In turbulent flows at low Reynolds numbers localized structures are observed which can grow or spontaneously decay. Viewed as a dynamical system, a turbulent evolution forms a path through a phase space built upon exact invariant solutions of the Navier-Stokes equations. The leading stable and unstable manifolds of these solutions organise the local dynamics. In small periodic domains many of these solutions are known. However, to understand the full spatial-temporal nature of turbulence requires localized solutions which are unstable and live in a very high dimensional system. In the first half of this thesis we consider two problems in small, periodic domains where turbulence is global. We consider the geometry of the edge of chaos, a manifold which divides phase space and how such a manifold can be understood in the context of turbulent decay. We demonstrate that the edge is not separate from the turbulent dynamics but is wrapped up into these dynamics. Next we consider how the dynamics on the edge in short pipes are affected by Reynolds number and find new high Reynolds number solutions. In this second half we attack the problem of finding and understanding the origins of localized solutions. These solutions hold the key to expanding the theory towards physically realisable systems. Building upon the short pipe research we find the origin of the first localized pipe flow solution in a bifurcation from a downstream-periodic solution. Moving to a model for plane Couette flow, we attempt to find evidence of homoclinic-snaking as a route to spanwise localization. Instead we find a different route which matches recent work in duct flow. Finally, motivated by questions of how localized structures interact, we introduce a new flow, "localized Couette flow", and investigate the stability of this flow.

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This Philosophiae Doctor thesis presents the motivation, objectives and reasoning behind the undertaken project. This research, study the capability of compressible Implicit Large Eddy Simulation (ILES) in predicting free shear layer flows, under different free stream regimes (Static and Co-flow jets). Unsteady flows or jet flows are non-uniform in structure, temperature, pressure and velocity. Turbulent mixing is of particular importance for the developing of this class of flows. As a shear layer is formed immediately downstream of the jet exhaust, an early linear instability involving exponential growth of small perturbations is introduced at the jet discharge. Beyond this development stage, in the non-linear Kelvin-Helmholtz instability region large scale vortex rings roll up, and their dynamics of formation and merging become the defining feature of the transitional shear flow into fully developed regime. This class of flows is particularly relevant to numerical predictions, as the extreme nature of the flow in question is considered as a benchmark; however, experimental data should be selected carefully as some results are controversial. To qualify the behaviour of unsteady flows, some important criteria have been selected for the analysis of the flow quantities at different regions of the flow field (average velocities, Reynolds stresses and dissipation rates). A good estimation of high-order statistics (Standard Deviation, Skewness and Kurtosis) correspond to mathematical steadiness and convergence of results. From the physical point of view, similarity analysis between jet’s wake sections reveals physical steadiness in results. Spectral analysis of the different regions of the flow field could be used as a sign that the energy cascade is correctly predicted or efficiently enough since this is where the smallest scales are usually present and which in effect require to be modelled by the different numerical schemes. The flow solver has been reviewed and improved. The former, a revised version of the reconstruction numerical schemes (WENO 5th and WENO 9th orders) has been performed and tested, the correspondent results have been compared against analytical data; the latter, correction of the method to compute the Jacobian of the transformation (singularity correction), by changing from the standard algebraic to geometric method, and augmented with transparent boundary condition, giving mathematical and physical meaning to the obtained results. The flow solver improvements and review have been verified and validated through simulations of a compressible Convergent-Divergent Nozzle (CDN), and the standard and a modified version of the Shock tube test cases, where the results are gained with minimal modelling effort. The study of numerical errors associated with the simulations of turbulent flows, for unsteady explicit time step predictions, have been performed and a new formula proposed. Ten different computational methods have been employed in the framework of ILES and computations have been performed for a jet flow configuration for which experimental data and DNS are available. It can be seen that a numerical error bar can be defined that takes into account the errors arising from the different numerical building blocks of the simulation method. The effects of different grids, Riemann solvers and numerical reconstruction schemes have been considered, however, the approach can be extended to take into account the effects of the initial and boundary conditions as well as subgrid scale modelling, if applicable. From the physical analysis several observations were established, revealing that differences in terms of jet’s core size are not an important parameter in terms of quantification and qualification of predictions, in other words, data should be reduced to the jet’s inertial reference system. Moreover, the comparative study has been performed to identify the differences between Riemann solvers (CBS and HLLC), Low Mach number Limiting/ Corrections (LMC), numerical reconstruction schemes (MUSCL and WENO) and spatial order of accuracy (2nd-order LMC, 5th-order LMC and 9th-order schemes) in combination with the most efficient cost/resolution discretization level (Medium mesh). The comparisons between results reveals for the Static and Co-Flow jets that the CBS MUSCL 5th-order LMC and the HLLC MUSCL 5th-order LMC as the most accurate schemes in predicting this class of flows, accordingly. Furthermore, the selected numerical methods show to be in accordance with the empirical (Static) and experimental (Co-flow) results in terms of resonance frequency and/or Strouhal number; also, the expected behaviour in terms of spectral energy decay rate throughout the jet’s central line is observed. To conclude the study of the Static jet case, a possible explanation for the jet’s buoyancy effect is presented.

