Les vésicules sont gouttes de rayon de quelques dizaines de micromètres, limitées par une membrane lipidique imperméable d'environ 4 nm d'épaisseur, et immergées dans un fluide visqueux externe. Les propriétés spécifiques de la membrane de la vésicule rendent le système très déformable et très contraint dans le même temps. Les vésicules représentent également un modèle simplifié intéressant pour les globules rouges, car ils partagent aussi certains comportements mécaniques similaires.Ce manuscrit s’intéresse à la modélisation d'une vésicule soumise à des contraintes externes d'origine hydrodynamique, dans le régime Stokes et dans des domaines confinés. À partir d'un modèle BEM déjà existant pour des fluides infinis, des méthodes numériques originales sont développés pour faire face au calcul des interactions entre la membrane de la vésicule et les frontières solides. Une attention particulière est accordée à la situation d'une vésicule qui sédimente vers un mur horizontal et une vésicule soumise à un écoulement de Poiseuille dans un capillaire étroit. / Vesicles are drops of radius of a few tens micrometers, bounded by an impermeable lipid membrane of approximately 4 nm thickness, and embedded in an external viscous fluid. The specific properties of the vesicle membrane make the system very deformable and very constrained at the same time. Vesicles represent also an interesting simplified model for red blood cells, since they also share some similar mechanical behaviours.This manuscript deals with the modeling of a vesicle subjected to external stresses of hydrodynamical origin, in the Stokes regime and in confined domains. Starting from an existing BEM model for free space flows, original numerical methods are developed to deal with the computation of interactions between the vesicle membrane and solid boundaries. A particular attention is paid to the situation of a vesicle sedimenting towards a planar wall and a vesicle submitted to a Poiseuille flow in a narrow capillary.

A presente tese se refere a três principais objetivos. Um objetivo foi desenvolver um código de simulação numérica direta para simulação de ondas de instabilidade em um escoamento de Poiseuille plano. O outro objetivo foi analisá-Io através do Método das Soluções Manufaturadas (MMS), e por fim, um terceiro objetivo foi estudar o regime não-linear da evolução de trens de ondas modulados em um escoamento de Poiseuille plano. O código resolve numericamente, com diferenças finitas de ordem de precisão alta e métodos pseudo espectrais, as equações de Navier-Stokes tri-dimensionais e incompressíveis numa formulação vorticidade-velocidade. O MMS é um método de verificação de código mais completo que os normalmente usados, por exemplo, comparação com teoria de estabilidade linear. O código usa diferenças finitas de ordem alta de precisão, mas com diferentes ordens em diferentes regiões do domínio. O MMS é pouco utilizado neste tipo de código. Concluiu-se que estes códigos em geral não operam na chamada faixa assintótica de erro. Na faixa de trabalho, a ordem do erro varia no domínio computacional de forma consistente com os métodos numéricos empregados. Isto permite, entre outras coisas, a otimização do esquema numérico. Após os testes de verifição, simulações numéricas dos trens de ondas foram realizadas. A análise dos resultados foi feita através das teorias de instabilidade primária e secundária e teoria fracamente não-linear. Foi estudado um trem de ondas modulado numa região do diagrama de instabilidade onde vários estudos para ondas mono cromáticas foram realizados. Os resultados sugeriram que nesta região o regime não-linear de transição dos trens de ondas modulados é governado pela instabilidade tipo-K. Com a redução da amplitude inicial de perturbação um cenário mais complexo, que pode estar envolvendo outros mecanismos, foi observado. Casos mais próximos ao primeiro ramo do diagrama também foram estudados. Nesta região a teoria linear prevê ondas tri-dimensionais sendo as mais instáveis, fato que poderia favorecer a ocorrência da chamada transição oblíqua. Os resultados indicaram que o trem de ondas modulado se divide em duas regiões que tendem-se afastar uma da outra. Apesar de estar associado com a instabilidade linear, este comportamento não havia sido antecipado na literatura. Neste cenário, para trens de ondas modulados isolados, o regime não-linear não pode ser correlacionado claramente com nenhum dos cenários clássicos de transição. Neste contexto