Dissertations / Theses on the topic 'Coherent structures dynamics'

This thesis reports on the work done in studying coherent dynamics of excitons in quantum wells and exciton spins in quantum dots. Four-wave-mixing experiments were performed in a magnetic field on GaAs/AlGaAs single quantum wells known to contain spatially large monolayer islands. The properties of the dynamics of the signals are discussed, and compared to previous values. Beating was observed between the monolayer islands, and the variation of the phase of these beats was examined in an attempt to determine the mechanism for coupling between them. The majority of the data suggests the monolayer islands are not coherently coupled, however, the behaviour under some conditions brought this into question and required further modelling. Models for a three-level system and two on-interacting two-level systems including the effects of a local field are presented. Neither model was able to reproduce the experimental data on its own, however, a combination of the two was successful. On the basis of the modelling, it was shown that the contribution to the signal from coherently coupled transitions decreases as a function of magnetic field. This gives some insight into the possible coupling mechanisms, and these are discussed. Pump-probe experiments are performed on InGaAs/GaAs quantum dots in an attempt to obtain details of the coherent exciton-spin dynamics in such systems. Decoherence of the exciton spin is observed in sufficiently high magnetic fields, and the dependence of the dephasing time on field strength and temperature are studied. To my knowledge, these are the first reported experimental results showing decoherence of exciton spin. Comparisons of the observed behaviour with existing predictions are made in an attempt to determine the mechanism for loss of exciton spin coherence in quantum dots. None of the predicted mechanisms were able to fit my experimental data adequately, suggesting the presence of some other more efficient mechanism.

This thesis examines the statistics and dynamics of turbulent flow structures generated by towing a grid through a tank of water. The structures were made visible by recording the paths of aluminum tracers moving with the water surface. Flow patterns recorded using a time-exposure method were manually analyzed to extract information on the structure statistics. This two-dimensional flow field was found to be composed of closed rotating 'surface eddies', open and largely translational 'river' motion and stagnant regions. Energy distributions of the eddies and rivers were obtained and characterized by Boltzmann type distributions. A newly developed computer-automated structure identification and flow field analysis system was used to study the structure dynamics. The system analyzes digital images obtained from video recordings of the tracer motion. The predominant evolution processes of initial vortex production, eddy pairing, viscous decay and the omega decay were examined. Flow Reynolds numbers, based on bar spacing, of about 10,000 were examined. The structure statistics and dynamics study was performed in order to examine the validity and viability of a new model for turbulence. The model predicts the evolution of a population of structures using rate equations where the rate coefficients are determined by the individual structure dynamics. A summary of the model is presented and contrasted with models based the the Reynolds stresses as well as computational models.
Science, Faculty of
Physics and Astronomy, Department of
Graduate

The term spatiotemporal chaos refers to physical phenomena that exhibit irregular oscillations in both space and time. Examples of such phenomena range from cardiac dynamics to fluid turbulence, where the motion is described by nonlinear partial differential equations. It is well known from the studies of low dimensional chaotic systems that the state space, the space of solutions to the governing dynamical equations, is shaped by the invariant sets such as equilibria, periodic orbits, and invariant tori. State space of partial differential equations is infinite dimensional, nevertheless, recent computational advancements allow us to find their invariant solutions (exact coherent structures) numerically. In this thesis, we try to elucidate the chaotic dynamics of nonlinear partial differential equations by studying their exact coherent structures and invariant manifolds. Specifically, we investigate the Kuramoto-Sivashinsky equation, which describes the velocity of a flame front, and the Navier-Stokes equation for an incompressible fluid in a circular pipe. We argue with examples that this approach can lead to a theory of turbulence with predictive power.

Understanding surface erosion in tokamaks due to contact with hot plasma is critical in designing new high power devices. The propagation of the plasma through the scrape off layer (SOL) ultimately defines the spatio-temporal characteristics of this erosion, hence modelling of this region is an important area of research. Transport in the SOL is attributed to advective motions of plasma blobs, for which the advective velocity is estimated in the literature. A new paradigm for comparing the theory of plasma blobs with experimental data is developed, which treats density and velocity data as sets of coherent structures via a peak detection algorithm. The phase difference of plasma density and radial velocity peaks take values depending on the dominating physics of the blob motion. Values of this phase difference are predicted in the interchange and drift wave cases for a strongly nonlinear plasma. Analysis of MAST data reveals interchange activity in the edge and SOL, and a phase structure typical of sheath limited models in the SOL. A further application of the paradigm examines the blob velocity-density scaling v ∝ nα. A new sheath limited model for blob advection with divertor density nt constant gives α = 1. Predictions in the zero parallel current case depend on the blob nonlinearity; we examine the dependency of α on the nonlinearity by solving the time independent equation of blob motion for a range of density profiles, finding α ∼ 0.3 for MAST nonlinearity strength. The α parameter is estimated statistically from MAST data, and it found to peak at α ∼ 1 near the last closed flux surface (LCFS) and fall to zero further from the plasma. The scaling behaviour is further examined using the TOKER code. A numerical model, hTOKER, is developed. A subgrid model is employed that terminates the plasma at a chosen scale with defined spectral properties, which allows a physically accurate way to reduce resolution and computational burden. We examine sheath potential drop (SPD) and finite ion temperature (FTI) effects on SOL transport in the cases of constant (CTI) and flute (SI) nt boundary conditions. For the advection of individual blobs, SPD effects that are stable in the SI case are found to be unstable in the CTI case, and FTI effects are found to be stabilising in all cases. SOL plasma simulations are used to examine the differences in particleenergy flux and peak phase difference using floating or plasma potential. Floating potential overestimates flux by a factor 2, and shifts phase differences from 0◦ to ∼ −30◦. FTI effects are without cancellation from the gyro-viscous counterparts.

