Modern unsteady (multi-)field visualizations require an effective reduction of the data to be displayed. From a huge amount of information the most informative parts have to be extracted. Instead of the fuzzy application dependent notion of feature, a new approach based on information theoretic concepts is introduced in this paper to detect important regions. This is accomplished by extending the concept of local statistical complexity from finite state cellular automata to discretized (multi-)fields. Thus, informative parts of the data can be highlighted in an application-independent, purely mathematical sense. The new measure can be applied to unsteady multifields on regular grids in any application domain. The ability to detect and visualize important parts is demonstrated using diffusion, flow, and weather simulations.

Au cours des dernières décennies, la théorie de la stabilité a été intensivement utilisée pour caractériser le comportement instationnaire d'écoulements. Cela a donné naissance à un grand nombre d'approches, mais malheureusement chacune d'entre elles semble présenter ses propres limitations. De plus, leurs conditions de validité sont encore très mal connues, ce qui soulève la question de la fiabilité de ce genre de méthodes dans un cas général.Cette problématique est traitée dans cette thèse en s'intéressant dans un premier temps aux approches classiques de stabilité, qui étudient l'évolution de petites perturbations autour d'une solution stationnaire -- un champ de base -- des équations de Navier-Stokes. Pour cela, le phénomène du screech -- un bruit tonal que peuvent causer les jets sous-détendus -- est étudié d'un point de vue de la stabilité linéaire. Les résultats obtenus montrent que la dynamique non-linéaire du phénomène est correctement prédite par une analyse linéaire de stabilité du champ de base. Une confrontation avec d'autres analyses similaires montre qu'un tel résultat n'est pas toujours observé. Cependant, lorsque les oscillations auto-entretenues d'un écoulement sont provoquées par un bouclage acoustique, comme c'est le cas entre autres pour le screech, l'écoulement de cavité ou encore les jets impactants, alors les non-linéarités ont une faible influence sur le phénomène de sélection de fréquence. Cela explique la capacité d'une analyse linéaire à caractériser ces écoulements, même dans le régime non-linéaire.Une autre approche, consistant à étudier la stabilité linéaire du champ moyen, a montré de bons résultats dans certaines configurations qui ne peuvent être correctement étudiées par une analyse linéaire du champ de base. Cela est justifié dans cette thèse en mettant en évidence le rôle que joue la résolvante autour du champ moyen dans la dynamique d'un écoulement. Il est montré que lorsque cet opérateur présente une forte séparation de valeurs singulières, ce qui correspond à l'existence d'un mécanisme d'instabilité fort, alors les modes de Fourier de l'écoulement sont proportionnels aux modes de résolvante dominants. Ce résultat fournit des conditions mathématiques et physiques pour l'utilisation et le sens de diverses méthodes d'analyse du champ moyen, telles qu'une analyse d'équations de stabilité parabolisées (Parabolised Stability Equations). De plus, cela permet de mettre en place un modèle de prédiction du spectre fréquentiel en tout point d'un écoulement, à partir d'une ou de quelques mesures ponctuelles et du champ moyen. L'ensemble de ces résultats est illustré et validé sur un cas de marche descendante turbulente. Enfin, cela est exploité dans un cadre expérimental, afin de reconstruire le comportement instationnaire d'un jet rond transitionnel, à partir de la seule connaissance du champ moyen et d'une mesure ponctuelle. L'étude montre que, sous certaines précautions expérimentales, la reconstruction est très précise et robuste. / Linear stability theory has been intensively used over the past decades for the characterization of unsteady flow behaviors. While the existing approaches are numerous, none has the ability to address any general flow. Moreover, clear validity conditions for these techniques are often missing, and this raises the question of their general reliability.In this thesis, this question is addressed by first considering the classical stability approach, which focuses on the evolution of small disturbances about a steady solution -- a base flow -- of the Navier-Stokes equations.To this end, the screech phenomenon -- a tonal noise that is sometimes generated by underexpanded jets -- is studied from alinear stability point of view. The results reveal that the nonlinear dynamics of this phenomenon is well-predicted by a linear base flow stability analysis. A confrontation with other similar analyses from the literature shows that such a satisfactory result is not always observed. However, when a self-sustained oscillating flow is driven by an acoustic feedback loop, as it is the case for the screech phenomenon, cavity flows and impinging jets for instance, then the nonlinearities have a weak impact on the frequency selection process, explaining the ability of a linear analysis to characterize the flow, even in the nonlinear regime.Another alternative approach, based on a linearization about the mean flow, is known to be successful in some cases where a base flow analysis fails. This observation from the literature is explained in this thesis by outlining the role of the resolvent operator, arising from a linearization about the mean flow, in the dynamics of a flow. The main finding is that if this operator displays a clear separation of singular values, which relates to the existence of one strong convective instability mechanism, then the Fourier modes areproportional to the first resolvent modes. This result provides mathematical and physical conditions for the use and meaning of several mean flow stability techniques, such as a parabolised stability equations analysis of a mean flow.Moreover, it leads to a predictive model for the frequency spectrum of a flow field at any arbitrary location, from the sole knowledge of the mean flow and the frequency spectrum at one or more points. All these findings are illustrated and validated in the case of a turbulent backward facing step flow. Finally, these results are exploited in an experimental context, for the reconstruction of the unsteady behavior of a transitional round jet, from the sole knowledge of the mean flow and one point-wise measurement. The study shows that, after following a few experimental precautions, detailed in the manuscript, the reconstruction is very accurate and robust.