transição oblíqua pode estar restrito a situações que envolvem a interação entre trens de ondas modulados. / The current thesis had three objectives. The first objective was to develop a code of direct numerical simulation (DNS) to simulation of waves of instability in a plane Poiseuille flow. The other main objective was to analyze it through the method of manufactured solutions (MMS). Finally, a third objective was to study the nonlinear regime of spanwise modulated wavetrains in a plane Poiseuille flow. Using high-order finite differences and pseudo-spectral methods, the DNS code solved the incompressible three-dimensional Navier-Stokes equations in a vorticity-velocity formulation. The MMS is a verification method more complete than the others more often used, for example, comparison with linear stability theory. The code used different high-order finite differences in different regions of the domain. The MMS has been little used for this type of code. It was concluded that these codes generally do not operate in the so-called errar asymptotic range. In the working range, the observed arder changes in the computational domain in a manner consistent with the numerical methods employed. This allows, among other things, optimization of the numerical scheme. After testing, numerical simulations of the wavetrains were performed. The analysis of the results was made based on the primary and secondary instability theories and weakly non-linear theory. A modulated wavetrain was studied in a region of the stability diagram where several studies for monochromatic waves were performed. The results suggested that in this region the non-linear regime of transition of the modulation wavetrain is governed by the K-type instability. With the reduction of the magnitude of the initial disturbance, a more complex scenario, which may involve other mechanisms, was observed. Cases near the first branch of the instability diagram were also studied. In this region, the linear theory predicts tri-dimensional waves are the most unstable, a fact that could lead to the so-called oblique transition. The results indicated that the modulated wavetrain divided into two regions, which tend move further from each other. Despite being associated with the linear instability, this behavior was not anticipated in the literature. In this scenario, for isolated modulated wavetrains, the non-linear system could not be clearly correlated with any of the classic scenarios of transition. In this context, oblique transition may perhaps to situations involving the interaction between modulated wavetrains.

A presente tese se refere a três principais objetivos. Um objetivo foi desenvolver um código de simulação numérica direta para simulação de ondas de instabilidade em um escoamento de Poiseuille plano. O outro objetivo foi analisá-Io através do Método das Soluções Manufaturadas (MMS), e por fim, um terceiro objetivo foi estudar o regime não-linear da evolução de trens de ondas modulados em um escoamento de Poiseuille plano. O código resolve numericamente, com diferenças finitas de ordem de precisão alta e métodos pseudo espectrais, as equações de Navier-Stokes tri-dimensionais e incompressíveis numa formulação vorticidade-velocidade. O MMS é um método de verificação de código mais completo que os normalmente usados, por exemplo, comparação com teoria de estabilidade linear. O código usa diferenças finitas de ordem alta de precisão, mas com diferentes ordens em diferentes regiões do domínio. O MMS é pouco utilizado neste tipo de código. Concluiu-se que estes códigos em geral não operam na chamada faixa assintótica de erro. Na faixa de trabalho, a ordem do erro varia no domínio computacional de forma consistente com os métodos numéricos empregados. Isto permite, entre outras coisas, a otimização do esquema numérico. Após os testes de verifição, simulações numéricas dos trens de ondas foram realizadas. A análise dos resultados foi feita através das teorias de instabilidade primária e secundária e teoria fracamente não-linear. Foi estudado um trem de ondas modulado numa região do diagrama de instabilidade onde vários estudos para ondas mono cromáticas foram realizados. Os resultados sugeriram que nesta região o regime não-linear de transição dos trens de ondas modulados é governado pela instabilidade tipo-K. Com a redução da amplitude inicial de perturbação um cenário mais complexo, que pode estar envolvendo outros mecanismos, foi observado. Casos mais próximos ao