Model-H is used to describe structures found in the phase separation in films of binary liquid mixture that have a surface that is free to deform and also may energetically prefer one of the components. The film rests on a solid smooth substrate that has no preference for any component. On the one hand the study focuses on static aspects by investigating steady states that are characterised by their concentration and film height profiles. A large variety of such states are systematically analysed by numerically constructing bifurcation diagrams in dependence of a number of control parameters. The numerical method used is based on minimising the free energy functional at given constraints within a finite element method for a variable domain shape. The structure of the bifurcation diagrams is related to the symmetry properties of the individual solutions on the various branches. On the other hand the full time dependent model-H is linearised about selected steady states, in particular, the laterally invariant, i.e.\ layered states. The resulting dispersion relations are discussed and related to the corresponding bifurcation points of the steady states. In general, the results do well agree and confirm each other. The described analysis is performed for a number of important cases whose comparison allows us to gain an advanced understanding of the system behaviour: We distinguish the critical and off-critical case that correspond to zero and non-zero mean concentration, respectively. In the critical case the investigation focuses on (i) flat films without surface bias, (ii) flat films with surface bias, (iii) height-modulated films without surface bias, and (iv) height-modulated films with surface bias. Each case is analysed for several mean film heights and (if applicable) energetic bias at the free surface using the lateral domain size as main control parameter. Linear stability analyses of layered films and symmetry considerations are used to understand the structures of the determined bifurcation diagrams. For off-critical mixtures our study is more restricted. There we consider height-modulated films without and with surface bias for several mean film heights and (if applicable) energetic bias employing the mean concentration as main control parameter.

Since the past decade, use of electro-osmotic flow (EOF) as an alternative flow mechanism in microdevices is becoming more popular due to its less bulky and low maintenance system design. However, one of the biggest shortcomings for its usage in mainstream applications is that it requires the concerned liquid to be electrically conductive. One idea can be to use the flow of conductive fluids to transport non-conductive liquids passively via interfacial shear transfer. Such an idea can has numerous applications in a wide range of fields like bio-chemical processing (e.g. lab-on-a-chip reactors, mixers, etc.), to oil extraction from porous rock formations. One of the significant characteristics of micro-scale flows is high surface to volume ratio, which significantly highlights the role of multi-phase interfaces in such dynamics. The presence of a fluid-fluid interface in an EOF necessitates the characterization of the parameters responsible for hydrodynamic instability of such systems. The present work focuses on the role of steady and time-dependent electric stress (Maxwell stress), capillary force and disjoining pressure on fluid-fluid interfacial instability. A linear stability analysis of interfacial perturbation was performed for a thin film of electrolyte under DC and AC electric fields. Through long wave asymptotic analysis of the Orr-Sommerfeld equations, parametric stability thresholds of a thin aqueous film explored. Further, a set of experiments were performed in order to characterize the EOF in a rectangular microchannel. With the help of a Particle Tracking Velocimetry analysis, velocity distributions were obtained which agreed well to the theoretical values. This was further used to estimate PDMS zeta potential, which was found to be within the reported values in the existing literature. Liquid-liquid interfacial deformation was also explored under a time-periodic EOF and a wide range of the magnitudes of capillary force, and diffusive and convective transport.