Dans cette thèse, on propose un nouveau modèle de couplage auto-cohérent entre des structures magnétiques cohérentes sur les échelles ioniques et des ondes dites de sifflement (whistlers, en anglais) à plus hautes fréquences, afin d’interpréter les données expérimentales recueillies par les satellites Cluster pendant un sous-orage magnétique dans la région nocturne de la magnétosphère terrestre. Le couplage fournit un mécanisme pour confiner et transporter les ondes whistlers par l’intermédiaire d’ une onde nonlinéaire qui se propage obliquement par rapport au champ magnétique. Cette étude s’appuie sur une analyse des données expérimentales, sur une modélisation théorique ainsi que sur des simulations numériques. Pendant les sous-orages magnétiques, la magnétosphère est soumise à de fortes perturbations magnétiques et électriques dans une vaste gamme de fréquences, qui vont des basses fréquences, inférieures ou de l’ordre de l’échelle temporelle typique ionique, aux hautes fréquences, supérieures ou de l’ordre de l’ échelle temporelle typique électronique. Afin de connaître les processus physiques qui déterminent la dynamique de la magnétosphère pendant les sous-orages, il est fondamental de comprendre si, et avec quel méchanisme, des couplages peuvent se produire entre des ondes qui se propagent sur des temps caractéristiques différents. Des structures magnétiques à basse fréquence ont déjá été obsérvées dans des régions comme la magnétogaine et le vent solaire, éventuellement associées à des ondes whistlers à plus haute fréquence. Dans cette thèse, on montre que des structures similaires sont obsérvées dans la couche de plasma à l’intérieur de la magnétosphère. On s’intérroge ensuite sur la façon dont l’inhomogénéité de telles structures peut influencer la propagation des ondes à plus haute fréquence. Grâce à ses quatre satellites en configuration tetraédrique et à ses mésures à haute résolution temporelle, la mission Cluster nous offre une occasion unique de pouvoir analyser la structure spatiale des perturbations stationnaires (ou se propageant) et d’étudier la dynamique du plasma sur des échelles temporelles plus courtes, telles que celles des ondes whistlers. Ainsi, je décrirai les émissions d’ondes whistlers détectées par les satellites Cluster à l’intérieur de structures magnétiques cohérentes situées dans un écoulement de plasma rapide pendant le sous-orage du 17 Août 2003. Au cours de cette période, les satellites Cluster sont situés dans la couche de plasma, séparés d’une distance de l’ordre des échelles spatiales typiques ioniques(le rayon de giration ou la longueur d’inertie des ions). Les ondes whistlers sont corrélées avec des structures magnétiques characterisées par un minimum du module du champ magnétique et un maximum de densité du plasma. Ces dernières ont été modélisées comme des ondes planes nonlinéaires de type lent qui piègent et transportent les ondes whistlers. A partir d’une étude théorique et numérique en utilisant une approche bi-fluide, on peut alors reproduire les données observationnelles. Le rôle possible de telles structures couplées dans la physique des sous-orages est aussi discuté. Ce nouveau mécanisme de piégeage, étudié ici en utilisant comme guide pour les whistlers une onde oblique de type magnétosonique, est d’intérêt plus général par rapport au contexte spécifique des observations présentées dans cette thèse. En effet, d’autres ondes nonlinéaires, comme par exemple les ondes d’ Alfvén obliques ou d’ Alfvén cinétiques dans les plasmas à beta fort (où beta est le rapport de la pression thermique du plasma sur la pression magnétique), pourraient aussi transporter les whistlers. Ce modèle de piégeage constitue aussi une explication alternative aux modèles existants qui considèrent une inhomogénéité stationnaire sous la forme d’un canal de densité. Enfin, l’étude décrite dans cette thèse concerne des problématiques fondamentales en physique des plasmas, comme la propagation d’ondes dans les milieux inhomogènes et l’interaction entre modes sur des échelles temporelles différentes
A new model of the self-consistent coupling between low frequency, ion-scale coherent magnetic structures and high frequency whistler waves is proposed in order to interpret space data gathered by Cluster satellites during substorm events, in the night sector of the Earth’s magnetosphere. The coupling provides a mechanism to spatially confine and transport whistler waves by means of a highly oblique, propagating nonlinear carrier wave. The present study relies on a combination of data analysis of original in situ measurements, theoretical modeling and numerical investigation. During substorms, the magnetosphere undergoes strong magnetic and electric field fluctuations ranging from low frequencies, of the order or less than the typical ion-time scales, to higher frequencies, of the order or higher than the typical electron time-scales. To understand basic plasma physical processes which characterize the magnetosphere dynamics during substorms an analysis of whether, and by which mechanism, waves occurring at these different time scales are coupled, is of fundamental interest. Low frequency magnetic structures are commonly detected in environments such as the magnetosheath and the solar wind, as well as in the dusk magnetosphere, possibly correlated with higher frequency whistler waves. In this Thesis it is shown that similar magnetic structures, correlated with whistler waves, are observed in the magnetospheric plasma sheet during substorms. The interesting question arises as to how the inhomogeneity associated with such magnetic structures affects the propagation of higher frequency waves. The Cluster mission, thanks to its four satellites in tetrahedron configuration and high temporal resolution measurements, provides a unique opportunity on the one hand to explore the spatial structure of stationary and propagating perturbations observed at low frequencies and on the other hand to study dynamics occurring at higher temporal scales, via whistler mode waves. With regard to this, I will describe the Cluster spacecraft detection of large amplitude whistler wave packets inside coherent ion-scale magnetic structures embedded in a fast plasma flow during the August 17th 2003 substorm event. In this period the Cluster satellites were located in the plasma sheet region and separated by a distance which is less than the magnetotail typical ion-scale lengths, namely the ion gyroradius and the ion inertial length. The observed whistler emissions are correlated with magnetic field structures showing magnetic depletions associated with density humps. As a first step, the latter have been modeled as one dimensional nonlinear slow waves which spatially confine and transport whistlers, in the framework of a two-fluid approximation. This schematic model is investigated through a theoretical and numerical study by means of a two-fluid code, and it is shown that the proposed model goes quite well with data interpretation. Its possible role in substorm dynamics is also discussed. This new trapping mechanism, studied here by using a highly oblique slow magnetosonic soliton as a guide for whistler waves, is of more general interest beyond the specific context of the observations reported in this Thesis. Other nonlinear structures showing similar features, for example highly oblique nonlinear Alfvén waves or kinetic Alfvén waves in high beta plasmas, can in principle act as wave carriers. The model proposed provides an explanation for the recurrent detection of whistlers inside ion-scale magnetic structures which is alternative to usual models of stationary magnetic structures acting as channels. Moreover, the study described in this Thesis addresses more general questions of basic plasma physics, such as wave propagation in inhomogeneous plasmas and the interaction between wave modes at different temporal scales

This study aimed to understand the processes that govern free surface behaviour in depth-limited turbulent flows. Experimental data has shown that the turbulence properties at a point near the free surface relate directly to the properties of the free surface pattern. This would suggest a direct linkage between the free surface and the underlying turbulence field, but this cannot be true since the free surface pattern is strongly dynamic while the sub-surface turbulence field is relatively persistent. An oscillatory spatial correlation function was derived which explains the de-linkage, showing that the turbulence-generated surface pattern periodically inverts as it advects downstream. A model was developed, which shows that the observed free surfaces can be considered as an ensemble of overlapping but behaviourally independent oscillons. These are shown to influence a zone of fluid beneath the surface and invert at a frequency which is a function of the root-mean-square roughness height of the free surface. The spatial frequency of free surface oscillation relates strongly to the spatial frequency of turbulent structures, suggesting that the oscillon motion may form the trigger for near-bed bursting events. Given these relationships, it is proposed that measurement of the free surface behaviour may allow remote measurement of flow conditions. An acoustic wave probe was developed, which is able to remotely recover the key features of the water surface pattern. An array of such probes is proposed for the accurate measurement of temporal and spatial properties of turbulent free surfaces and hence the underlying bulk flow conditions.