No description available.

Cette étude s'inscrit dans l'effort de réduction des nuisances sonores des avions au décollage. Une des principales composantes est le bruit de jet, dont la partie à basse fréquence peut notamment être imputée au rayonnement acoustique directif des structures cohérentes de grande échelle engendrées par les instabilités dans la couche de mélange du jet. L'évolution de ces ondes d'instabilité peut être décrite au moyen des équations de Stabilité Parabolisées (PSE). Un premier objectif a été de déterminer si dans le cas d'un jet turbulent naturel, les interactions non linéaires entre les ondes d'instabilité ont un impact significatif sur sa dynamique et sur son rayonnement acoustique. À cet effet, une modélisation PSE non linéaire a été développée et appliquée à une configuration réaliste. La possibilité de manipuler ces ondes d'instabilité par non linéarité a ensuite été étudiée en vue d'une réduction du rayonnement acoustique. Pour cela, une analyse PSE a été menée pour déterminer l'effet sur le bruit de jet de l'excitation d'un ou plusieurs modes instables. Ces travaux de thèse ont permis de montrer, d'une part, que les non linéarités semblent avoir un impact mineur sur la dynamique des ondes d'instabilité dans le cas des jets turbulents naturels, et d'autre part, qu'il est possible de réduire le rayonnement acoustique des modes dominants par interactions non linéaires. / This study is part of the effort to reduce aircraft noise during take-off. Jet noise is oneof the main contributors, of which lower frequency component can be attributed to thedirective acoustic field generated by the large-scale coherent structures arising from jetmixing-layer instabilities. The development of these instability waves can be describedusing Parabolized Stability Equations (PSE). A first objective was to determine if inthe case of a natural turbulent jet, nonlinear interactions between instability waveshave a significant impact on its dynamic and acoustic behaviour. For this purpose,a nonlinear PSE model has been developed and applied to a realistic configuration.Then, the possibility to manipulate these instability waves by means of nonlinearity wasinvestigated with a view to reduce noise. To this end, a PSE analysis has been carried outto assess the impact on jet noise of exciting one or more unstable modes. The findingsof this doctoral work demonstrate a minor impact of nonlinearities on the dynamics ofinstability waves for natural turbulent jets on the one hand, and the possibility to makethe initially dominant instability acoustically ineffective using nonlinear interactions onthe other hand.

