Large-scale unsteady flow structures play an influential role in the dynamics of many practical flows, such as those found in gas turbine combustion chambers. This thesis is concerned primarily with large-scale unsteady structures that arise due to self-sustained hydrodynamic oscillations, also known as global hydrodynamic instability. Direct numerical simulation (DNS) of the Navier--Stokes equations in the low Mach number limit is used to obtain a steady base flow, and the most unstable direct and adjoint global modes. These are combined, using a structural sensitivity framework, to identify the region of the flow and the feedback mechanisms that are responsible for causing the global instability. Using a Lagrangian framework, the direct and adjoint global modes are also used to identify the regions of the flow where steady and unsteady control, such as a drag force or heat input, can suppress or promote the global instability. These tools are used to study a variety of reacting and non-reacting flows to build an understanding of the physical mechanisms that are responsible for global hydrodynamic instability in swirling diffusion flames. In a non-swirling lifted jet diffusion flame, two modes of global instability are found. The first mode is a high-frequency mode caused by the instability of the low-density jet shear layer in the premixing zone. The second mode is a low-frequency mode caused by an instability of the outer shear layer of the flame. Two types of swirling diffusion flames with vortex breakdown bubbles are considered. They show qualitatively similar behaviour to the lifted jet diffusion flames. The first type of flame is unstable to a low-frequency mode, with wavemaker located at the flame base. The second type of flame is unstable to a high-frequency mode, with wavemaker located at the upstream edge of the vortex breakdown bubble. Feedback from density perturbations is found to have a strong influence on the unstable modes in the reacting flows. The wavemaker of the high-frequency mode in the reacting flows is very similar to its non-reacting counterpart. The low-frequency mode, however, is only observed in the reacting flows. The presence of reaction increases the influence of changes in the base flow mixture fraction profiles on the eigenmode. This increased influence acts through the heat release term. These results emphasize the possibility that non-reacting simulations and experiments may not always capture the important instability mechanisms of reacting flows, and highlight the importance of including heat release terms in stability analyses of reacting flows.

Une des grandes problématiques en écologie est d’identifier les liens qui existent entre ce qui se passe au niveau de la physiologie et du comportement des individus et les propriétés émergentes qui apparaissent au niveau de la population et des écosystèmes dans leur globalité.Dans cette thèse, nous avons abordé cette problématique à travers la modélisation du phénomène de prédation, en nous intéressant plus particulièrement à la représentation mathématique de la réponse fonctionnelle. Cette fonction représente la quantité de proies consommées par prédateur et par unité de temps. Elle synthétiseau niveau de la population un ensemble de processus survenant à différentes échelles d’organisation. La modélisation du phénomène de prédation rencontre diverses limitations liées à la complexité de ce processus biologique, et il existe donc une forte incertitude sur la nature de la réponse fonctionnelle à utiliser.A travers l’étude d’un modèle prédateur-proie en chemostat d’une part, et l’utilisation de méthodes de changement d’échelle sur un modèle prédateur-proie en patchs d’autre part, nous avons cherché à déterminer les sources de variations dans la représentation de cette réponse.Tout d’abord, nous avons mis en évidence l’influence de la variabilité des données sur la paramétrisation de la réponse fonctionnelle ainsi que sur la robustesse des sorties du modèle. Une étude de sensibilité a également permis de montrer la forte sensibilité structurelle du modèle face à cette formulation, qui peut-être plus importante que face à des changements de paramètres.De plus, il apparait que la représentation mathématique de la réponse fonctionnelle dépend fortement de l’échelle d’observation considérée. En effet, la nature de la réponse peut être modifiée lorsque l’on passe de l’échelle d’une population à celle de la communauté. / One of the major issues in ecology is to identify the links between what happens in terms of physiology and behavior of individuals and the emergent properties that appear at the population and ecosystems level. In this thesis, we addressed this problem through modeling of the phenomenon of predation, especially by focusing on the mathematical functional response representation. This function represents the amount of prey consumed by predator per unit time. It synthesizes at the population level a set processes occurring at different scales of organization. Modeling of the phenomenon of predation encounters various limitations related to the complexity of this biological process, and there is, therefore, considerable uncertainty aboutthe nature of the functional response to use.Through the study of a predator-prey model in chemostat on the one hand, and use of scaling methods in a patches predator-prey model on the other hand, we seek to determine sources of variations in therepresentation of that response.First, we demonstrated the influence of data variability on the parameterization of the functional response as well as the robustness of the model outputs. A sensitivity study has also demonstrated the high structural sensitivity of the model to the formulation of this response, which may be more important than to parameterchanges.In addition, it appears that the mathematical representation of the functional response depends strongly on the scale of observation considered. The nature of the response can, indeed, be modified when changing the scale from the population to the community level.