L’étude des processus physiques d’un système d’upwelling est essentielle pour comprendre sa variabilité actuelle et ses changements passés et futurs. Cette thèse présente une étude interdisciplinaire du système d’upwelling côtier à partir de différentes données acquises par satellite, l’accent étant mis principalement sur le système d’upwelling d’Afrique du Nord-Ouest (NWA). Cette étude interdisciplinaire aborde (1) le problème de l’identification et de l’extraction automatiques du phénomène d’upwelling à partir d’observations satellitaires biologiques et physiques. (2) Une étude statistique de la variation spatio-temporelle de l’upwelling de la NWA tout au long de son extension et de ses différents indices d’upwelling. (3) Une étude des relations non linéaires entre le mélange de surface et l’activité biologique dans les régions d’upwelling. (4) études lagrangiennes de tourbillons cohérents; leurs propriétés physiques et identification automatique. (5) L’étude des transports effectués par les tourbillons lagrangiens de la NWA Upwelling et leur impact sur l’océan
Studying physical processes of an upwelling system is essential to understand its present variability and its past and future changes. This thesis presents an interdisciplinary study of the coastal upwelling system from different satellite acquired data, with the main focus placed on the North West African (NWA) upwelling system. This interdisciplinary study covers (1) the problem of the automatic identification and extraction of the upwelling phenomenon from biological and physical satellite observations. (2) A statistical study of the spatio-temporal variation of the NWA upwelling throughout its extension and different upwelling indices. (3) A Study of the nonlinear relationships between the surface mixing and biological activity in the upwelling regions. (4) Lagrangian studies of coherent eddies; their physical properties and automatic identification. (5) The study of transport made by Lagrangian eddies off the NWA Upwelling and their impact on the open ocean. [...]

The Lagrangian dynamics of two-dimensional incompressible fluid flows is considered, with emphasis on transport processes in atmospheric and oceanic flows. The dynamical-systems-based approach is adopted; the Lagrangian motion in such systems is studied with the aid of Kolmogorov-Arnold-Moser (KAM) theory, and results relating to stable and unstable manifolds and lobe dynamics. Some nontrivial extensions of well-known results are discussed, and some extensions of the theory are developed. In problems for which the flow field consists of a steady background on which a time-dependent perturbation is superimposed, it is shown that transport barriers arise naturally and play a critical role in transport processes. Theoretical results are applied to the study of transport in measured and simulated oceanographic and atmospheric flows. Two particular problems are considered. First, we study the Lagrangian dynamics of the zonal jet at the perimeter of the Antarctic Stratospheric Polar Vortex during late winter/early spring within which lies the "ozone hole". In this system, a robust transport barrier is found near the core of a zonal jet under typical conditions, which is responsible for trapping of the ozone-depleted air within the ozone hole. The existence of such a barrier is predicted theoretically and tested numerically with use of a dynamically-motivated analytically-prescribed model. The second, oceanographic, application considered is the study of the surface transport in the Adriatic Sea. The surface flow in the Adriatic is characterized by a robust threegyre background circulation pattern. Motivated by this observation, the Lagrangian dynamics of a perturbed three-gyre system is studied, with emphasis on intergyre transport and the role of transport barriers. It is shown that a qualitative change in transport properties, accompanied by a qualitative change in the structure of stable and unstable manifolds occurs in the perturbed three-gyre system when the perturbation strength exceeds a certain threshold. This behavior is predicted theoretically, simulated numerically with use of an analytically prescribed model, and shown to be consistent with a fully observationally-based model.

The understanding of the physics of the Coherent Structures and their interaction with the remaining fluid motions is of paramount interest in Turbulence Research.

Indeed, recently had been suggested that separating and understanding the the different physical behavior of Coherent Structures and "uncoherent" background might very well be the key to understand and predict Turbulence. Available understanding of Coherent Structures shows that their size is considerably larger than the turbulent macro-scale, making permissible the application of Large Eddy Simulation to their simulation and study, with the advantage to be able to study their behavior at higher Re and more complex geometry than a Direct Numerical Simulation would normally allow. Original purpose of the present work was therefore the validation of the use of Large Eddy Simulation for the study of Coherent Structures in Shear-Layer and the its application to different flow cases to study the effect of the flow topology on the Coherent Structures nature.

However, during the investigation of the presence of Coherent Structures in numerically generated LES flow fields, the aging in house Large Eddy Simulation (LES) code of the Environmental & Applied Fluid Dynamics Department has shown a series of limitations and shortcomings that led to the decision of relegating it to the status of Legacy Code (from now on indicated as VKI LES legacy code and of discontinuing its development. A new natively parallel LES solver has then been developed in the VKI Environmental & Applied Fluid Dynamics Department, where all the shortcomings of the legacy code have been addressed and modern software technologies have been adopted both for the solver and the surrounding infrastructure, delivering a complete framework based exclusively on Free and Open Source Software (FOSS ) to maximize portability and avoid any dependency from commercial products. The new parallel LES solver retains some basic characteristics of the old legacy code to provide continuity with the past (Finite Differences, Staggered Grid arrangement, Multi Domain technique, grid conformity across domains), but improve in almost all the remaining aspects: the flow can now have all the three directions of inhomogeneity, against the only two of the past, the pressure equation can be solved using a three point stencil for improved accuracy, and the viscous terms and convective terms can be computed using the Computer Algebra System Maxima, to derive discretized formulas in an automatic way.

For the convective terms, High Resolution Central Schemes have been adapted to the three-dimensional Staggered Grid Arrangement from a collocated bi-dimensional one, and a system of Master-Slave simulations has been developed to run in parallel a Slave simulation (on 1 Processing Element) for generating the inlet data for the Master simulation (n - 1 Processing Elements). The code can perform Automatic Run-Time Load Balancing, Domain Auto-Partitioning, has embedded documentation (doxygen), has a CVS repository (version managing) for ease of use of new and old developers.

As part of the new Frame Work, a set of Visual Programs have been provided for IBM Open Data eXplorer (OpenDX), a powerful FOSS Flow visualization and analysis tool, aimed as a replacement for the commercial TecplotTM, and a bug tracking mechanism via Bugzilla and cooperative forum resources (phpBB) for developers and users alike. The new M.i.O.m.a. (MiOma) Solver is ready to be used again for Coherent Structures analysis in the near future.
Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished

Une écoulement de cavité ouverte tridimensionnel saturé non-linéairement est étudié par une approche spatio-temporelle utilisant des données expérimentales résolues à la fois en temps et en espace. Ces données ont été acquises dans deux plans longitudinaux, respectivement perpendiculaire et parallèle au fond de la cavité, dans le régime incompressible, en air ou en eau. À l'aide de multiples méthodes de décompositions globales en temps et en espace, les ondes et les structures cohérentes constituant la dynamique dans le régime permanent et pouvant être produites par des mécanismes d'instabilités différents sont identifiées et caractérisées.Tout d'abord, on approfondit la compréhension de l'effet des non-linéarités sur les oscillations auto-entretenues de la couche cisaillée impactante et leurs interactions avec l'écoulement intra-cavitaire. En particulier, l'analyse spectrale d'une portion de l'espace des paramètres permet de mettre en évidence un lien entre l'accrochage des modes d'oscillations auto-entretenues, la modulation d'amplitude au niveau du coin impactant et l'intermittence de ces modes. De plus, l'observation des basses fréquences intéragissant fortement avec les oscillations de la couche de mélange démontre l'existence d'une dynamique tridimensionnelle intrinsèque à l'intérieur de la cavité malgré les perturbations causées par la couche cisaillée instable.Les analyses de stabilité linéaire ont montré que des instabilités centrifuges peuvent résulter de la courbure induite par la recirculation. L'étude de la dynamique après saturation révèle de nombreuses structures cohérentes dont les propriétés sont quantifiées et classées en s'appuyant sur la forme des instabilités sous-jacentes: des ondes transverses progressives ou stationnaires. Enfin, certains comportements des structures saturées suggèrent que les mécanismes non-linéaires gouvernant le développement de l'écoulement une fois sorti du régime linéaire pourraient être étudiés dans le cadre des équations d'amplitude
A space-time study of a three-dimensional nonlinearly saturated open cavity flow is undertaken using time-resolved space-extended experimental data, acquired in both cross-stream and spanwise planes, in incompressible air and water flows. Through use of multiple modal decompositions in time and space, the waves and coherent structures composing the dynamics in the permanent regime are identified and characterised with respect to the instabilities arising in the flow.Effects of nonlinearities are thoroughly investigated in the impinging shear layer, regarding the self-sustained oscillations and their interactions with the inner-flow. In particular, the analysis conducted throughout the parameter space enlightens a global connection between the selection of locked-on modes and the amplitude modulation at the impingement and the mode switching phenomenon. Furthermore, observations of low frequencies interacting drastically with the shear layer flapping motion underline the existence of intrinsic coherent three-dimensional dynamics inside the cavity in spite of the shear layer disturbances.Linear stability analyses have demonstrated that centrifugal instabilities are at play along the main recirculation. The present investigation of the dynamics after onset of the saturation reveals numerous space-time coherent structures, whose properties are quantified and classified with respect to the underlying instabilities: travelling or standing spanwise waves. Finally, some patterns exhibited by the saturated structures suggest that the nonlinear mechanisms governing the mutations of the flow after the linear regime could gain more insight in the frame of amplitude equations