A numerical model based on the full Navier-Stokes equations is developed to study the dynamics and deposit patterns of turbidity currents. The equation system is simplified using the dilute flow condition which allows one set of momentum equations. The model allows to simulate multiparticle flows in an ambient of pure or sea-water. The solution of the mathematical model is done extending the Characteristic-Based-Split (CBS) Finite Element algorithm to particle-laden flows. The algorithm is implemented by developing a computer program coded in Fortran 90. Additionally, a Box model based on mass balance is developed, which allows to account for the sedimentation, multiple particles and slope changes. Two dimensional and radial flows can be modelled using the proposed Box model just by changing the initial and boundary conditions. The confidence of both the Navier-Stokes based model and the mass-balance based Box model are successfully tested using laboratory experimental data.

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L’énergie renouvelable générée en sortie de systèmes de production éolienne et hydrolienne est très fluctuante. Ces fortes variations de la puissance sont liées à la turbulence intrinsèque au vent et aux courants. Ce phénomène est également appelé intermittence et il s’agit d’une contrainte majeure pour le développement de ce type d’énergie. Cette thèse présente l’analyse et la caractérisation de ces fluctuations stochastiques grâce à une approche statistique. Le cadre théorique est celui des cascades d’énergie multifractales. Les outils et méthodes utilisés visent à étudier l’influence de la turbulence pleinement développée sur les turbines horizontales tripales. Cette approche offre une méthode d’analyse multi-échelle de la turbulence, indépendamment de la taille du système considéré. L’analyse spectrale de la vitesse du vent et du courant permet la caractérisation des propriétés scalaires de la turbulence à partir d’une estimation de la dissipation. La décomposition modale empirique offre d’autre part, l’observation de l’interaction multi-échelle entre l’entrée et la sortie de tels systèmes de production. L’étude de l’intermittence de la puissance permet en particulier, la création d’outils de prévision qui reposent sur des bases physiques liées à l’intermittence et à l’invariance d’échelle. Ces outils peuvent répondre au besoin d’adaptation du réseau électrique face aux fluctuations de l’énergie éolienne. / The renewable energy output from wind and tidal turbines generates large fluctuations. Such large power variability are inherent to the turbulent wind and currents nature. This phenomenon is also called intermittency and it is a major obstacle for the development of this kind of energy. This thesis presents the analysis and characterization of stochastic fluctuations through a statistical approach. The theoretical framework is the multifractal energy cascades. The tools and methods aim to study the influence of the fully developed turbulence on a three-blade horizontal axis turbine. This approach provides a method for multiscale turbulence analysis, regardless the size of the considered system. The spectral analysis of wind and current velocity allows the characterization of flow scaling properties from a dissipation estimate. The Empirical Mode Decomposition offers on the other hand, an observation of the multiscale interaction between the input and output of such energy production systems. The study of the power intermittency allows in particular the conception of forecasting tools based on physical principles related to intermittency and to scaling. These tools are able to provide a solution for grid adaptation facing the wind and tidal energy fluctuations.