En période hivernale, le golfe du Lion est sujet à des conditions de vents régionaux forts (Mistral et/ou Tramontane) qui transportent des masses d'air continentales froides et sèches au dessus de la mer. Ces événements, les Cold Air Outbreaks (CAO) , conduisent à d'intenses échanges air-mer et donc à un pompage de chaleur qui favorise la formation d'eaux denses et le déclenchement de la convection océanique profonde. La bonne représentation de ces échanges air-mer intenses dans les modèles de climat et de prévision numérique du temps reste à l'heure actuelle une problématique majeure. Elle est au cœur du projet ASICS-MED centré sur compréhension des mécanismes de formation d'eaux denses en Méditerranée et qui s'inscrit dans le cadre de la thématique " Échanges air-mer intenses " du programme HyMeX dédié à l'étude du cycle de l'eau en Méditerranée. Les processus qui s'opèrent au sein de la couche limite atmosphérique marine (CLAM) et de la couche de mélange océanique (CMO) interagissent entre eux à différentes échelles spatiales et temporelles. La compréhension de l'évolution globale de la CLAM mais également des mécanismes locaux nécessitent la prise en compte de l'ensemble des processus. L'étude présentée ici est consacrée à la structure moyenne et turbulente de la CLAM en conditions de vents forts. L'objectif est de déterminer comment l'organisation du champ turbulent est impactée lors d'épisodes de CAO et d'estimer les flux de surface associés à ces conditions de vents forts. La méthodologie adoptée est basée sur l'utilisation conjointe d'observations aéroportées collectées lors de la campagne de mesure SOP2 d'HyMeX et de simulations numériques. La campagne de mesure SOP2 d'HyMeX qui a eu lieu au cours de l'hiver 2013 dans le golfe du Lion a permis de documenter grâce à l'avion de recherche ATR42 la structure moyenne et turbulente de la CLAM lors de 11 épisodes de CAO. Une analyse spectrale s'appuyant sur un modèle analytique a été réalisé sur 181 paliers (i.e. segments de vol rectilignes et stabilisés en altitude). Les profils verticaux des échelles turbulentes caractéristiques ainsi que la forme du spectre de la vitesse verticale ont permis de mettre en évidence un allongement des structures énergétiques dans l'axe du vent moyen associé à l'organisation du champ turbulent sous la forme de rouleaux longitudinaux. Une description unidirectionnelle du champ turbulent tridimensionnel peut conduire à une représentativité limitée des structures cohérentes au sein des échantillons. Cependant, la connaissance des profils de flux sur toute l'épaisseur de la CLAM est nécessaire pour l'estimation des échanges air-mer. Une méthode de correction des flux turbulents calculés par eddy correlation a été appliqué afin de prendre en compte les erreurs systématique et aléatoire relatives à la mesure et au traitement de données. Cette correction a permis de déterminer les meilleures estimations possibles des flux extrapolés à la surface avec une marge d'incertitude pour les 11 épisodes de CAO documentés lors de la campagne SOP2 d'HyMeX. La comparaison de ces estimations aéroportées aux autres sources d'information dérivées de paramétrisations des flux a permis de mettre en évidence une sous-estimation systématique du flux de chaleur latente en conditions de vents forts. Une approche numérique a permis de compléter l'analyse de la structure moyenne et turbulente de la CLAM lors d'épisodes de CAO. / During winter, local strong winds (Mistral or Tramontana) occurred in the Gulf of Lion which bring cold and dry continental air over a warmer sea. Those events, the cold air outbreaks, can lead to intense air-sea interactions which favour dense water formation and deep oceanic convection. The representation of air-sea exchanges is a fundamental aspect of of climate modelling and numerical weather forecasting. The ASICS-MED project aims to identify fine-scale processes leading to dense water formation and is a part of the "Intense air-sea exchanges" topic of the HyMeX program devoted to hydrological cycle in the Mediterranean. The processes occurring within the marine atmospheric boundary layer (MABL) and the oceanic mixing layer (ML) interact with one another at different spatial and temporal scales. Understanding the overall evolution of the MABL but also the local mechanisms requires taking into account all the processes. The study presented here is devoted to the mean and turbulent structure of the MABL under strong wind conditions. The objective is to determine how the organization of the turbulent field is impacted during CAO events and to estimate the surface fluxes associated with these strong wind conditions. The methodology adopted is based on the joint use of airborne observations collected during the HyMeX-SOP2 field campaign and numerical simulations. The HyMeX-SOP2 field campaign took place during the winter of 2013 in the Gulf of Lion. The research aircraft ATR42 was operated to document the mean and turbulent structure of the MABL during 11 CAO events. A spectral analysis based on an analytic model was carried out on 181 legs (i.e. stacked straight and level runs stabilized in altitude). The vertical profiles of the turbulent characteristic scales as well as the shape of the vertical velocity spectrum revealed an elongation of the energy structures in the mean wind direction associated with the organization of the turbulent field into longitudinal rolls. A unidirectional sampling of the three-dimensional turbulent field may lead to a limited representativeness of the coherent structures within the samples. However, knowledge of kinematic fluxes profiles over the entire thickness of the CLAM is necessary to estimate air-sea exchanges. A correction method was applied to turbulent fluxes calculated by eddy correlation in order to take into account systematic and random errors related to measurement and data processing. This correction made it possible to determine the best possible estimates of the extrapolated surface fluxes with a margin of uncertainty for the 11 CAO events documented during the HyMeX-SOP2 field campaign. The comparison of these airborne estimates with the other sources of information derived from bulk parameterizations show a systematic underestimation of the latent heat flux under strong wind conditions. A numerical approach allowed to complete the analysis of the mean and turbulent structure of the MABL during CAO events. The numerical study, based on the non-hydrostatic Meso-NH model, focuses on an episode of strong Tramontana with winds greater than 25m/s documented during the HyMeX-SOP2 field campaign. In a first step, a one-dimensional framework made it possible to understand the forcing terms necessary to reproduce in a realistic way the development of the observed MABL. This reference configuration allowed, in a second time, a Large-Eddy Simulation of the CAO event. This simulation has been validated using airborne data and has allowed to deepen the description of the turbulent field as well as the evolution of the coherent structures oriented in the axis of the mean wind.