Les courants turbulents de bord ouest sont l'un des phénomènes les plus dominants des océans, il en existe aux faibles latitudes aussi. Ils sont caractérisés par une dynamique très turbulente avec une forte production d'énergie cinétique, et une forte variabilité interne. Plusieurs régions existent où les courants de bord ouest se rétrofléchissent (décollage de la côte) pour former des structures cohérentes: des anticyclones, des bursts (arrachements) et des dipoles. Circulant le long de la côte, les courants de bord ouest interagissent très fortement avec le bord ouest et la bathymétrie et sont donc un problème de couche limite. Cependant aucune étude du point de vue de la théorie de couche limite n'a été jamais été faite. Cette thèse aborde le problème d'un point de vue de couche limite par l'utilisation d'un modèle idéalisé "shallow water" à très haute résolution (2.5km) afin d'isoler et de comprendre les processus. Les résultats sont ensuite appliqués à des sorties de modèle réaliste Drakkar (~10km) basé sur le code NEMO. Le courant de Somali est ensuite pris pour cette application
Strong western boundary currents are one of dominant features of the world oceans, also at low latitudes. They exhibit a turbulent dynamics and their region is a source of strong kinetic energy production and internal variability of the worlds oceans. Several places exists where the western boundary currents retrofect (i.e separation from the coast) and generate coherent structures as anticyclonic eddies, bursts and dipoles. The dynamics of turbulent western boundary currents has so far not been extensively studied in the viewpoint of turbulent boundary-layer theory. The approach followed in this thesis is to use a fine resolution (2.5km) reduced-gravity shallow water model to understand the turbulent boundary-layer processes and then apply these findings to the Ocean General Circulation Model NEMO in the Drakkar configuration (~10km). The case of the Somali Currentis considered for this application

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.

Cette thèse présente une étude numérique des régimes turbulents au sein d'un écoulement de Poiseuille plan forcé par un gradient de pression constant. L'effort numérique a porté principalement sur le concept d'Unité Minimale. Dans la première partie, des simulations en régime turbulent ont été conduites en géométrie périodique. Les DNS en Unité Minimale montrent que, l'activité turbulente se trouve localisée à proximité d'une des parois, et que la dynamique aux temps longs s'organise autour de renversements abrupts. Dans la seconde partie, on recherche par le calcul les états cohérents exactes en particulier les états dits frontière. Ces états frontière, obtenus par dichotomie, sont caractérisés par tourbillons longitudinaux et une paire unique de stries toujours localisées à proximité d'une seule paroi. Des représentations de la dynamique dans l'espace des phases sont reconstruites à l'aide de divers observables. La dynamique d'un renversement s'articule autour de visites transitoires vers un espace de solutions quasi-symétriques. Une onde progressive exacte, instable et quasi-symetrique a ainsi été identifiée. L'analyse de stabilité révèle que ses vecteurs propres séparent l'espace des phases en deux basins distincts. La dernière partie remet en question l'auto-similarité des différents régimes d'équilibre d'écoulement. Contrairement aux études récentes qui se concentrent sur les solutions à structure symétrique imposée, nos résultats suggèrent que les unités de parois sont également pertinentes pour les états frontière lorsqu'ils sont localisés près d'une paroi, meme si l'auto-similarité n'est pas aussi flagrante que pour les régimes turbulents
This thesis numerically investigates the dynamics of turbulence in plane Poiseuille flow driven by a fixed pressure gradient. The focus is especially on computations carried out within the minimal flow unit (M.F.U.). In the first part, turbulent simulations are carried out in spatially periodic channels. In the M.F.U. simulations, the turbulent activity appears to be localised near one wall and the long term dynamics features abrupt reversals. In the next part, we look numerically for exact coherent states in the M.F.U. system. Edge states, which are computed using bisection exhibit streamwise vortices and a single pair of streaks localised near only wall at all times. Different state space representations and phase portraits were constructed using appropriately chosen variables. The dynamics along a turbulent reversal is organised around transient visits to a subspace of (almost) symmetric flow fields. A nearly-symmetric exact travelling wave (TW) solution was found in this subspace. Stability analysis of the TW revealed that its unstable eigenvectors separate the state space into two symmetric basins. In the last part of this thesis, the self-similarity of the different non-trivial equilibrium flow regimes computed in this work, is addressed. Contrarily to most studies focusing on symmetric solutions, the present study suggests that inner scaling is relevant for the description of edge regimes as well although the self-similarity is not as satisfactory as for the turbulent regimes

Esta tese trata o escoamento ao redor de um cilindro logo após a sua primeira instabilidade, dentro do seu regime bidimensional periódico. A abordagem é principalmente teórica, passa por experimentos e culmina em uma importante parte numérica que complementa a teoria com evidências e ilustrações. As principais contribuições são a análise sobre a composição modal da solução dentro do regime periódico e o método desenvolvido para identificar autovetores de uma linearização da equação de Navier-Stokes presentes em uma dada solução. As bases compostas pelos autovetores identificados servem para a projeção da equação de Navier-Stokes e dão a essência dos modelos reduzidos deste estudo. A aplicação numérica apresentada para Re = 60 traz duas iterações do processo, com duas bases de autovetores de dimensões 12 e 24. Os modelos reduzidos são numericamente estáveis e a sua integração apresenta custo várias ordens mais baixo que o da simulação numérica completa. As séries temporais das coordenadas e as bases de autovetores possibilitam a recomposição do escoamento e a sua comparação com a simulação numérica de referência. A análise de aderência foi baseada nas médias temporais, nos valores de Strouhal e na estrutura dos harmônicos. Ambos modelos reduzidos têm correspondência próxima com o comportamento assintótico do escoamento e a tendência convergente das iterações é clara. As simetrias espaciais e temporais dos harmônicos são facilmente identificadas na estrutura dos modelos, de forma que as bases construídas podem ser entendidas como conjuntos de estruturas coerentes do fenômeno.
This thesis concerns the flow past a cylinder just after its first bifurcation, within its two-dimensional periodic regime. The approach is mainly theoretical, goes through experiments and is concluded by an important numerical part which complements the theory with evidences and illustrations. The main contributions are the analysis concerning the modal composition of the solution within the periodic regime and a method to identify eigenvectors of some linearizaton of the Navier-Stokes equation participating on a given solution. The bases spanned by the identified eigenvectors are employed in the projection of the Navier-Stokes equation and are central to the reduced models of this study. The numerical results for Re = 60 present two iterations of the process, with two bases of dimensions 12 e 24. The reduced models are numerically stable and their integration is many orders less costly than that of the full simulation. The time series of the modal coordinates and the eigenvectors bases allow the recomposition of the flow and its comparison with the full simulation results. The convergence analysis was based on the time averages, the Strouhal number values and the harmonic structure. Both reduced models have close correspondence with the asymptotic behavior of the flow and the convergent trend of the iterations is clear. The space and time symmetries of the harmonics have a simple representation within the structure of the models, therefore the identified bases can be understood as sets of coherent structures of the phenomenon.

