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A investigação dos mecanismos de instabilidade pode ter um papel importante no entendimento do processo laminar para turbulento de um escoamento. Análise de instabilidade de uma camada limite de uma linha de estagnação compressível foi realizada no contexto de teoria linear BiGlobal. O estudo dos mecanismos de instabilidade deste escoamento pode proporcionar uma visão útil no desenho aerodinâmico das asas. Um novo procedimento foi desenvolvido e implementado computacionalmente de maneira sequencial e paralela para o estudo de instabilidade BiGlobal. O mesmo baseia-se em formar a matriz esparsa associada ao problema discretizado por dois métodos: pontos de colocação de Chebyshev-Gauss-Lobatto e diferenças finitas, além das combinações destes métodos. Isto permitiu o uso de bibliotecas computacionais eficientes para resolver o sistema linear associado ao problema de autovalor utilizando o algoritmo de Arnoldi. O desempenho do método numérico e código computacional proposto são analisados do ponto de vista do uso de métodos de ordenação dos elementos da matriz, coeficientes de preenchimento, memória e tempo computacional a fim de determinar a solução mais eficiente para um problema físico geral com técnicas de matrizes esparsas. Um estudo paramétrico da instabilidade da camada limite de uma linha de estagnação foi realizado incluindo o estudo dos efeitos de compressibilidade. O excelente desempenho código computacional permitiu obter as curvas neutras e seus respectivos valores críticos para a faixa de número de Mach 0 \'< OU =\' Ma \'< OU =\' 1. Os resultados confirmam a teoria assintótica apresentada por (THEOFILIS; FEDOROV; COLLIS, 2004) e mostram que o incremento do número de Mach reduz o numero de Reynolds crítico e a faixa instável do número de ondas. / Investigation of linear instability mechanisms is essential for understanding the process of transition from laminar to turbulent flow. An algorithm for the numerical solution of the compressible BiGlobal eigenvalue problem is developed. This algorithm exploits the sparsity of the matrices resulting from the spatial discretization of the enigenvalue problem in order to improve the performance in terms of both memory and CPU time over previous dense algebra solutions. Spectral collocation and finite differences spatial discretization methods are implemented, and a performance study is carried out in order to determine the best practice for the efficient solution of a general physical problem with sparse matrix techniques. A combination of spectral collocation and finite differences can further improve the performance. The code developed is then applied in order to revisit and complete the parametric analyses on global instability of the compressible swept Hiemenz flow initiated in (THEOFILIS; FEDOROV; COLLIS, 2004) and obtain neutral curves of this flow as a function of the Mach number in the 0 \'< OU =\' Ma \'< OU =\' 1 range. The present numerical results fully confirm the asymptotic theory results presented in (THEOFILIS; FEDOROV; COLLIS, 2004). This work presents a complete parametric study of the instability properties of modal three dimensional disturbances in the subsonic range for the flow conguration at hand. Up to the subsonic maximum Mach number value studied, it is found that an increase in this parameter reduces the critical Reynolds number and the range of the unstable spanwise wavenumbers.