Nous proposons dans ce mémoire de thèse une méthodologie permettant la résolution du problème de la décomposition de Hodge-Helmholtz discrète sur maillages polyédriques. Le défi de ce travail consiste à respecter les propriétés de la décomposition au niveau discret. Pour répondre à cet objectif, nous menons une étude bibliographique nous permettant d'identifier la nécessité de la mise en oeuvre de schémas numériques mimétiques. La description ainsi que la validation de la mise en oeuvre de ces schémas sont présentées dans ce mémoire. Nous revisitons et améliorons les méthodes de décomposition que nous étudions ensuite au travers d'expériences numériques. En particulier, nous détaillons le choix d'un solveur linéaire ainsi que la convergence des quantités extraites sur un ensemble varié de maillages polyédriques et de conditions aux limites. Nous appliquons finalement la décomposition de Hodge-Helmholtz à l'étude de deux écoulements turbulents : un écoulement en canal plan et un écoulement turbulent homogène isotrope. / We propose in this thesis a methodology to compute the Helmholtz-Hodge decomposition on discrete polyhedral meshes. The challenge of this work isto preserve the properties of the decomposition at the discrete level. In our literature survey, we have identified the need of mimetic schemes to achieve our goal. The description and validation of our implementation of these schemes are presented inthis document. We revisit and improve the methods of decomposition we then study through numerical experiments. In particular, we detail our choice of linear solvers and the convergence of extracted quantities on various series of polyhedral meshes and boundary conditions. Finally, we apply the Helmholtz-Hodge decomposition to the study of two turbulent flows: a turbulent channel flow and a homogeneous isotropic turbulent flow.