2008/2009
In this work the turbulent field developing in case of local erosion around a 45° wing-wall bridge abutment was investigated numerically. Three different scour conditions were considered: beginning of the process, logarithmic phase and equilibrium stage. The flow field was computed using a wall-resolving large eddy simulation (a simulation where the near-wall viscous sub-layer is directly resolved) and the bathymetric data were taken from physical experiments with an equivalent geometry. The dynamics of the coherent structures forming around the obstacle and inside the scour-hole was investigated and its influence on the modeling of the problem and on the erosion process was discussed. The analysis suggested that the full dynamics of the vortex system should be directly solved since simple eddy-viscosity models, as the k-ε model in RANS approach, were found to be not suited for this kind of problem and since high-order statistics were found to be important for the evolution of the local scour. The results of the present study may be helpful to formulate new physical-based local scour models to be used for practical evaluation of the scour depth around bridge abutments.
XXII Ciclo
1981

Efficient analysis and storage of data is an integral but often challenging task when working with computation fluid dynamics mainly due to the amount of data it can output. Methods centered around the proper orthogonal decomposition were used to analyze, compress, and model various simulation cases. Two different high-fidelity, time-accurate turbomachinery simulations were investigated to show various applications of the analysis techniques. The first turbomachinery example was used to illustrate the extraction of turbulent coherent structures such as traversing shocks, vortex shedding, and wake variation from deswirler and rotor blade passages. Using only the most dominant modes, flow fields were reconstructed and analyzed for error. The reconstructions reproduced the general dynamics within the flow well, but failed to fully resolve shock fronts and smaller vortices. By decomposing the domain into smaller, independent pieces, reconstruction error was reduced by up to 63 percent. A new method of data compression that combined an image compression algorithm and the proper orthogonal decomposition was used to store the reconstructions of the flow field, increasing data compression ratios by a factor of 40.The second turbomachinery simulation studied was a three-stage fan with inlet total pressure distortion. Both the snapshot and repeating geometry methods were used to characterize structures of static pressure fluctuation within the blade passages of the third rotor blade row. Modal coefficients filtered by frequencies relating to the inlet distortion pattern were used to produce reconstructions of the pressure field solely dependent on the inlet boundary condition. A hybrid proper orthogonal decomposition method was proposed to limit burdens on computational resources while providing high temporal resolution analysis.Parametric reduced order models were created from large databases of transient and steady conjugate heat transfer and airfoil simulations. Performance of the models were found to depend heavily on the range of the parameters varied as well as the number of simulations used to traverse that range. The heat transfer models gave excellent predictions for temperature profiles in heated solids for ambitious parameter ranges. Model development for the airfoil case showed that accuracy was highly dependent on modal truncation. The flow fields were predicted very well, especially outside the boundary layer region of the flow.

The thesis describes state of the art volumetric measurement techniques and applies a 3D measurement technique, 3D Scanning Particle Tracking Velocimetry, to the transitional backward facing step flow. The measurement technique allows the spatial and temporal analysis of coherent structures apparent at the backward facing step. The thesis focusses on the extraction and interaction of coherent flow structures like shear layers or vortical structures.

Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2008.
Turgay Uzer, Committee Chair ; M. Raymond Flannery, Committee Member ; Chandra Raman, Committee Member ; Dragomir Davidovic, Committee Member ; Chongchun Zeng, Committee Member.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2013.
Some pages landscape orientation. Cataloged from PDF version of thesis.
Includes bibliographical references (pages 211-218).
The identification of coherent structures enhances the understanding of transport by complex flows such as those found at the ocean surface. The rapidly developing approach of Lagrangian Coherent Structures (LCSs) is based on the identification of codimension-1 structures that are locally the strongest repelling material surfaces in forwards or backwards-time over a given time window. Current theory and methods regarding LCSs are surveyed, and we present a modified algorithm for their detection, highlighting the pros and cons of the modified approach. One beneficial aspect of the modified approach is that it is possible to classify and advect LCSs through the time window. We apply the improved detection scheme as well as the classification to a high quality, validated simulation of ocean surface flow near the Ningaloo reef along the coast of Western Australia. This region is home to the longest fringing reef in Australia, a diverse marine environment, and a growing offshore drilling industry, and understanding the surface flows will enable better informed decisions to be made in this environmentally delicate domain. In addition to applying the LCS techniques, for the first time we account for the impact of surface winds on the LCS field by creating a hybrid current-wind velocity field. While the LCS approach is based on rigorous dynamical systems theory, its reliance on an accurate velocity field restricts potential ocean applications to simulations or regions with surface velocity measurements via systems like HF radar stations. An untapped resource is the data collected from float trajectories. With the goal of eventual application to these data sets, we develop a coherent structure detection algorithm utilizing sparse trajectory data. This new approach is based on the application of tools from braid theory, which produce a simplified perspective of the mixing of two-dimensional systems that enables rapid analysis. As a first application, our braid-based approach is applied to a periodically stirred system.
by Michael R. Allshouse.
Ph. D.

In many problems in dynamical systems one is interested in the identification of sets which have qualitatively different fates. The finite-time Lyapunov exponent (FTLE) method is a general and equation-free method that identifies codimension-one sets which have a locally high rate of stretching around which maximal exponential expansion of line elements occurs. These codimension-one sets thus act as transport barriers. This geometric framework of transport barriers is used to study various problems in phase space transport, specifically problems of separation in flows that can vary in scale from the micro to the geophysical. The first problem which we study is of the nontrivial motion of inertial particles in a two-dimensional fluid flow. We use the method of FTLE to identify transport barriers that produce segregation of inertial particles by size. The second problem we study is the long range advective transport of plant pathogen spores in the atmosphere. We compute the FTLE field for isobaric atmospheric flow and identify atmospheric transport barriers (ATBs). We find that rapid temporal changes in the spore concentrations at a sampling point occur due to the passage of these ATBs across the sampling point. We also investigate the theory behind the computation of the FTLE and devise a new method to compute the FTLE which does not rely on the tangent linearization. We do this using the 925 matrix of a probability density function. This method of computing the geometric quantities of stretching and FTLE also heuristically bridge the gap between the geometric and probabilistic methods of studying phase space transport. We show this with two examples.
Ph. D.