Diese numerische Arbeit untersucht, wie sich die laminar-turbulente Transition in der Grenzschicht einer ebenen Platte mit elektromagnetischen Kräften verzögern lässt. Erzeugt von einer Elektroden-Magnet-Anordnung in der Platte wirken jene Kräfte im wandnahen Bereich der Strömung. Sie sind wandparallel sowie stromab gerichtet und besitzen zwei Parameter, die Amplitude und die Eindringtiefe. Zwei- und dreidimensionale Direkte Numerische Simulationen, Grenzschichtgleichungslöser sowie lineare Stabilitätsanalyse werden eingesetzt, um zwei Ansätze der Transitionsverzögerung zu verfolgen: Zum einen die aktive Wellenauslöschung, bei der ankommende Grenzschichtinstabilitäten von gegenphasig angeregten Wellen bis zu 97% ausgelöscht werden. Zum anderen können elektromagnetische Kräfte die Grenzschicht beschleunigen und so zu deutlich stabilieren Grenzschichtprofilen führen. Über evolutionäre Optimierung wurde eine räumliche Verteilung von Eindringtiefe und Kraftamplitude gefunden, die den Energieeinsatz minimiert und gleichzeitig laminare Strömung sicherstellt; dennoch bliebt die energetische Effizienz der Beeinflussung unter Eins. / This numerical work investigates how electromagnetic forces may delay laminar-turbulent transition of a flat plate boundary layer. Generated by an array of electrodes and magnets flush mounted in the wall, those forces act within the wall-near flow. They are oriented in wall-parallel, downstream direction and are characterized by two parameters, namely amplitude and penetration depth. Two- and three-dimensional Direct Numerical Simulations, numerical solutions of boundary layer equations and linear stability analysis are applied to study two possible ways of transition delay: first, the so-called active wave cancellation, where an anti-wave cancels incoming boundary layer instabilities by up to 97%. A second option is have electromagnetic forces accelerate the boundary layer, thereby modifying its mean velocity profile for greatly enhanced stability. Using evolutionary optimization, a spatial distribution of force amplitude and penetration depth was obtained that maintains laminar flow while minimizing electrical power consumption of the actuator. However, the energetic efficiency of actuation remains less than unity.

Recently, a new kind of turbulence has been discovered in the flow of concentrated polymer melts and solutions. These flows, known as purely elastic flows, become unstable when the elastic forces are stronger than the viscous forces. This contrasts with Newtonian turbulence, a more familiar regime where the fluid inertia dominates. While there is little understanding of purely elastic turbulence, there is a well-established dynamical systems approach to the transition from laminar flow to Newtonian turbulence. In this project, I apply this approach to purely elastic flows. Laminar flows are characterised by ordered, locally-parallel streamlines of fluid, with only diffusive mixing perpendicular to the flow direction. In contrast, turbulent flows are in a state of continuous instability: tiny differences in the location of fluid elements upstream make a large difference to their later locations downstream. The emerging understanding of the transition from a laminar to turbulent flow is in terms of exact coherent structures (ECS) — patterns of the flow that occur near to the transition to turbulence. The problem I address in this thesis is how to predict when a purely elastic flow will become unstable and when it will transition to turbulence. I consider a variety of flows and examine the purely elastic instabilities that arise. This prepares the ground for the identification of a three-dimensional steady state solution to the equations, corresponding to an exact coherent structure. I have organised my research primarily around obtaining a purely elastic exact coherent structure, however, solving this problem requires a very accurate prediction of the exact solution to the equations of motion. In Chapter 2 I start from a Newtonian ECS (travelling wave solutions in two-dimensional flow) and attempt to connect it to the purely elastic regime. Although I found no such connection, the results corroborate other evidence on the effect of elasticity on travelling waves in Poiseuille flow. The Newtonian plane Couette ECS is sustained by the Kelvin-Helmholtz instability. I discover a purely elastic counterpart of this mechanism in Chapter 3, and explore the non-linear evolution of this instability in Chapter 4. In Chapter 5 I turn to a slightly different problem, a (previously unexplained) instability in a purely elastic oscillatory shear flow. My numerical analysis supports the experimental evidence for instability of this flow, and relates it to the instability described in Chapter 3. In Chapter 6 I discover a self-sustaining flow, and discuss how it may lead to a purely elastic 3D exact coherent structure.