primeiro ramo do diagrama também foram estudados. Nesta região a teoria linear prevê ondas tri-dimensionais sendo as mais instáveis, fato que poderia favorecer a ocorrência da chamada transição oblíqua. Os resultados indicaram que o trem de ondas modulado se divide em duas regiões que tendem-se afastar uma da outra. Apesar de estar associado com a instabilidade linear, este comportamento não havia sido antecipado na literatura. Neste cenário, para trens de ondas modulados isolados, o regime não-linear não pode ser correlacionado claramente com nenhum dos cenários clássicos de transição. Neste contexto transição oblíqua pode estar restrito a situações que envolvem a interação entre trens de ondas modulados. / The current thesis had three objectives. The first objective was to develop a code of direct numerical simulation (DNS) to simulation of waves of instability in a plane Poiseuille flow. The other main objective was to analyze it through the method of manufactured solutions (MMS). Finally, a third objective was to study the nonlinear regime of spanwise modulated wavetrains in a plane Poiseuille flow. Using high-order finite differences and pseudo-spectral methods, the DNS code solved the incompressible three-dimensional Navier-Stokes equations in a vorticity-velocity formulation. The MMS is a verification method more complete than the others more often used, for example, comparison with linear stability theory. The code used different high-order finite differences in different regions of the domain. The MMS has been little used for this type of code. It was concluded that these codes generally do not operate in the so-called errar asymptotic range. In the working range, the observed arder changes in the computational domain in a manner consistent with the numerical methods employed. This allows, among other things, optimization of the numerical scheme. After testing, numerical simulations of the wavetrains were performed. The analysis of the results was made based on the primary and secondary instability theories and weakly non-linear theory. A modulated wavetrain was studied in a region of the stability diagram where several studies for monochromatic waves were performed. The results suggested that in this region the non-linear regime of transition of the modulation wavetrain is governed by the K-type instability. With the reduction of the magnitude of the initial disturbance, a more complex scenario, which may involve other mechanisms, was observed. Cases near the first branch of the instability diagram were also studied. In this region, the linear theory predicts tri-dimensional waves are the most unstable, a fact that could lead to the so-called oblique transition. The results indicated that the modulated wavetrain divided into two regions, which tend move further from each other. Despite being associated with the linear instability, this behavior was not anticipated in the literature. In this scenario, for isolated modulated wavetrains, the non-linear system could not be clearly correlated with any of the classic scenarios of transition. In this context, oblique transition may perhaps to situations involving the interaction between modulated wavetrains.

The Poiseuille Flow is the flow of a viscous incompressible fluid in a channel between two infinite parallel plates. The behaviour of flow is properly described by the well-known Navier-Stokes Equations. The fact that Navier-Stokes equations are partial differential equations makes their solution difficult. They can rarely be solved in closed form. On the other hand, numerical techniques can be applied successfully to the well-posed partial differential equations. In the present study pseudo-spectral method is implemented to analyze the Poiseuille Flow. The pseudo-spectral method is a high-accuracy numerical modelling technique. It is an optimum choice for the Poiseuille flow analysis due to the flows simple geometry. The method makes use of Fourier Transform and by handling operations in the Fourier space reduces the difficulty in the solution. Fewer terms are required in a pseudo-spectral orthogonal expansion to achieve the same accuracy as a lower order method. Karhunen-Lo&egrave / ve (KL) decomposition is widely used in computational fluid dynamics to achieve reduced storage requirements or construction of relatively low-dimensional models. In this study the KL basis is extracted from the flow field obtained from the direct numerical simulation of the Poiseuille flow.