Les systèmes écologiques sont des systèmes complexes qui ne peuvent pas être d´écrits par un unique modèle mathématique. De nombreux modèles peuvent être construits pour un même système, selon les internets du modélisateur et ses choix dans la construction du modèle. Quel est l’impact de ces choix dans la construction du modèle sur les prédictions de la dynamique des systèmes écologiques et les informations qu’elles fournissent sur la résilience de ces systèmes est la question générale qui guide le travail présente dans cette thèse. Cette thèses focalise sur un choix entre formulations de modèle basées sur des mécanismes biologiques et qui décrivent les données empiriques avec la même efficacité. Ces modèles sont proches l’un de l’autre, donc on s’attendrait `a ce que leurs prédictions soient similaires. Cependant, nous montrons avec un exemple générique de modèle prédateur-proie que des formulations similaires du processus de prédation peuvent prédire des dynamiques qualitativement différentes en terme de: (i) nombre et type d'états stables, et (ii) réponse et résilience du système face à une perturbation extérieure. Ces différences dans les prédictions du modèle sont expliquées par une analyse mathématique détaillée du modèle prédateur-proie. Ensuite, ce modèle est étendu à des réseaux trophiques compos´es de dizaines d’espèces. La complexité de ces réseaux (nombre d'espèces et d’interactions) explique leur persistance, alors que leur dynamique temporelle est fortement affectée par la fonction utilisée pour modéliser la prédation. Des méthodes sont ´également proposées pour quantifier la sensibilités d’un modèle. Finalement, nous montrons que si un minimum de détails biologiques sont pris en compte, des modèles prédateurs-proies sont moins sensibles `a la formulation de la prédation. Ceci nous donne des pistes pour gérer les incertitudes dans la construction d’un modèle, qui sont intrinsèques à la complexité des systèmes naturels. / Ecological systems are complex systems which cannot be described by a single mathematical model. Multiple modelsof a same system can be built, depending on modeller’s interests and on its choices during model construction. Howfar these choices in model construction can affect the predicted dynamics of ecological systems and the informationthey provide on their resilience? is the general question that leads the research presented in this thesis. This thesisfocuses on a choice between model formulations that are based on biological mechanisms and describe empiricaldata with the same accuracy. These models are close to each other, so they are expected to predict similar systemdynamics. However, we show through a generic example of predator-prey model that similar formulations of thepredation process can predict qualitatively different system dynamics in term of: (i) number and type of stablestates, and (ii) system response to external disturbance and its potential for recovery. These differences in modelpredictions are explained by a detailed mathematical analysis of the predator-prey model. Next, this model isextended to complex food webs made of tens of species. The complexity of these networks (number of species andinteractions) drives their persistence, whereas their temporal dynamics is strongly affected by the function used tomodel predation. Methods to quantify model sensitivity are also proposed. Finally, we show that if a minimumlevel of biological details is included, predator-prey models are less sensitive to predation formulation. This providea clue to deal with uncertainties in model construction, which are intrinsic to the complexity of natural systems.

This work represents the initial steps in a wider project that aims to map out the sensitive areas in fuel injectors and combustion chambers. Direct numerical simulation (DNS) using a Low-Mach-number formulation of the Navier–Stokes equations is used to calculate direct-linear and adjoint global modes for axisymmetric low-density jets and lifted jet diffusion flames. The adjoint global modes provide a map of the most sensitive locations to open-loop external forcing and heating. For the jet flows considered here, the most sensitive region is at the inlet of the domain. The sensitivity of the global-mode eigenvalues to force feedback and to heat and drag from a hot-wire is found using a general structural sensitivity framework. Force feedback can occur from a sensor-actuator in the flow or as a mechanism that drives global instability. For the lifted flames, the most sensitive areas lie between the inlet and flame base. In this region the jet is absolutely unstable, but the close proximity of the flame suppresses the global instability seen in the non-reacting case. The lifted flame is therefore particularly sensitive to outside disturbances in the non-reacting zone. The DNS results are compared to a local analysis. The most absolutely unstable region for all the flows considered is at the inlet, with the wavemaker slightly downstream of the inlet. For lifted flames, the region of largest sensitivity to force feedback is near to the location of the wavemaker, but for the non-reacting jet this region is downstream of the wavemaker and outside of the pocket of absolute instability near the inlet. Analysing the sensitivity of reacting and non-reacting variable-density shear flows using the low-Mach-number approximation has up until now not been done. By including reaction, a large forward step has been taken in applying these techniques to real fuel injectors.