[pt] No presente trabalho estudou-se numericamente a instabilidade das ondas na interface do escoamento estratificado de água e óleo em um canal plano. Esse padrão de escoamento, associado ao estágio inicial da formação de golfada, é comum em aplicações industriais, de áreas como produção de petróleo, nuclear, química e muitas outras. Através da introdução de perturbações controladas na interface do escoamento estratificado, analisou-se a evolução dessas perturbações à luz das teorias de estabilidade hidrodinâmica. Os experimentos numéricos foram realizados utilizando o método de Volume of Fluid (VOF) do simulador comercial ANSYS Fluent versão 15.0. Analisou-se o comportamento do escoamento em dois regimes distintos com relação a amplitude das ondas interfaciais. No primeiro regime, empregaram-se ondas pequenas o suficiente para que efeitos não lineares fossem desprezíveis. Os resultados obtidos apresentaram boa concordância com as previsões fornecidas por um solver das equações de Orr-Sommerfeld, para escoamento bifásico estratificado em um canal, indicando que a ferramenta numérica foi capaz de reproduzir o comportamento das ondas interfaciais. Mostrou-se que existe uma faixa de amplitudes, em torno de 0,2 porcento da altura do canal, a partir da qual os efeitos não lineares se tornam relevantes. No regime não linear foram avaliados diferentes cenários de interação não linear entre ondas, os quais geralmente são associados a transição do regime do escoamento estratificado para golfadas. Identificou-se o cenário mais relevante, analisando-se,a eficiência de cada uma dessas interações isoladamente. Observou-se que interações não lineares entre ondas de comprimento parecido são as que crescem mais rapidamente. Esse mecanismo parece ser dominante também na presença de um grande número de ondas, como é o caso esperado em um evento natural. Utilizou-se um modelo fracamente não linear, baseado nas equações de Stuart-Landau, para modelar o comportamento das ondas no escoamento, obtendo-se excelente concordância com os resultados das simulações. Isso é interessante do ponto de vista prático, pois sugere que modelos não lineares simples, como é o caso da equação de Stuart-Landau, podem ser implementados para melhorar as ferramentas utilizadas para prever mudanças de regime em escoamentos bifásicos. / [en] In the present work, the instability of waves at the interface of the stratified flow of water and oil in a plane channel was numerically studied. This flow pattern, which is associated with the initial stages of slug formation, is common in industrial application in areas such as oil production, nuclear, chemical and many others. Through the introduction of controlled perturbations at the interface of a stratified flow, the evolution of the perturbations was analyzed based on hydrodynamics stability theories. Numerical experiments were performed using the Volume of Fluid (VOF) method of the ANSYS Fluent release 15.0 commercial simulator. The behavior of the flow in two different regimes with respect to the amplitude of the interfacial waves was analyzed. In the first regime, small enough waves were employed so that non-linear effects were negligible. The results obtained presented good agreement with the predictions provided by a solver of the Orr-Sommerfeld equations for stratified two-phase flow in a channel, indicating that the numerical tool was able to reproduce the behavior of the interfacial waves. It was shown that there is a range of amplitudes, around 0.2 per cent of the channel height, above which the non-linear effects become relevant. In the nonlinear regime, different scenarios of nonlinear interaction between waves, which are usually associated with transition from stratified flow pattern to slug flow, were evaluated. The most relevant scenario was identified, based on the efficiency of each independent interaction. It was observed that non-linear interactions between waves of similar length present the fastest growth. This mechanism seems to be dominant also in the presence of a large number of waves, as present in natural events. A weakly nonlinear model, based on the Stuart- Landau equations, was employed to model the wave behavior in the flow, obtaining an excellent agreement with the results of the simulations. This is interesting from a practical point of view, since it suggests that simple nonlinear models, such as the Stuart-Landau equation, can be implemented to improve the tools used to predict regime changes in two-phase flows.