La dilution en faible concentration de chaînes polymériques longues dans un fluide newtonien peut réduire la traînée turbulente, phénomène nommé ici DR (drag reduction). Les polymères s’étirent et s’enroulent successivement, en interaction avec les structures turbulentes, imposant à DR un comportement transitoire. Il en résulte que la DR traverse trois stades. Lors du premier, la DR démarre à zéro et descend à des valeurs négatives en raison d’un étirement considérable du polymère au début du processus, ce qui exige de l’énergie de l’écoulement. Une fois atteint le niveau minimal de réduction de la traînée, les polymères commencent leur cycle d’étirement-enroulement et la DR augmente en réponse au développement de structures turbulentes, pour en arriver à une valeur maximale, menant au début du deuxième stade. Cependant, les polymères peuvent subir une dégradation mécanique à la suite d’un étirement polymérique intense. Lorsque la dégradation polymérique devient assez prononcée, la DR redescend pour atteindre une valeur finale qui indique que la dégradation s’est arrêtée. Le processus de dégradation polymérique caractérise le troisième stade. Dans le présent travail, ces trois stades sont examinés à l’aide de simulations numériques directes d’écoulements turbulents viscoélastiques FENE-P en géométries du type Poiseuille plan et Couette plan, sur un large éventail de nombres de Reynolds, de nombres de Weissenberg et d’extension maximale de la chaîne polymérique. Les deux premiers stades sont étudiés à partir des analyses tensorielle, énergétique et spectrale. Un nouveau modèle de dégradation polymérique est proposé afin de reproduire numériquement le stade final. / The addition of a small amount of polymers of high molecular weight can lead to a pressure drop decrease in turbulent flows. The polymers successively stretch and coil by interacting with the turbulent structures, which imposes a transient behaviour on the drag reduction (DR). As a result, DR undergoes three stages over time: A, B, and C. In stage A, DR departs from zero and assumes negative values due to a significant polymer stretching at the beginning of the process, which requires energy from the flow. After the minimum DR is reached, the polymers start their coil-stretch cycle and DR increases in response to the development of turbulent structures, achieving a maximum value, which makes for the beginning of stage B. However, during their coil-stretch cycle, polymers can be mechanically degraded as a result of an intense polymer stretching, which reduces their ability to act as energy exchange agents. Hence, when polymer degradation becomes pronounced, DR decreases until achieving a final value. The polymer degradation process characterizes the stage C. In the present work, numerical analyses are conducted aiming to investigate the stages A, B and C. The transient aspects of the polymer induced drag reduction phenomenon are explored with the aid of direct numerical simulations of turbulent plane Poiseulle and Couette flows of viscoelastic FENE-P fluids taking into account a large range of Reynolds number, Weissenberg number and maximum polymer molecule extensibility. Stages A and B are carefully studied from tensor, energy budget and spectral perspectives. A polymer scission model is developed in order to numerically reproduce the stage C.

La famille la plus commune des organismes dans le zooplancton est un groupe connu intitulé copépodes. Les copépodes ont un rôle majeur dans l’écosystème marin, car ils sont les producteurs secondaires dans la chaîne alimentaire écologique reliant les cellules de phytoplancton à des larves de poissons et même aux grands mammifères comme les baleines. Le comportement de nage de copépodes présente des sauts puissants et rapides. Une telle aptitude est utilisée pour échapper à des régions de cisaillement élevées, qui peuvent être causés soit par des perturbations d’écoulement, soit par un grand prédateur ou par la dynamique de fortes turbulences inhérentes à l’océan. La recherche présentée dans cette thèse se compose trois étapes. Tout d’abord, les données de vitesse de copépodes affichant réaction de fuite des sauts dans l’eau stagnante sont utilisées pour définir et affiner un modèle copépode lagrangien (CL). Deuxièmement, le modèle développé est utilisé pour simuler le comportement de milliers de copépodes dans un écoulement turbulent hydrodynamique entièrement développé obtenu par simulation numérique directe des équations de Navier-Stokes. Troisièmement, des analyses des données numériques sont réalisées pour quantifier la dynamique de copépodes en turbulence et pour faire une comparaison avec les observations expérimentales disponibles de copépodes en turbulence. Grâce à une étude expérimentale et numérique combinée, nous étudions l’impact du comportement de saut, l’effet de l’intensité de saut, d’orientation de saut, du temps de latence et rapport d’aspect géométrique des copépodes sur la distribution spatiale à petite échelle dans un environnement turbulent. / The most common family of multi-celled organisms in the zooplankton is a rather diversified group of crustaceans known with the name of copepods. Copepods have a major role in the marine ecosystem because they are the secondary producers in the ecological food-chain linking phytoplankton cells to fish larvae and even to large mammals such as whales. Copepods swimming behavior exhibits quick powerful jumps. Such an aptness is used to escape from high shear regions, which may be caused either by flow perturbations, produced by a large predator (i.e., fish larvae), or by the inherent highly turbulent dynamics of the ocean. The research presented this thesis goes into three steps. Firstly, recorded velocity tracks of copepods displaying escape response jumps in still water are used to define and tune a Lagrangian copepod (LC) model. Secondly, the model is further employed to simulate the behavior of thousands of copepods in a fully developed hydrodynamic turbulent flow obtained by direct numerical simulation of the Navier-Stokes equations. Thirdly, numerical data analysis is performed to quantify copepods’ dynamics in turbulence and make a comparison with available experimental observations of copepods in turbulence.Through a combined experimental and numerical study, we investigate the impact of jumping behavior on the small-scale patchiness of copepods in a turbulent environment. We further investigate the effect of jump intensity, jump orientation, jump latency time and geometrical aspect ratio of the copepods on the small-scale spatial distribution. At last, possible ecological implications of the observed clustering on encounter rates and mating success are provided.