The linear stability of high speed-viscous plane Couette and Couette-Poiseuille flows are investigated numerically. The conservation equations along with Sutherland&amp / #65533 / s viscosity law are studied using a second-order finite difference scheme. The basic velocity and temperature distributions are perturbed by a small-amplitude normalmode disturbance. The small-amplitude disturbance equations are solved numerically using a global method using QZ algorithm to find all the eigenvalues at finite Reynolds numbers, and the incompressible limit of these equations is investigated for Couette-Poiseuille flow. It is found that the instabilities occur, although the corresponding growth rates are often small. Two families of wave modes, Mode I (odd modes) and Mode II (even modes), were found to be unstable at finite Reynolds numbers, where Mode II is the dominant instability among the unstable modes for plane Couette flow. The most unstable mode for plane Couette &amp / #65533 / Poiseuille flow is Mode 0, which is not a member of the even modes. Both even and odd modes are acoustic modes created by acoustic reflections between a will and a relative sonic line. The necessary condition for the existence of such acoustic wave modes is that there is a region of locally supersonic mean flow relative to the phase speed of the instability wave. The effects of viscosity and compressibility are also investigated and shown to have a stabilizing role in all cases studied. Couette-Poiseuille flow stability is investigated in case of a choked channel flow, where the maximum velocity in the channel corresponds to sonic velocity. Neutral stability contours were obtained for this flow as a function if the wave number,Reynolds number and the upper wall Mach number. The critical Reynolds number is found as 5718.338 for an upper wall Mach number of 0.0001, corresponding to the fully Poiseuille case.

Submitted by RODRIGO KOITI ISHIZAKA (rodrigo_ishizaka@hotmail.com) on 2018-04-09T20:10:27Z No. of bitstreams: 1 Dissertação Final PDF.pdf: 10461391 bytes, checksum: a78974d2db3d166540e03d4cee7def37 (MD5) / Rejected by ALESSANDRA KUBA OSHIRO ASSUNÇÃO (alessandra@fct.unesp.br), reason: Solicitamos que realize correções na submissão seguindo as orientações abaixo: - Número de página das referências no sumário está incorreto (consta p.86 quando é p.87); - No sumário consta Apêndices, porém no trabalho não. É finalizado nas referências. Agradecemos a compreensão. on 2018-04-10T12:44:45Z (GMT) / Submitted by RODRIGO KOITI ISHIZAKA (rodrigo_ishizaka@hotmail.com) on 2018-04-10T16:09:35Z No. of bitstreams: 1 Dissertação Final PDF.pdf: 10461372 bytes, checksum: 679a6e28fa80deb9079156b9b6b70c36 (MD5) / Approved for entry into archive by ALESSANDRA KUBA OSHIRO ASSUNÇÃO (alessandra@fct.unesp.br) on 2018-04-10T20:02:48Z (GMT) No. of bitstreams: 1 ishizaka_rk_me_prud.pdf: 10461372 bytes, checksum: 679a6e28fa80deb9079156b9b6b70c36 (MD5) / Made available in DSpace on 2018-04-10T20:02:48Z (GMT). No. of bitstreams: 1 ishizaka_rk_me_prud.pdf: 10461372 bytes, checksum: 679a6e28fa80deb9079156b9b6b70c36 (MD5) Previous issue date: 2018-02-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O presente trabalho de mestrado consiste em apresentar uma modelagem para escoamentos isotérmicos viscoelásticos em que a viscosidade varia de acordo com a pressão e estudos numéricos para alguns problemas bidimensionais, como escoamentos entre placas paralelas e expansão planar 1:4. Para este trabalho é utilizado o modelo viscoelástico Oldroyd-B e uma modelagem linear da viscosidade com relação a pressão. O método numérico desenvolvido é baseado no método da projeção para desacoplar velocidade e pressão nas equações de Navier-Stokes e depois calcula os tensores pela equação constitutiva com a informação da viscosidade variando com a pressão. As equações são discretizadas em uma malha deslocada pelo método de diferenças finitas. Os resultados numéricos são obtidos das simulações de escoamentos em um canal e expansão planar 1:4 bidimensional, cujo foco é destacar algumas diferenças entre o modelo Oldroyd-B Standard e o modelo Oldroyd-B sob influência da viscosidade que varia linearmente com a pressão. Este trabalho de mestrado também tem por objetivo resolver problemas, com fluidos viscoelásticos, em que haja regiões com variações da pressão e estudar estes resultados numéricos comparando-os com o modelo Oldroyd-B Standard. / The present master's work consists in presenting a model for viscoelastic isothermal flows with pressure-dependent viscosity and numerical studies for some two-dimensional problems, such as channel flow and planar expansion 1:4. In this work will be considered the Oldroyd-B viscoelastic model and a linear modeling viscosity with a linear relationship between viscosity and pressure. The numerical method developed is based on the projection method to decouple velocity and pressure in the Navier-Stokes equations and then calculates the tensor from the constitutive equation taking account the pressure-dependent viscosity. The equations are discretized on a staggered grid by using the finite diference method. The numerical results are obtained for two problems: two-dimensional channel and planar expansion 1:4 flows, whose focus is to highlight some diferences between the standard Oldroyd-B model and the Oldroyd-B model under the influence of viscosity that varies linearly with pressure. This master's work aims to solve problems of viscoelastic fluids in which there exist regions where pressure varies and to study these numerical results comparing them with the standard Oldroyd-B model.