Escoamentos sobre superfícies côncovas estão sujeitos à instabilidade centrífuga, dando origem a vórtices longitudinais, conhecidos como vórtices de Görtler. Esses vórtices são responsáveis por gerar distorções fortes nos perfis de velocidade. Como os vórtices são contra-rotativos, duas regiões surgem entre os mesmos: uma região de upwash e uma região de downwash. Na região de upwash o fluido próximo à parede é jogado para longe da mesma. Na região de downwash acontece o contrário, o fluido que se desloca a uma velocidade maior é jogado em direção à parede. Os vórtices se amplificam inicialmente de forma linear. À jusante na região não linear de desenvolvimento dos vórtices, a amplitude dos mesmos já é elevada, e há a formação de uma estrutura do tipo cogumelo com a distribuição da componente de velocidade na direção principal do escoamento . Essa nova distribuição de velocidade é tridimensional e difere em muito da camada limite obtida com a solução das equações de Blasius. Levando-se em consideração a camada limite térmica, já foi observado que, na média, há um aumento de transferência de calor na direção da parede. No presente trabalho, é verificado numericamente a transferência de calor na presença de vórtices de Görtler. Para tal, foi desenvolvido e implementado um código de simulação numérica direta espacial (DNS - do inglês Direct Numerical Simulation). Os resultados deste trabalho mostram a intensificação da transferência de calor através dos vórtices de Görtler, tanto no regime não-linear como na instabilidade secundária / Flows over concave surfaces are subject to centrifugal instability. It gives rise to stramwise vortices known as Görtler vortices. These vortices are responsible for generating strong distortions in the velocity profiles. As the vortices are counterrotating, two regions arise between them: a region of uowash and a region of downwash. In the upwash region, the fluid near the wall is convected away from it. In the downwash region the opposite happens, the fluid moving at a faster speed is moved towards the wall. The vortices initially amplify linearly in the downstream. When their amplitude is already high, in the non-linear development region, a mushroom-type structure, with the velocity distribution in the main flow direction, is formed. This new three-dimensional velocity distribution is different from the boundary layer obtained with the solution of Blasius equations. Taking into account a thermal boundary layer, on average, an increase in the heat transfer in the wall direction has been observed. In the present work, it is verified numerically the heat transfer in the presence of Görtler vortices. A simulation code was developed and implemanted usin Direct Numerical Simulation (DNS). The results of this work show the intensification of heat transfer through the Görtler vortices both in the non-linear regime and in the secondary instability

Cette thèse s'inscrit dans un contexte d'étude de la dynamique des fronts atmosphériques et océaniques et de l'origine des ondes de gravité dans l'atmosphère. Pour cela on s'intéresse à un front composé de deux couches de fluides miscibles en milieu tournant et soumis à un cisaillement vertical. Un travail à la fois expérimental et numérique met en évidence des phénomènes agéostrophiques qui vont au-delà de la configuration équilibrée usuelle d'un front barocline. D'abord, l'étude des différents régimes instables d'un front en configuration annulaire en terme de nombre de Rossby et de Burger révèle une instabilité agéostrophique couplant des mouvements équilibrés et divergents grâce à la résonance entre une onde de Rossby et une onde de Kelvin. Cette instabilité Rossby-Kelvin a été confirmée numériquement grâce aux structures des perturbations en champs de vitesse dans chaque couche. Ensuite, des structures de petite échelle présentes sur le front ont aussi été observées expérimentalement. Les caractéristiques de l'interface en terme de nombre de Richardson et épaisseurs de l'interface en vitesse et en densité suggère une instabilité de cisaillement de Hölmböe. Une simulation directe numérique axisymmétrique avec un nombre de Schmidt valant 700 confirme cette conjecture. Des ondes inertie-gravité supplémentaires sont observées numériquement sur un mode instable Rossby-Kelvin et le mécanisme de génération de ces ondes est discuté. Enfin l'étude numérique d'un front stable a mis en évidence la présence de couches d'Ekman internes avec une structure additionnelle pour des valeurs élevées de nombre de Schmidt et un faible nombre de Rossby. Dans le cas de front en in/outcropping, la dynamique est modifiée par l'interaction du front avec les couches d'Ekman au niveau du point singulier d'épaisseur nulle. Elle dépend à la fois de la circulation verticale et du mélange sur le nez du front et des nombreuses instabilités possibles associées à des résonances d'ondes horizontalement et verticalement. / This thesis has to be seen within the general study of atmospheric and oceanic fronts and the origin of gravity waves in the atmosphere. In this context we focus on a front in a rotating two-layer miscible fluid under vertical shear. Both experimental and numerical study highlights ageostrophic phenomena going beyond the usual geostrophic equilibrated configuration of a baroclinic front. First, the classification of different instability regimes of a front in an annular configuration as a fonction of Rossby number and Burger number reveals an ageostrophic instability coupling equilibrated and divergent motions due to a resonance between a Rossby wave and a Kelvin wave. This Rossby-Kelvin instability is confirmed numerically by the structure of the perturbation velocity fields in each layer. Second, small-scale structures have also been observed experimentally. Caracteristics of the interface in function of Richardson number and density and velocity interface thicknesses suggests the presence of the Hölmböe shear instability. A direct numerical simulation with an axisymmetric configuration and with a Schmidt number 700 confirms this conjecture. Other smalle-scale perturbations compatible with inertia-gravity waves have been observed numerically superimposed on an unstable Rossby-Kelvin front and the wave generation mechanism is discussed. In addition, a numerical study of a stable front highlighted the presenec of internal Ekman layers with an additional interfacial structure in the case of high Schmidt number and small Rossby number. For fronts in in/outcropping, front dynamics is modified by interaction with Ekman boundary layer at the location of the intersection zero-thickness singular point. It depends on both vertical circulation and mixing on the nose of the front and the various possible instabilities associated to horizontal or vertical wave resonances.