L’objectif de ce travail est d’étendre l’étude locale de la stabilité linéaire des interactions fluide-structure à des domaines peu ou pas encore abordés dans la littérature ; l’influence des interfaces poroélastiques sur les couches limites bidimensionnelles, tridimensionnelles, ou aspirées, ainsi que l’écoulement dans une canopée modélisé par un profil de vitesse réaliste, sont ainsi traités. Les résultats révèlent que dans les couches limites 3D, la compliance réduit le domaine d’instabilité du mode TS dominant mais fait apparaître des modes hydroélastiques ; à l’inverse, la perméabilité stabilise ces derniers tout en déstabilisant l’onde TS, s’apparentant en cela à un amortissement. Sur les ailes en flèche, la transition dépend localement d’instabilités nommées tourbillons Crossflow (CF) d’origine non-visqueuse ; l’effet déstabilisant de la perméabilité sur celles-ci est presque nul tandis que son action positive sur les modes hydroélastiques reste intact, offrant des perspectives prometteuses. Dans le domaine des couches limites aspirées, la quasi-totalité des études publiées reposent sur l’hypothèse d’une perméabilité négligeable et d’une paroi rigide ; or il est démontré ici que la perméabilité (indissociable de la succion) exerce même à faible dose une déstabilisation sur la perturbation dominante et que la compliance (pouvant résulter d’un allègement) provoque l’apparition d’une instabilité absolue. Pour finir, l’attention est portée sur les écoulements dans une canopée -assimilables à des couches de mélange. La stabilité linéaire de l’onde nommée monami ou honami est étudiée sur la base d’un profil de vitesse moyenne réaliste calculé numériquement, puis comparé aux résultats obtenus avec le profil en lignes brisées usuellement employé. L’effet de la force de traînée, communément considéré comme amortissant, se révèle au contraire déstabilisant lorsqu’il est pris en compte dès le calcul du profil de vitesse moyenne. / Local linear stability of fluid-structure interactions is investigated in uncustomary fields such as swept, unswept and asymptotic suction incompressible boundary layers developing over compliant, porous plates –in the limit of small permeability– or relatistically-modeled incompressible flows over a canopy. Results show that compliance has a stabilizing effect on the 3D most instable hydrodynamic mode but allows hydroelastic modes to emerge, which take the form of travelling wave flutter instabilities ; conversely, permeability tends to damp the latter ones but to destabilize the former ones. Transition on swept wings also locally depends on 3D unviscid instabilities called Crossflow vortices, hardly unstabilized by permeability ; this provides promizing outlets, since permeability has still a strong positive effect on 3D hydroelastic modes. In the field of incompressible parallel boundary layer flows with uniform suction through the wall, most of the existing studies are based on the assumption that plate’s porosity and flexibility are negligible. Nevertheless, proof is given here that permeability (linked to suction) exerts a strong destabilizing effect on the Tollmien-Schlichting most instable mode. Besides, compliance (that can result from lightering measures) reveals to provoke an absolute instability that is likely to contaminate the entire domain. Finally, attention is paid to incompressible flows across a canopy, that are similar to mixing layers. Linear stability of the coherent motions called monami or honami is adressed using a relatistically-computed velocity profile, then compared to the results obtained with the customary piecewise linear velocity profile. Then, drag force variations are taken into account as soon as velocity profile computing. The result is that drag happens to have a destabilizing effect on the flow, instead of the commonly admitted damping effect.

Para o projeto de estruturas com perfis de aço formados a frio, é fundamental a compreensão dos fenômenos da instabilidade local e global, uma vez que estes apresentam alta esbeltez e baixa rigidez à torção. A determinação do carregamento crítico e a identificação do modo de instabilidade contribuem para o entendimento do comportamento dessas estruturas. Este trabalho avalia três metodologias para a análise linear de estabilidade de perfis de aço formados a frio isolados, com o objetivo de determinar os carregamentos críticos elásticos de bifurcação e os modos de instabilidade associados. Estritamente, analisa-se perfis de seção U enrijecido e Z enrijecido isolados, de diversos comprimentos e diferentes condições de vinculação e carregamento. Determinam-se os carregamentos críticos elásticos de bifurcação e os modos de instabilidade globais e locais por meio de: (i) análise com o Método das Faixas Finitas (MFF), através do uso do programa computacional CUFSM; (ii) análise com elementos finitos de barra baseados na Teoria Generalizada de Vigas (MEF-GBT), via uso do programa GBTUL; e (iii) análise com elementos finitos de casca (MEF-cascas) por meio do uso do programa ABAQUS. Algumas restrições e ressalvas com relação ao uso do MFF são apresentadas, assim como limitações da Teoria Generalizada de Viga e precauções a serem tomadas nos modelos de cascas. Analisa-se também a influência do grau de discretização da seção transversal. No entanto, não é feita avaliação em relação aos procedimentos normativos e tampouco análises não lineares, considerando as imperfeições geométricas iniciais, tensões residuais e o comportamento elastoplástico do material. / For the design of cold formed steel members, it is essential to understand the effects of local and global instability, since these members typically have a high slenderness and low torsion stiffness. The determination of critical loads and the associated buckling modes contribute to understand the behavior of these members. This work performs a evaluation of three methods for linear stability analysis of isolated cold-formed steel members in order to determine the elastic critical loads and the corresponding buckling modes. Specifically, Ue and Ze shape members were studied with various length, different boundary conditions and loads. The elastic critical loads and buckling modes are determined by means of: (i) analysis with the Finite Strip Method (FSM), by the computer program CUFSM, (ii) beam finite element analysis based on the Generalized Beam Theory (FEM-GBT), by GBTUL program, and (iii) Finite Element Method with shell analysis using ABAQUS program. Some restrictions and warnings regarding the use of the FSM are presented, as well as limitations of the Generalized Beam Theory and precautions to be taken in the shell models. It is also analyzed the influence of the degree of discretization of the cross section. In the present study, no evaluation was made with respect to normative procedures neither nonlinear analyses considering the initial geometric imperfections, residual stresses and elastoplastic behavior of the material.