Dans cette thèse on cherche à étudier le flux péristaltique des liquides dans un canal à onde de pression déterminée aux confins. Dans la plupart des recherches de systèmes de transportation péristaltiques la variation des coordonnées de la paroi est prédéfinie pour les raisons de commodité. Cependant les parois d’organes creux (comme oesophage intestin grêle, côlon urètre, vaisseaux lymphatiques) dont le fonctionnement consiste à transmettre des produits par la voie péristaltique, sont dotées de barorécepteurs – capteurs qui perçoivent la pression dans la couche limite de fluides et servent à réguler le calibre des vaisseaux. Pour créer le modèle du comportement des systèmes biologiques pareils il nous semble plus adéquat de prédéfinir l’onde de pression aux confins des vaisseaux. Cette approche réalisée dans notre thèse permet de découvrir et décrire des effets nouveaux, inexplorés auparavant. Dans cette thèse nous étudions aussi l’influence des pulsations transversales des parois du canal sur la transmission du produit dues aux chutes de pression. Cet objectif est apparu lors de la détermination de la viscosité du liquide utilisant la méthode des canaux compressibles (squeezing flow viscometry). Des problèmes similaires sont assez répandus dans l’étude d’une variété des systèmes biologiques, en particulier, des mouvements de lubrification des articulations ou des micro-vaisseaux des muscles. Nous avons aussi étudié l’influence du son sur l’interaction d’une particule solide tombante et d’une bulle de gaz montante dans le liquide. La pertinence de ce travail est liée à l’importance de recherche des solutions possibles pour augmenter l’efficacité de flottation, méthode d’enrichissement basée sur l’accrochage des particules minérales par des bulles de gaz / The thesis studies the peristaltic flow of fluid in a channel with the specified pressure wave at the boundary. The law of wall’s coordinate variation isn’t determined a priori. It is found from the initially definite law of pressure-variation on the wall. This way is based on the fact that some hollow organs change diameter under the signals of baroreceptors (sensors that detects the pressure). We studied the effects of various parameters on flow rate and structure of flow. Besides we studied the influence of vibration on the peristaltic flow under long wave approximation. The paper also considers the influence of the wall transverse pulsation on the fluid transport under the pressure drop. This problem arises in defining the liquid viscosity by squeezing flow viscometry. The same problems occur in analyzing different biological systems, including the lubricant movement in joints or in the microvessels of working muscles. The influence of sound on the interaction of a solid particle and a gas bubble in fluid is studied as well.