Ocean submesoscales are the subject of increasing focus in the oceanographic literature; with instrumentation now more capable of observing them in situ and numerical models now able to reach the resolution required to more fully capture them. Submesoscales are typified by horizontal spatial scales of O(1 − 10) km, vertical scales O(100) m and time-scales of O(1) day and are known to be associated with regions of high vertical velocity and vorticity. Occurring most commonly at density fronts at the ocean surface they can control mixed layer restratification and provide an important control on fluxes between the atmosphere and the deep ocean. This thesis sets out to better understand the fundamental physical processes underpinning submesoscale instabilities using a number of idealised process models. Linear stability analysis complemented by non-linear, high-resolution simulations will be used initially to explore the ways in which submesoscale instabilities in the mixed layer may compete and interact with one another. In particular, we will investigate the way in which symmetric and ageostrophic baroclinic instabilities interact when simultaneously present in a flow, with focus on the growth rates and energetic pathways of previously unexplored dynamic instabilities that arise in this paradigm; three-dimensional, mixed symmetric-baroclinic instabilities. Further, these non-linear simulations will allow us to investigate the transition to dissipative scales that can occur in the classical Eady model via a multitude of small-scale secondary instabilities that result from primary submesoscale instabilities. Finally, observational data, taken aboard the SMILES project cruise to the Southern Ocean, helps to motivate the consideration of a new dynamical paradigm; the Eady model with superimposed high amplitude barotropic jet. Non-linear simulations investigate the extent to which the addition of such a jet is capable of damping submesoscale growth. The causes of this damping are then investigated using linear analysis. With this approach eventually demonstrated as being unable to fully explain growth rate reductions, we introduce a new framework combining potential vorticity mixing by submesoscale instabilities with geostrophic adjustment, which relaxes the flow back to a geostrophic balanced state. This framework will help to explain, conceptually, how non-linear eddies control the linear stability of the flow.

This is an experimental and theoretical study of a laminar separation bubble and the associated transition dynamics in its early stages. The separation of a laminar boundary layer from a solid surface is prevalent in very many flow situations such as over gas turbine blades (especially in the low-pressure turbine stage) and the wings of micro-aero-vehicles (MAVs) that operate at fairly low Reynolds numbers. Flow separation occurs in such cases due to the presence of an adverse pressure gradient. The separated shear layer becomes unstable due to the presence of an inflection point and presumably transitions to turbulence rapidly. Eventually, there is reattachment back to the solid surface further downstream, if conditions are right. The region enclosed by the shear layer is called a laminar separation bubble and has been a subject of many studies in the past. The present experiments have been conducted in a closed-circuit wind tunnel. A separation bubble was obtained on the upper surface of a flat plate by appropriately contouring the top wall of the tunnel. Four different techniques were used for qualitative and quantitative study viz. surface flow visualisation, smoke flow visualisation, surface pressure measurements and hotwire anemometry. Response of the bubble to both natural as well as artificial (impulsive excitation) disturbance environment has been studied. Linear stability analyses (both Orr-Sommerfeld and Rayleigh calculations), in the spatial framework, have been performed for the mean velocity profiles starting from an attached adverse pressure gradient boundary layer all the way up to the front portion of the separation bubble region (i.e. up to the end of the dead-air region where linear evolution of disturbances could be expected). The measured velocity profiles (both attached and separated) were fitted with analytical model profiles for doing stability calculations. A separation bubble consists of aspects of both wall-bounded and wall-free shear layers and therefore both viscous and inviscid mechanisms are expected to be at play. Most of the studies in the literature point to the inviscid instability associated with the shear layer to be the main mechanism. The main aim of the present work is to understand the exact origin of the primary instability mechanism responsible for the amplification of disturbances. We argue that at least up to the front portion of the bubble, the instability mechanism is due to the inflectional