The effect of rotation on the stability of multiple jets in planetary atmospheres is system- atically investigated. Typically in Jovian planetary atmospheres, multiple zonal jets have been observed and their morphology has been systematically studied. The formation of jets has always been viewed as a nonlinear problem where most work has followed from the ideas of potential vorticity (PV) homogenization or turbulent mixing on a β-plane. In our present work, we have aimed to look at the linear stability of multiple jets in a geophysical fluid, and hope to add further insight into the observed jet profiles in β-plane turbulence. In addition, we also study the evolution and life-cycle of these jets as they interact with each other in a non linear fashion. We begin with the linear stability of the \Bickley jet" using the linearized shallow water quasigeostrophic (QG) equations. We have included a finite deformation radius in our calculations to partially mimic the effects of compressibility. A family of synthetically generated velocity profiles with east-west jets are then studied. In particular, a variety of flow configurations with two jets have been considered with a parameter sweep across jet separation, relative jet strength and thickness. As a broad observation, it is noted that an asymmetric east-west jet profile with a stronger and sharper eastward jet is the most stable of all the profiles considered, and a finite deformation radius further stabilizes such profiles. More realistic jet profiles have also been considered and the role of a finite deformation radius in stabilizing such jets is elucidated. We also examined the nonlinear evolution of multiple jets in a periodic domain and in a channel geometry, as we undertake freely decaying long time simulations of the governing QG equation. As per the \Selective Decay" principle we observe that arbitrary initial conditions approach the flow configuration of the prescribed \suitable end states". In addition, we have shown how a finite deformation length scale modifies these \suitable end states". As a broad observation, we have noted that a linearly unstable jet flow configuration, in the presence of β, breaks down into turbulence and reforms into a more asymmetric jet profile with a stronger and sharper eastward jet. The inclusion of a finite deformation length scale in our calculations, is observed to suppress such jet formation. Similar numerical experiments have been performed in a channel and the results have been compared. Chiefly, for the end states, the nature of the observed jet asymmetry is reversed, i.e., the westward jets are observed to be stronger in a channel.