L'objectif de cette thèse est d'analyser l'influence des non linéarités, du comportement rhéologique des fluides rhéofluidifiants, sur les conditions de stabilité et de transition vers la turbulence. Dans un premier temps, une analyse linéaire de stabilité avec une approche modale a été réalisée. Les résultats obtenus mettent clairement en évidence l'effet stabilisant de la rhéofluidification. Ensuite, une analyse faiblement non linéaire de stabilité a été menée en vue d'examiner l'influence de la perturbation de la viscosité sur la stabilité vis à vis de perturbations d'amplitude finie. L'analyse de la contribution des termes non linéaires d'inertie et visqueux montre que, contrairement aux termes d'inertie, les termes non linéaires visqueux ont tendance à accélérer l'écoulement et favoriser une bifurcation sur-critique. Les effets rhéofluidifiants tendent à réduire la dissipation visqueuse. Finalement, une analyse fortement non linéaire de stabilité a été conduite en utilisant les techniques de suivi de branches de solutions par des méthodes de continuation. Pour pouvoir traiter les termes visqueux fortement non linéaires, un code de calcul pseudo-spectral a été développé. Des solutions non linéaires d'équilibre ont été obtenues et caractérisées pour différentes valeurs des paramètres rhéologiques / The aim of this study is to understand the influence of the nonlinear rheological behaviour of the shear-thinning fluids on the flow stability and transition to turbulence. First, a linear stability analysis using modal approach was carried out. Results clearly highlight the stabilizing effect of shear-thinning. Then, as a first approach to take into account nonlinear effects of viscosity perturbation on the flow stability, a weakly nonlinear stability analysis is performed in the neighbourhood of the critical conditions. Results indicate that shear-thinning reduces the viscous dissipation and, in contrast to inertial terms, the nonlinear viscous terms tend to accelerate the flow and act in favour of supercritical bifurcation. Finally, a nonlinear stability analysis is done by following solution branches in the parameter space using continuation techniques. To deal with highly nonlinear viscous terms, a pseudo-spectral code is developed. Nonlinear equilibrium solutions was found and characterized for various values of the rheological parameters

EDF exploite sur son parc de production de nombreuses machines électriques tournantes. Les contraintes thermiques subies par celles-ci engendrent des échauffements locaux qui nuisent à leur intégrité. Le présent travail contribue à fournir des méthodes de calcul adaptées à la détection et à la localisation des points chauds. Il participe à améliorer la compréhension des écoulements en rotation et leurs effets sur les transferts thermiques. Plusieurs dispositifs expérimentaux, de complexité ascendante, ont été utilisés pour comprendre et valider les simulations numériques. Une première étude sur une marche descendante (demi-pôle) parcourue par un jet de paroi non-confiné a mis en avant des différences par rapport à un jet confiné ; ces deux cas existent dans un alternateur. Une seconde étude menée sur une cavité tournante confinée a analysé l’impact d’un écoulement de Taylor-Couette-Poiseuille sur la température et la position des points chauds créés, en balayant l’ensemble des régimes d’écoulement. Ces études ont mis en exergue une première méthode de calcul fiable, fondée sur l’étude numérique CHT. Une autre méthode, basée sur la FEM couplée à une méthode inverse, a été testée sur une maquette d’alternateur hydraulique afin de pallier aux temps de calcul longs de la première. Cette méthodologie remonte aux coefficients d’échanges convectifs numériques à partir des mesures du champ thermique du rotor, mais n’est envisageable que lorsque l’on dispose de données expérimentales suffisantes. Ces travaux ont aussi mis en évidence de nouvelles techniques de mesures sans contact, comme l’utilisation d’un pyromètre à haute fréquence pour la mesure de température sur des machines tournantes. / EDF operates a large number of electrical rotating machines in its electricity generation capacity. Thermal stresses which affect them can cause local heating, sufficient to damage their integrity. The present work contributes to provide methodologies for detecting hot spots in these machines, better understanding the topology of rotating flows and identifying their effects on heat transfer. Several experimental scale model were used by increasing their complexity to understand and validate the numerical simulations. A first study on a turbulent wall jet over a non-confined backward-facing step (half-pole hydrogenerator) notes significant differences compared to results from confined case : both of them are present in an hydrogenerator. A second study was done on a small confined rotating scale model to determinate the effects of a Taylor-Couette-Poiseuille on temperature distribution and position of hot spots on the heated rotor, by studying the overall flow regimes flow. These studies have helped to obtain a reliable method based on conjugate heat transfer (CHT) simulations. Another method, based on FEM coupled with the use of an inverse method, has been studied on a large model of hydraulic generator so as to solve the computation time issue of the first methodology. It numerically calculates the convective heat transfer from temperature measurements, but depends on the availability of experimental data. This work has also developped new no-contact measurement techniques as the use of a high-frequency pyrometer which can be applied on rotating machines for monitoring temperature.

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.