mode associated with the mean velocity profile. However, the seeds of this inviscid inflectional instability could be traced back to the attached boundary layer upstream of separation. In other words, the inviscid inflectional instability of the separated shear layer should be logically seen as an extension of the instability of the upstream attached adverse-pressure-gradient boundary layer. This modifies the traditional view that pegs the origin of the instability in a separation bubble to the free shear layer outside the bubble with its associated Kelvin-Helmholtz mechanism. Our contention is that only when the separated shear layer has moved considerably away from the wall (and this happens near the maximum height of the mean bubble) that a description by Kelvin-Helmholtz instability paradigm with its associated scaling principles could become relevant. We also propose a new scaling for the most amplified frequency for a wall-bounded shear layer in terms of the inflection point height and the vorticity thickness, and show its universality. Next, we theoretically investigate the role played by the re-circulating region of the separation bubble in the linear instability regime. In the re-circulating region near the wall, associated with the so-called wall mode, the production of disturbance kinetic energy is found to be negative. This is a very interesting observation which has been cursorily noted in earlier studies. Here we show that the near-wall negative production region exerts a stabilising influence on the downstream travelling disturbances. A theoretical support for such a mechanism to exist close to the wall is presented. It is shown that the stabilising wall-proximity effect is not a peripheral aspect but has a significant effect on the overall stability especially for the waves close to the upper neutral branch. We demonstrate the appropriateness of inviscid analysis for the stability of the separated flow velocity profile away from the wall, by comparing the numerical solutions of Rayleigh and Orr-Sommerfeld equations. Following this, the analytical consequences of the Rayleigh equation such as the inflection point criterion and the Fjortoft criterion are derived for the wall-bounded inflectional velocity profiles. Furthermore, we also discuss the relevance of the negative production region towards flow control and management for the wall-bounded flows. It appears fruitful to divide the separation bubble region into two parts with respect to the nature of disturbance dynamics: one outside the mean dividing streamline (which behaves as an amplifier) and the other inside the bubble corresponding to the re-circulating region (having oscillator type characteristics). To explore the oscillator-like behaviour of the bubble further, we have carried out spatio-temporal stability analysis of the reversed flow velocity profiles and determined the conditions for the onset of absolute instability. We contend that the presence of the negative production region for the upstream travelling waves has a restraining effect arresting the tendency of the flow (both wall-free and wall-bounded) to become absolutely unstable and thereby requiring a particular threshold of the backflow velocity to be crossed for its realisation. Moreover, the delay in the onset of absolute instability for a wall-bounded profile as compared to a free shear layer is attributed to a certain ‘negative-drag’ effect of the wall on the overall flow which increases the group velocities for the wall-bounded flows. A related theme in the literature regarding the dynamics of laminar separation bubbles is the so-called ‘bursting’ of the bubble wherein there is a sudden increase in the length and height of the bubble as some critical conditions are reached. Bubbles before bursting are termed as ‘short’ bubbles and those after bursting as ‘long’ bubbles. In this work, we provide a criterion to predict bursting which is a refinement over the existing criteria. The proposed criterion takes into account not just the length of the bubble but also the maximum height and it is shown to be more universal in differentiating short bubbles from the long ones, as compared to the other criteria. We also present a hypothesis regarding the sequence of events leading to bubble bursting by relating its onset to the instability of the re-circulating region. For this we observe that as the amount of backflow velocity is increased for a reversed flow velocity profile, the inflection point moves inside the mean dividing streamline and this happens before the onset of absolute instability. This causes a vorticity maximum to develop inside the re-circulating region which could lead to the instability of the closed streamlines with respect to two-dimensional cylindrical disturbances. The actual bursting process may be expected to involve non-linear interactions of the disturbances and the long