This thesis presents how sources of coherent sources extreme ultraviolet (XUV) and soft X-ray wavelengths can be generated and how these sources may be used to study both the dynamics and structure of molecular systems. Developmental work on a beam line designed to generate XUV radiation using high harmonic generation is presented. In addition to commissioning experimental work using both a flat-field XUV spectrometer and magnetic bottle electron spectrometer, software development work towards building a scalable and future proof acquisition framework for future experiments is presented. The remainder of the thesis presents results obtained from experiments performed at the Linac Coherent Light Source (LCLS) X-ray free electron laser (FEL). We demonstrate that by using a UV femtosecond pulse and a weakly focused X-ray pulse of duration 70 fs, the evolution of UV induced photoisomerisation of 1-3 cyclohexadiene can be tracked. Over timescales of ≈1 ps after UV excitation, the ion yields of the H+ and C+ species were observed to increase by 10% and the observed kinetic energy of all fragments is observed to increase over the same time scale, which can be explained by the structural change of the molecule into the hexatriene isomers. There has been a recent focus in FEL science in using tightly focused X-rays to generate so called hollow atoms, with a completely empty inner shell. Study of the products of the creation of these states ideally requires a measurement in coincidence of multiple particles. We demonstrate that by using the technique of partial covariance mapping (PCM) in conjunction with a high efficiency electron time-of-flight spectrometer, multiple processes in the core ionisation of neon can be resolved. We also use the scheme to successfully measure single site double-core hole states in the hydrocarbons of acetylene and ethane. We discuss how this technique will be a powerful tool in future experiments designed for chemical analysis of the core hole states of systems.

The theory of Lagrangian Coherent Structures (LCS) enables prediction of material transport by turbulent winds, such as those observed in the Earth's Atmospheric Boundary Layer. In this dissertation, both theory and experimental methods are developed for utilizing small fixed-wing unmanned aircraft systems (UAS) in detecting these atmospheric coherent structures. The dissertation begins by presenting relevant literature on both LCS and airborne wind estimation. Because model-based wind estimation inherently depends on high quality models, a Flight Dynamic Model (FDM) suitable for a small fixed-wing aircraft in turbulent wind is derived in detail. In this presentation, some new theoretical concepts are introduced concerning the proper treatment of spatial wind gradients, and a critical review of existing theories is presented. To enable model-based wind estimation experiments, an experimental approach is detailed for identifying a FDM for a small UAS by combining existing computational aerodynamic and data-driven approaches. Additionally, a methodology for determining wind estimation error directly resulting from dynamic modeling choices is presented and demonstrated. Next, some model-based wind estimation results are presented utilizing the experimentally identified FDM, accompanied by a discussion of model fidelity concerns and other experimental issues. Finally, an algorithm for detecting LCS from a single circling fixed-wing UAS is developed and demonstrated in an Observing System Simulation Experiment. The dissertation concludes by summarizing these contributions and recommending future paths for continuing research.
Doctor of Philosophy
In a natural or man-made disaster, first responders depend on accurate predictions of where the wind might carry hazardous material. A mathematical theory of Lagrangian Coherent Structures (LCS) has shown promise in ocean environments to improve these predictions, and the theory is also applicable to atmospheric flows near the Earth’s surface. This dissertation presents both theoretical and experimental research efforts towards employing small fixed-wing unmanned aircraft systems (UAS) to detect coherent structures in the Atmospheric Boundary Layer (ABL). These UAS fit several “gaps” in available sensing technology: a small aircraft responds significantly to wind gusts, can be steered to regions of interest, and can be flown in dangerous environments without risking the pilot’s safety. A key focus of this dissertation is to improve the quality of airborne wind measurements provided by inexpensive UAS, specifically by leveraging mathematical models of the aircraft. The dissertation opens by presenting the motivation for this research and existing literature on the topics. Next, a detailed derivation of a suitable Flight Dynamic Model (FDM) for a fixed-wing aircraft in a turbulent wind field is presented. Special attention is paid to the theories for including aerodynamic effects of flying in non-uniform winds. In preparation for wind measurement experiments, a practical method for obtaining better quality FDMs is presented which combines theoretically based and data-driven approaches. A study into the wind-measurement error incurred solely by mathematical modeling is presented, focusing on simplified forms of the FDM which are common in aerospace engineering. Wind estimates which utilize our best available model are presented, accompanied by discussions of the model accuracy and additional wind measurement concerns. A method is developed to detect coherent structures from a circling UAS which is providing wind information, presumably via accurate model based estimation. The dissertation concludes by discussing these conclusions and directions for future research which have been identified during these pursuits.

This thesis describes the development of several spectroscopic methods based on impulsive vibrational spectroscopy as well as of the technique itself. The first chapter describes the ultrafast time domain Raman spectrometer including the development of two noncollinear optical parametric amplifiers for sub-10 fs pulse generation with 343 or 515 nm pumping. In the first spectroscopic study we demonstrate, for the first time, that impulsive vibrational spectroscopy can be used for recording transient Raman spectra of molecules in excited electronic states. We obtain spectra of beta-carotene with comparable, or better, quality than established frequency domain based nonlinear Raman techniques. The following two chapters address the questions on the fate of vibrational coherences when generated on a reactive potential energy surface. We photoexcite bacteriorhodopsin and observe anharmonic coupling mediated vibrational coherence transfer to initially silent vibrational modes. Additionally, we are able to correlate the vibrational coherence activation with the efficiency of the isomerisation reaction in bR. Upon generation of vibrational coherence in the second excited electronic state of beta-carotene, by excitation from the ground electronic state, we are able to follow the wavepacket motion out of the Franck-Condon region. We observe vibrationally coherent internal conversion, through a conical intersection, into the first excited electronic state and are hence able to demonstrate that electronic surface crossings can occur in a vibrationally coherent fashion. Additionally, we find strong evidence for vibronic coupling mediated back and forth crossing between the two electronic states. As a combination of this work we develop a IVS based technique that allows for the direct recording of background and baseline free Raman spectra in the time domain. Several proof of principle experiments highlight the capabilities of this technique for time resolved Raman spectroscopy. In the final chapter we present work on weak-field coherent control. Here, we address the question of whether a photochemical reaction can be controlled by the phase term of an electric excitation field, in the one photon excitation limit. We study the systems rhodamine 101, bacteriorhodopsin, rhodopsin and isorhodopsin and, contrary to previous reports, find no evidence for one photon control.

