signatures en SSH et les signatures thermohalines: les premières montrent des intensités et des structures horizontales toujours liées aux changements structurels des Meddies, alors que les deuxièmes sont plutôt pilotées par la dynamique locale de surface.Enfin, nos résultats montrent que le suivi automatique des tourbillons de subsurface est plutôt envisageable à partir des techniques altimétriques, en valorisant aussi l'apport des futures missions satellitaires à haute résolution, comme SWOT. / Subsurface-intensified vortices are ubiquitous in the world ocean. They are often generated by water mass exchanges between semi-closed evaporation basins (e.g.: Mediterranean Sea, Red Sea, Persian Gulf) and the open ocean or during deep convection processes. These vortices can maintain a coherent geometry during inter-annual timescales and, due to their migration, they are able to carry large amounts of heat, salt and nutrients. Hence, the class of subsurface-intensified vortices participates to the redistribution of oceanic tracers along the three dimensions and at global scale, justifying the interest in determining their positions and mean pathways in the ocean. In general, vortices are able to locally modify the ocean surface generating anomalies that allow one to track them via satellite sensors. Our study, based on the use of analytical and numerical models, deals with the characterization of the sea-surface anomalies generated by subsurface-intensified vortices in terms of Sea-Surface Height (the elevation of the oceanic free-surface, SSH), Sea-Surface Temperature (SST) and Sea-Surface Salinity (SSS).In a first analysis, we have studied the SSH anomalies generated by subsurface vortices in an idealized context. Their properties have been related to the three-dimensional structure of the vortex, allowing us to state that only subsurface mesoscale vortices can be detected by the presentday altimetric observations. Furthermore, using a realistic model, we have studied the sea-surface expression of Mediterranean Water Eddies (MEDDIES) in SSH, SST and SSS. The study has evidenced the main differences between the Meddies-induced SSH anomalies and their thermohaline surface anomalies (i.e., SST and SSS): the first exhibit horizontal structures and intensities that can always be related to the Meddy structural changes at depth, while the second are mostly driven by the local surface dynamics.These studies show that the automatic tracking of subsurface-intensified vortices is mostly possible in an altimetric perspective, further confirming the importance of future high-resolution altimetric satellite missions, like SWOT.