bubble could be a nonlinearly saturated state of the instability of the re-circulating region. In order to explore the three-dimensionality associated with the bubble, extensive surface flow visualisation experiments have been performed. The surface streamline pattern is obtained for the entire span of the plate for three different freestream velocities. The patterns have been interpreted using topological ideas and various critical points have been identified. It is shown that the arrangement of critical points satisfies the ‘index theorem’ which is a topological necessity and the streamline patterns are ‘structurally stable’. An interesting observation from these patterns is the presence of three-dimensionality upstream of the separation line close to the wall even though the oncoming flow is nominally two-dimensional. Using the critical point theory, we propose a hypothesis which could be used to construct a semi-empirical model wherein the critical points are assigned with a quantity called ‘strength’ for determining the extent of upstream influence of a given separation line. Finally, we derive a necessary condition for the existence of inviscid spatial instability in plane parallel flows. It states that for spatial instability the curvature of the velocity profile should be positive in some region of the profile. This includes Rayleigh’s inflection point theorem (which was proposed and proved by Rayleigh for temporal instability) as a special case. It thus provides a rigorous basis for applying the inflection point criterion to the flows in the framework of spatial stability theory (which we have used extensively in the present thesis). Moreover, the condition derived here is more general as it also includes velocity profiles with the curvature positive everywhere which are excluded by Rayleigh’s theorem in the temporal framework. An example of such a profile is presented (Couette-Poiseuille flow with adverse pressure gradient) and it is shown that this flow is an exceptional case which is temporally stable but spatially unstable. Eigenvalue calculations as well as energy considerations suggest that the mechanism governing instability of this flow is inviscid and non-inflectional in character. This is a new result which could have important implications in understanding the instability dynamics of parallel flows.

Syfte: Att skapa förståelse för hur situationen på en marknad kan påverka den finansiella stabiliteten. Med det som grund göra en samlad bedömning om vilka risker som finns på Sveriges bostadsmarknad för att utvärdera hur och om de kan påverka finansiell stabilitet idag. Metod: För att ge oss en ökad förståelse om hur finansiell instabilitet uppstår på en marknad har vi tagit hjälp av Hyman P. Minskys teoretiska modell “The Financial Instability Hypothesis”. Teorin har vi sedan applicerat på utvalda finansiella kriser för att studera vad som karaktäriserat dem i sin utformning. Vår forskning har bedrivits med kvalitativa intervjuer med olika organisationer som arbetar aktivt för att upprätthålla och se över den finansiella stabiliteten i Sverige. Slutsats: Vi har identifierat externa och interna faktorer som kan påverka finansiell stabilitet. Oro inom det europeiska bankväsendet utgör största hotet mot finansiell stabilitet idag. Problem kopplade till Sveriges bostadsmarknad utgör inget direkt hot mot finansiell stabilitet, dock visar marknaden tendenser på ineffektivitet. Lågt bostadsbyggande och allmänt lågt utbud matchar inte efterfrågan, detta driver upp priser men även skulder. Priser och skulder kan till stor del förklaras med logiskt ekonomiskt resonemang. / Purpose: To create an understanding of how the situation in a market may affect financial stability. With that as a foundation make an overall assessment of the risks that exist on the Swedish housing market to assess whether and how they can affect financial stability today. Method: In order to obtain increased understanding of how financial instability arises in a market we have used Hyman P. Minskys theoretical model “The Financial Instability Hypothesis”. We have then applied the theory on chosen financial crises in order to study what characterizes them. Our study has been conducted with the help of qualitative interviews with various organizations such as banks and authorities that work to maintain and inspect the financial stability in Sweden. Conclusion: We have identified external and internal factors that could affect financial stability. Concern related to the European banking sector form the greatest threat to financial stability today. Problems related to the Swedish Real Estate Market constitute no direct threat to financial stability, however market trends shows inefficiency. Low housing and low supply in general do not match demand, this drives up prices, but also debts. Prices and debts can largerly be explained by logical economic reasoning.