Ce travail porte sur l'étude expérimentale et numérique de jets coaxiaux de rapports de vitesses débitantes intérieure/extérieure) inférieurs à l’unité, présentant une rotation dans le jet annulaire. Dans un premier temps, des visualisations par tomographie laser ont été réalisées dans les plans méridien et transversaux permettant une description tridimensionnelle de l'écoulement. Pour différents nombres de Reynolds, de rapport de vitesses et de nombre de Swirl, un inventaire des modes dominants a pu être établi. Les champs instantanés de vitesses ont ensuite été mesurés par Vélocimétrie par Imagerie de Particules (PIV). Les résultats de mesures de vitesses longitudinales et azimutales moyennées en temps sont présentés. Une comparaison avec les structures observées par tomographie est proposée. Une décomposition de Fourier a été effectuée permettant d'identifier les modes dominants ainsi que leur position dans la direction radiale. L'approche expérimentale a été suivie par une analyse de stabilité linéaire. Une attention particulière est portée sur l'état de base stationnaire reconstruit à partir des profils de vitesses mesurées par PIV à la sortie du jet. Étant donné que l'écoulement est non parallèle, une approche globale de la stabilité est utilisée. L'étude de la stabilité est basée sur la résolution numérique des équations de Navier-Stokes par des méthodes pseudo-spectrales. L'objectif de cette analyse est de retrouver la carte en mode de Fourier azimutaux observée expérimentalement. Nous nous sommes donc intéressés au taux de croissance le plus élevé de la perturbation pour chaque mode azimutal ainsi qu'à la nature convective/ absolue des modes. Pour finir, une com / This work concerns the experimental and numerical study of coaxial jets with outer to inner velocity ratio lower than unity, presenting a rotation in the annular jet. At first, flow visualizations by tomography laser were used in the meridian and transverse plans in order to provide a spatial description of the flow. For various values of the nondimensional parameters : numbers of Reynolds, outer to inner velocity ratio and Swirl number, an inventory of the dominant modes was be established. Instantaneous velocity fields were then measured by Particle lmaging Velocimetry (PIV). The results of longitudinal and azimuthal time-averaged Velocity fields are presented. A comparison with the structures observed by tomography is proposed. A Fourier decomposition was made allowing to identify the dominant modes as well as their position in the radial direction. Experimental investigation was followed by a linear stability analysis. Special attention is paid to the steady base-flow solution reconstructed from the velocity profiles measured by PIV at the end of the nozzle. Given that the is not parallel, a global approach was used. Study of the stability is based on the numerical solution of the incompressible Navier-Stokes equations with pseudo-spectral methods. The objective of this analysis is to the map of azimuthal Fourier modes observed experimentally. We were thus interested in the most amplified growth rate of the disturbance for every azimuthal mode as well as in the absolute/convective nature of the modes. To conclude, a comparison of the results obtained in both numerical and experimental approaches is proposed.

Cette thèse est consacrée à la vérification de l'analogie entre l'instabilité viscoélastique (VEI) et l'instabilité magnéto-rotationnel (MRI) dans un écoulement képlérien, afin de mieux comprendre le transport du moment dans les disques d'accrétion. Le discriminant de Rayleigh élasto-rotationnel est établi pour clarifier le rôle de l'élasticité dans le VEI. L'analyse de stabilité linéaire (LSA) avec le modèle d’Oldroyd-B est effectuée pour prédire les paramètres critiques des modes viscoélastiques. Il fait apparaître également l'influence de l'élasticité, la viscosité polymérique et d'autres paramètres de contrôle pour le VEI. Des expériences bien contrôlées avec des solutions aqueuses de polyoxyéthylène (POE) et de polyéthylène glycol (PEG) sont effectuées. Nous avons observé le mode stationnaire axisymétrique supercritique avec des solutions de faible élasticité et modes désordonnés sous-critiques avec des solutions de grande élasticité. Les formes et les valeurs critiques de ces modes sont en bon accord avec les prédictions théoriques de LSA. Selon l'analogie, le mode axisymétrique stationnaire est probablement l'analogue de MRI standard, tandis que le mode désordonné est probable que l'analogue de MRI hélicoïdale. La thèse contient aussi des résultats théoriques expérimentaux sur quatre autres régimes de rotation et un cas de limite d'élasticité infinie. / This thesis is devoted to the verification of the analogy between the viscoelastic instability (VEI) and the magnetorotational instability (MRI) in a Keplerian flow, in order to get better understanding of the momentum transportation in accretion disks.The elasto-rotational Rayleigh discriminant is deduced to clarify the role of the elasticity in the VEI. The linear stability analysis (LSA) with Oldroyd-B model is performed to predict critical parameters of viscoelastic modes, and it reveals the influence of the elasticity, polymer viscosity on the VEI. Experiments with well controlled aqueous solutions of polyoxyethylene (POE) and polyethylene glycol (PEG) are conducted. We have observed supercritical stationary axisymmetric mode with solutions of small elasticity and subcritical disordered modes with solutions of large elasticity. Both the flow patterns and the critical values of these modes are in good agreement with the LSA predictions. According to the analogy, the stationary axisymmetric mode is likely the analog of the standard MRI while the disordered mode is likely the analog of the helical MRI. The thesis contains also theoretical and experimental results with four other rotation regimes and the limit case of infinite elasticity.