The transport of material in geophysical fluid flows is a problem with important implications for fields as diverse as: agriculture, aviation, human health, disaster response, and weather forecasting. Due to the unsteady nature of geophysical flows, predicting how material will be transported in these systems can often be challenging. Tools from dynamical systems theory can help to improve the prediction of material transport by revealing important transport structures. These transport structures reveal areas of the flow where fluid parcels, and thus material transported by those parcels, are likely to converge or diverge. Typically, these transport structures have been uncovered by the use of Lagrangian diagnostics. Unfortunately, calculating Lagrangian diagnostics can often be time consuming and computationally expensive. Recently new Eulerian diagnostics have been developed. These diagnostics are faster and less expensive to compute, while still revealing important transport structures in fluid flows. Because Eulerian diagnostics are so new, there is still much about them and their connection to Lagrangian diagnostics that is unknown. This dissertation will fill in some of this gap and provide a mathematical bridge between Lagrangian and Eulerian diagnostics. This dissertation is composed of three projects. These projects represent theoretical, numerical, and experimental advances in the understanding of Eulerian diagnostics and their relationship to Lagrangian diagnostics. The first project rigorously explores the deep mathematical relationship that exists between Eulerian and Lagrangian diagnostics. It proves that some of the new Eulerian diagnostics are the limit of Lagrangian diagnostics as integration time of the velocity field goes to zero. Using this discovery, a new Eulerian diagnostic, infinitesimal-time Lagrangian coherent structures is developed. The second project develops a methodology for estimating local Eulerian diagnostics from wind velocity data measured by a fixed-wing unmanned aircraft system (UAS) flying in circular arcs. Using a simulation environment, it is shown that the Eulerian diagnostic estimates from UAS measurements approximate the true local Eulerian diagnostics and can predict the passage of Lagrangian diagnostics. The third project applies Eulerian diagnostics to experimental data of atmospheric wind measurements. These are then compared to Eulerian diagnostics as calculated from a numerical weather simulation to look for indications of Lagrangian diagnostics.
Doctor of Philosophy
How particles are moved by fluid flows, such as the oceanic currents and the atmospheric winds, is a problem with important implications for fields as diverse as: agriculture, aviation, human health, disaster response, and weather forecasting. Because these fluid flows tend to change over time, predicting how particles will be moved by these flows can often be challenging. Fortunately, mathematical tools exist which can reveal important geometric features in these flows. These geometric features can help us to visualize regions where particles are likely to come together or spread apart, as they are moved by the flow. In the past, these geometric features have been uncovered by using methods which look at the trajectories of particles in the flow. These methods are referred to as Lagrangian, in honor of the Italian mathematician Joseph-Louis Lagrange. Unfortunately, calculating the trajectories of particles can be a time consuming and computationally expensive process. Recently, new methods have been developed which look at how the speed of the flow changes in space. These new methods are referred to as Eulerian, in honor of the Swiss mathematician Leonhard Euler. These new Eulerian methods are faster and less expensive to calculate, while still revealing important geometric features within the flow. Because these Eulerian methods are so new, there is still much that we do not know about them and their connection to the older Lagrangian methods. This dissertation will fill in some of this gap and provide a mathematical bridge between these two methodologies. This dissertation is composed of three projects. These projects represent theoretical, numerical, and experimental advances in the understanding of these new Eulerian methods and their relationship to the older Lagrangian methods. The first project explores the deep mathematical relationship that exists between Eulerian and Lagrangian diagnostic tools. It mathematically proves that some of the new Eulerian diagnostics are the limit of Lagrangian diagnostics as the trajectory’s integration times is decreased to zero. Taking advantage of this discovery, a new Eulerian diagnostic is developed, called infinitesimal-time Lagrangian coherent structures. The second project develops a technique for estimating local Eulerian diagnostics using wind speed measures from a single fixed-wing unmanned aircraft system (UAS) flying in a circular path. Using computer simulations, we show that the Eulerian diagnostics as calculated from UAS measurements provide a reasonable estimate of the true local Eulerian diagnostics. Furthermore, we show that these Eulerian diagnostics can be used to estimate the local Lagrangian diagnostics. The third project applies these Eulerian diagnostics to real-world wind speed measurements. These results are then compared to Eulerian diagnostics that were calculated from a computer simulation to look for indications of Lagrangian diagnostics.

The turbulent boundary layer is an aspect of fluid flow which dominates the performance of many engineering systems - yet the analytic solution of such flows is intractable for most applications. Our understanding of boundary layers is therefore limited by our ability to simulate and measure them. Tomographic Particle Image Velocimetry (TPIV) is a recently developed technique for direct measurement of fluid velocity within a 3D region. This allows new insight into the topological structure of turbulent boundary layers. Increasing Reynolds Number increases the range of scales at which turbulence exists; a measurement technique must have a larger 'dynamic range' to fully resolve the flow. Tomographic PIV is currently limited in spatial dynamic range (which is also linked to the spatial and temporal resolution) due to a high degree of noise. Results also contain significant bias error. This work proposes a modification of the technique to use more than two exposures in the PIV process, which (for four exposures) is shown to improve random error by a factor of 2 to 7 depending on experimental setup parameters. The dynamic range increases correspondingly and can be doubled again in highly turbulent flows. Bias error is reduced by up to 40%. An alternative reconstruction approach is also presented, based on application of a reduction strategy (elimination of coefficients based on a first guess) to the tomographic weightings matrix Wij. This facilitates a potentially significant increase in computational efficiency. Despite the achieved reduction in error, measurements contain non-zero divergence due to noise and sampling errors. The same problem affects visualisation of topology and coherent fluid structures. Using Projection Onto Convex Sets, a framework for post-processing operators is implemented which includes a divergence minimisation procedure and a scale-limited denoising strategy which is resilient to 'false' vectors contained in the data. Finally, developed techniques are showcased by visualisation of topological information in the inner region of a high Reynolds Number boundary layer (δ+ = 1890, Reθ = 3650). Comments are made on the visible flow structures and tentative conclusions are drawn.

Cette thèse vise à démêler les principaux mécanismes impliqués dans les écoulements transitoires et turbulents. L’idée centrale est d'utiliser une technique d’optimisation non linéaire pour étudier l’origine et le rôle des structures cohérentes habituellement observées dans ces écoulements. Cette méthode a été utilisée dans trois contextes différents. Tout d’abord, un écoulement laminaire linéairement stable a été considéré et l'optimisation a été utilisée pour calculer les perturbations les plus amplifiées parmi toutes les perturbations capables de déclencher une transition vers la turbulence. Une fois que la turbulence est bien établie, une optimisation non linéaire entièrement 3D maximisant l'énergie cinétique turbulente est utilisée pour étudier les structures cohérentes qui peuplent l’écoulement turbulent et les mécanismes responsables de la croissance et de l’échange d’énergie (optimale) sont étudiés. Ensuite, une approche de type système dynamique est appliquée aux équations du mouvement. La géométrie de l’espace des phases est étudiée en utilisant la théorie de la croissance transitoire pour évaluer l’importance des variétés stable et instable dans la dynamique. Dans le même cadre, un algorithme de minimisation non linéaire est utilisé pour calculer les connexions hétérocliniques parmi les solutions invariantes des équations de Navier-Stokes
This thesis aims at unraveling the main mechanisms involved in transitional and turbulent flows. The central idea is that of using a nonlinear optimization technique to investigate the origin and role of coherent structures usually observed in these flows. This method has been used in three different contexts. First, a linearly stable laminar flow has been considered and the optimization has been used to compute the most amplified perturbations among all disturbances able to trigger transition to turbulence. Once turbulence is well established, a fully 3D nonlinear optimization maximizing the turbulent kinetic energy is used to study coherent structures populating turbulent shear flow as well as investigate the mechanisms responsible for the energy (optimally) growth and exchange. Then, a dynamical system approach is applied to fluid flow equations. The geometry of the state space is investigated by using transient growth theory to reveal the importance of the stable and unstable manifold. In the same framework, a nonlinear minimization algorithm is used to compute heteroclinic connections among invariant solutions of the Navier-Stokes equations