This Ph.D. thesis comprises of two parts. Part I develops a framework to provide insights into the understanding of several political macro-economy issues related to fiscal policy making. This framework links the overall macroeconomic performance to the public spending and borrowing decisions. The key feature of this framework is that it makes a distinction between productive (e.g. public investment) and non-productive public spending (e.g. popular spending). It is shown that a high level of political instability may lead to myopic and populist policies and may be associated with less favorable macroeconomic performance in terms of not only future output and inflation but also future popular spending. Part I also suggests an alternative channel for expansionary or Non-Keynesian fiscal contractions based on the productivity enhancing role of productive public spending. It is shown that if the incumbent government reduces popular (productive) spending rather than productive (popular) spending, then Non-Keynesian (Keynesian) effects are achieved. Furthermore, it is shown that the favorable effects of public investment depends positively on its quality in this framework. Moreover, the net effect of productive spending financed by borrowing on the next period&#039 / s macroeconomic performance depends on the benefits of productive spending relative to the costs of borrowing. Even under a capital borrowing rule higher public investment may yield unfavorable effects and also it may not necessarily prevent the strategic use of public investment, even though it prevents strategic debt accumulation. Part II investigates the effects of macroeconomic instability on capital accumulation and economic growth in the Turkish economy over the 1963-1999 period. Descriptive and econometric (time series) analyses suggest that macroeconomic instability not only deters capital accumulation and economic growth but it may also reverse the complementarity between public and private investment in the long-run.

[pt] A estabilidade das colunas de um pórtico plano depende da importância relativa da rigidez à flexão e rigidez lateral de cada coluna e elementos adjacentes. Um exemplo típico é a maior capacidade de carga de pórticos planos com restrição lateral em comparação com pórticos semelhantes, sem restrição lateral. Também esta restrição tem uma influência importante na resposta pós-crítica e na sensibilidade à imperfeição da estrutura. A carga de flambagem pode ser dominada pela rigidez à flexão da coluna ou pela rigidez das restrições laterais. Dependendo dos valores relativos desses parâmetros, pode ocorrer interação modal. Nesse caso, podem surgir vários caminhos pós-críticos, acoplados e desacoplados, levando a uma topologia complexa da energia potencial total com vários pontos críticos (máximos, mínimos e selas). Os caminhos pós-críticos instáveis influenciam na sua capacidade de carga e na sensibilidade da estrutura a imperfeições. Isso leva a um complexo comportamento dinâmico não linear da estrutura carregada axialmente. No presente trabalho, um modelo conceitual de dois graus de liberdade de um elemento de pórtico plano sob compressão é estudado. Uma análise detalhada é realizada a fim de estudar como a rigidez lateral influencia: os comportamentos pré- e pós-crítico, a instabilidade paramétrica do modelo sob uma excitação harmônica axial e o comportamento ressonante do sistema estrutural carregado axialmente sob uma excitação de base; contribuindo para uma melhor compreensão da resposta não linear desta classe de estruturas. A análise das bifurcações mostra que a estrutura pode exibir várias soluções estáveis e instáveis coexistentes, levando a bacias de atração entrelaçadas, cuja topologia controla a integridade dinâmica da estrutura em um ambiente dinâmico. Para estudar o comportamento não linear do modelo, foram utilizadas várias estratégias numéricas para obter os caminhos de equilíbrio não lineares, pontos fixos estáveis e instáveis, diagramas de bifurcação e bacias de atração. / [en] The stability of columns in a portal frame depends on the relative importance of the flexural and lateral stiffness of the column and connected elements. A typical example is the higher load capacity of non-sway frames as compared with that of similar frames with no lateral restrain. Also this restrain has an important influence on the post-critical response and imperfection sensitivity of the structure. The buckling load may be either dominated by the flexural stiffness of the columns or by the stiffness of the lateral restrains. Depending on the relative values of these parameters, interactive buckling may occur. In such case, several coupled and uncoupled post-buckling paths may arise, leading to a complex topology of the energy landscape with several critical points (maxima, minima and saddles). The resulting unstable post-buckling paths influence the structure s imperfection sensitivity and load carrying capacity of the structure. This leads to an involved nonlinear dynamic behaviour of the axially loaded structure. In the present work, a conceptual two-degree-of-freedom model of a plane-frame column is studied. A detailed analysis is conducted to study how the lateral stiffness influences the static buckling and post-buckling behavior, the parametric instability of the model under under axial harmonic excitation and the resonant behavior of the axially loaded structural system under base excitation, contributing to a better understanding of the nonlinear response of this class of structures. The bifurcation analysis shows that the structure may display several coexisting stable and unstable solutions, leading to intertwining basins of attraction, whose topology controls the dynamic integrity of the structure in a dynamic environment. To study the non-linear behavior of the model, several numerical strategies were used to obtain the nonlinear equilibrium paths, stable and unstable fixed points, bifurcation diagrams and basins of attraction.