Current lean-premixed fuel injector designs have shown great potential in terms of reducing emissions of pollutants, but such designs are susceptible to combustion instabilities in which aerodynamic instability plays a major role and also has an effect on mixing of air and fuel. In comparison to prototype testing with combustors running in operating conditions, computational approaches such as Large Eddy Simulations (LES) offer a much more cost-effective alternative in the design stage. However, computational models employed by LES require validation by experimental data. This is one of the main motivations behind the present experimental study. Combined particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) instrumentation allowed simultaneous measurements of velocity vector and a conserved scalar introduced into the fuel stream. The results show that the inner swirl shear layer features two pairs of vortices, which draw high concentration fuel mixture from the central jet into the swirl stream and causes it to rotate in their wakes. Such periodic entrainment also occurs with the characteristic frequencies of the vortices. This has clear implications for temporal variations in fuel/air ratio in a combusting flow; these bursts of mixing, and hence heat release, could be a possible cause of mixing-induced pressure oscillation in combusting tests. For the first time in such a flow, all 3 components of the turbulent scalar flux were available for validation of LES-based predictions. A careful assessment of experimental errors, particularly the error associated with spatial filtering, was carried out. Comparison of LES predictions with experimental data showed very good agreement for both 1st and 2nd moment statistics, as well as spectra and scalar pdfs. It is particularly noteworthy that comparison between LES computed and measured scalar fluxes was very good; this represents successful validation of the simple (constant Schmidt number) SGS model used for this complex and practically important fuel injector flow. In addition to providing benchmark data for the validation of LES predictions, a new experimental technique has been developed that is capable of providing spatially resolved residence time data. Residence times of combustors have commonly been used to help understand NOx emissions and can also contribute to combustion instabilities. Both the time mean velocity and turbulence fields are important to the residence time, but determining the residence time via analysis of a measured velocity field is difficult due to the inherent unsteadiness and the three dimensional nature of a high-Re swirling flow. A more direct approach to measure residence time is reported here that examines the dynamic response of fuel concentration to a sudden cutoff in the fuel injection. Residence time measurement was mainly taken using a time-resolved PLIF technique, but a second camera for PIV was added to check that the step change does not alter the velocity field and the spectral content of the coherent structures. Characteristic timescales evaluated from the measurements are referred to as convection and half-life times: The former describes the time delay from a fuel injector exit reference point to a downstream point of interest, and the latter describes the rate of decay once the effect of the reduced scalar concentration at the injection source has been transported to the point of interest. Residence time is often defined as the time taken for a conserved scalar to reduce to half its initial value after injection is stopped: this is equivalent to the sum of the convection time and the half-life values. The technique was applied to a high-swirl fuel injector typical of that found in combustor applications. Two test cases have been studied: with central jet (with-jet) and without central jet (no-jet). It was found that the relatively unstable central recirculation zone of the no-jet case resulted in increased transport of fuel into the central region that is dominated by a precessing vortex core, where long half-life times are also found. Based on this, it was inferred that the no-jet case may be more prone to NOx production. The technique is described here for a single-phase isothermal flow field, but with consideration, it could be extended to studying reacting flows to provide more insight into important mixing phenomena and relevant timescales.

No description available.

No description available.

This thesis is an experimental study of turbulent flows over smooth and rough walls in a channel that consists of an upstream parallel section to produce a fully developed channel flow and a diverging section to produce an adverse pressure gradient (APG) flow. The roughness elements used were two-dimensional square ribs of nominal height k = 3 mm. The ribs were secured to the lower wall of the channel and spaced to produce the following three pitches: 2k, 4k and 8k, corresponding to d-type, intermediate and k-type rough walls, respectively. For each rough wall type, the ribs were inclined at 90°, 45° and 30° to the approach flow. The velocity measurements were performed using a particle image velocimetry technique. The results showed that rib roughness enhanced the drag characteristics, and the degree of enhancement increased with increasing pitch. The level of turbulence production and Reynolds stresses were significantly increased by roughness beyond the roughness sublayer. It was observed that the population, sizes and the level of organization of hairpin vortices varied with roughness and more intense quadrant events were found over the smooth wall than the rough walls. APG reinforced wall roughness in augmenting the equivalent sand grain roughness height, turbulence production and Reynolds stresses. APG also reduced the sizes of the hairpin packets but strengthened the quadrant events in comparison to the results obtained in the parallel section. The secondary flow induced by inclined ribs significantly altered the distributions of the flow characteristics across the span of the channel. Generally, the mean flow was less uniform close to the trailing edge of the ribs compared to the flows at the mid-span and close to the leading edge of the ribs. The Reynolds stresses and hairpin packets were distinctly larger close to the trailing edge of the ribs. Rib inclination also decreased the drag characteristics and significantly modified the distributions of the Reynolds stresses and quadrant events. In the parallel section, the physical sizes of the hairpin packets were larger over 45° ribs whereas in the diverging section, the sizes were larger over perpendicular ribs.