A investigação dos mecanismos de instabilidade pode ter um papel importante no entendimento do processo laminar para turbulento de um escoamento. Análise de instabilidade de uma camada limite de uma linha de estagnação compressível foi realizada no contexto de teoria linear BiGlobal. O estudo dos mecanismos de instabilidade deste escoamento pode proporcionar uma visão útil no desenho aerodinâmico das asas. Um novo procedimento foi desenvolvido e implementado computacionalmente de maneira sequencial e paralela para o estudo de instabilidade BiGlobal. O mesmo baseia-se em formar a matriz esparsa associada ao problema discretizado por dois métodos: pontos de colocação de Chebyshev-Gauss-Lobatto e diferenças finitas, além das combinações destes métodos. Isto permitiu o uso de bibliotecas computacionais eficientes para resolver o sistema linear associado ao problema de autovalor utilizando o algoritmo de Arnoldi. O desempenho do método numérico e código computacional proposto são analisados do ponto de vista do uso de métodos de ordenação dos elementos da matriz, coeficientes de preenchimento, memória e tempo computacional a fim de determinar a solução mais eficiente para um problema físico geral com técnicas de matrizes esparsas. Um estudo paramétrico da instabilidade da camada limite de uma linha de estagnação foi realizado incluindo o estudo dos efeitos de compressibilidade. O excelente desempenho código computacional permitiu obter as curvas neutras e seus respectivos valores críticos para a faixa de número de Mach 0 \'< OU =\' Ma \'< OU =\' 1. Os resultados confirmam a teoria assintótica apresentada por (THEOFILIS; FEDOROV; COLLIS, 2004) e mostram que o incremento do número de Mach reduz o numero de Reynolds crítico e a faixa instável do número de ondas. / Investigation of linear instability mechanisms is essential for understanding the process of transition from laminar to turbulent flow. An algorithm for the numerical solution of the compressible BiGlobal eigenvalue problem is developed. This algorithm exploits the sparsity of the matrices resulting from the spatial discretization of the enigenvalue problem in order to improve the performance in terms of both memory and CPU time over previous dense algebra solutions. Spectral collocation and finite differences spatial discretization methods are implemented, and a performance study is carried out in order to determine the best practice for the efficient solution of a general physical problem with sparse matrix techniques. A combination of spectral collocation and finite differences can further improve the performance. The code developed is then applied in order to revisit and complete the parametric analyses on global instability of the compressible swept Hiemenz flow initiated in (THEOFILIS; FEDOROV; COLLIS, 2004) and obtain neutral curves of this flow as a function of the Mach number in the 0 \'< OU =\' Ma \'< OU =\' 1 range. The present numerical results fully confirm the asymptotic theory results presented in (THEOFILIS; FEDOROV; COLLIS, 2004). This work presents a complete parametric study of the instability properties of modal three dimensional disturbances in the subsonic range for the flow conguration at hand. Up to the subsonic maximum Mach number value studied, it is found that an increase in this parameter reduces the critical Reynolds number and the range of the unstable spanwise wavenumbers.