Le premier chapitre de cette thèse traite de l'importance des échelles temporelles et spatiales dans le contexte des systèmes vivants. J'y décris également les principaux composants de la réponse mécanique des cellules vivantes. Après ce chapitre introductif, le deuxième chapitre est dédié à la réponse mécanique des cellules évaluée avec l'AFM et en particulier, son aspect dynamique. Je présente d'abord l'analyse des courbes force-indentation, puis je propose une méthode alternative pour l'étude de la rhéologie cellulaire qui est basée sur l'excitation multifréquence du levier par bruit thermique. La DPM est l'objet du troisième chapitre où je revisite la méthode d'extraction de phase en utilisant la transformation en ondelette à deux dimensions. Ensuite je montre comment la DPM peut être utilisée pour caractériser les fluctuations temporelles et la morphologie de différents types de cellules du sang et de cellules adhérentes. Finalement, le chapitre quatre est un chapitre de conclusion où je fais une synthèse des résultats obtenus. Par exemple, je montre que, en comparaison avec des cellules saines, les cellules leucémiques subissent des changements morphologiques qui sont accompagnés par un comportement mécanique plus rigide et plus élastique. Cela indique que dans cet exemple la transformation cellulaire n'est pas seulement donnée par son cortex mais aussi par son cytosquelette et son couplage avec le noyau
In the first chapter of this thesis I discuss the importance of spatial and temporal scales in living systems, and I review the main components involved in the mechanical response of living cells. After this introductory chapter, the second one is dedicated to evaluating the mechanical response of single-cells with AFM, and in particular, its dynamical aspect. I present the analysis of force-indentation curves without any assumption on the linearity of the system, contrary to more typical analysis based on Sneddon’s or Hertz models. Then, I propose an alternative method to study the cell rheology based on the multi-frequency excitation of the cantilever by thermal noise. DPM is discussed on chapter three. I revisit the phase recovery method using the 2D wavelet transform, and I show how DPM can be used to characterize the temporal fluctuations and the morphology of different types of blood cells and adherent cells. Finally, chapter four is a conclusion chapter where I summarise our results by comparing healthy and pathological immature blood cells. For instance I show that, in comparison to healthy cells, leukaemic cells undergo morphological changes that are accompanied by a stiffer and more elastic behaviour. Altogether, our results indicate that this cell transformation involves the whole cytoskeleton and its coupling to the nucleus rather than simply the cell cortex

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2002.
Includes bibliographical references.
(cont.) Using this method, it is possible to determine the refractive index of a 1 mm thick sample with 7 significant figures. The unprecedented accuracy can potentially allow us to track subtle chemical changes in biological targets. Finally, we present the theoretical considerations of a method for suppressing turbidity in a scattering medium through the simultaneous use of phase conjugation and plane reflection. We show that the method is robust and warrants experimental investigation as a means for optical deep tissue imaging.
We report a novel optical imaging method based on the use of harmonically related light sources in a low coherence interferometer - harmonic phase-based low coherence interferometry (HPI). We demonstrate that, by processing the measured heterodyne phases appropriately, we can completely correct for motional jitter in the interferometer, which would otherwise make phase determination impossible. We apply the interferometer to study the phase velocity variation of ballistically propagating light traveling in a turbid medium and show that the phase velocity is dependent on the size of the scatterers. We next create a microscopy implementation of HPI. By exploiting the refractive index difference at the two wavelengths for contrast, the microscope is able to render details from unstained microscope sections based on their refractive index variations. We then exploit the property of low coherence interferometry to achieve depth resolution in our next adaptation of HPI - phase dispersion optical tomography. There, we demonstrate the ability to measure the reflection phase shift which can be used to determine properties of the reflecting materials. In addition, the technique can provide depth resolved dispersion information about a sample. We next apply HPI to tackle the challenge of tracking very small ([approx.] nm) arid very slow ([approx.] nm/s) cellular motions. Using a modified HPI system, we can study the cell membrane dynamics of a single cell without destroying it in the process. This system is about 2 orders of magnitude more sensitive than existing systems. In the final adaptation of the HPI, we demonstrate that HPI can be used to make absolute optical distance measurements with sub-nanometer accuracy.
by Changhuei Yang.
Ph.D.

Le but de ce travail de thèse est l'étude et la réalisation de sources laser de haute cohérence à semi-conducteurs III-V basées sur la technologie Vertical-External-Cavity-Surface-Emitting-Laser (VeCSEL) à puits quantiques (matériaux InGaAs/GaAs/AlGaAs), émettant dans le proche-IR sur des modes transverses du type Laguerre Gauss (LG) et Hermite Gauss (HG) d'ordre supérieur. Ces modes ont des structures de phase, d'amplitude et de polarisation complexes qui leur vaut souvent l'appellation de 'lumière complexe' ou 'structurée'. Nous mettrons l'accent particulièrement sur les modes LG possédant un moment angulaire orbital, et sur une source contrôlant le spin du photon. Ce type de sources laser présente un grand intérêt pour le développement de systèmes ou capteurs optiques dans différents domaines, tels que les télécommunications, les pinces optiques, et le piégeage et le refroidissement d'atomes, ainsi que la métrologie optique.Nous sommes amenés à étudier les modes propres des cavités optiques de haute finesse. Nous décrivons ces modes suivant les trois "axes" définissant l'état de photon: distributions longitudinal (fréquentiel), transverse (spatial) et de polarisation. Pour chacun de ces trois axes nous étudions les ingrédients physiques qui régissent la formation des modes, et développons les outils théoriques nécessaires à la manipulation et le calcul des états propres dans des cavités modifiées.Dans une seconde étape, puisque la sélection de modes dans une cavité laser passe par l'interaction matière-rayonnement, nous nous penchons sur la dynamique de ces systèmes en écrivant les équations de Maxwell-Bloch pour notre laser. Ces équations nous permettent d'étudier le rôle de la dynamique temporelle dans la sélection des modes lasers et le chemin vers l'état stationnaire. Nous nous appuyons sur ces modèles pour expliquer certaines questions non/mal comprises, et qui mènent parfois à des interprétations erronées dans la littérature scientifique, notamment la sélection spontanée du sens de rotation du front de phase dans les modes vortex.Une partie de ce travail est consacré au développement et la caractérisation d'une technologie à semiconducteurs III-V, qui permet de sélectionner efficacement un mode laser donné, dans la base propre. Nous développons une approche basée sur des méta-matériaux intégrés à la structure de gain (le 1/2-VCSEL) et qui agit comme un masque de phase et d'amplitude. Nous nous appuyons sur cette technologie pour réaliser une cavité laser qui lève la dégénérescence des modes vortex contrarotatif et brise légèrement leur symétrie, ces deux étapes sont cruciales pour pourvoir sélectionner la charge et le signe du vortex généré et stabilisé. Afin de contrôler les modes de polarisation nous étudions les propriétés de polarisation de la cavité et du milieu à gain à puits quantique : la biréfringence, le dichroïsme, et le temps de spin flip dans les puits quantiques. Nous exploitons ces paramètres pour générer les états de polarisation désirés : linéaire stable, circulaire avec un moment angulaire de spin contrôlé par le spin de pompage. À la fin nous présentons la conception et la réalisation d'un capteur laser sous rétro-injection optique (self-mixing) pour la vélocimétrie linéaire et rotationnelle, en utilisant une source laser émettant sur un mode vortex. Ce capteur montre un exemple de mesure inaccessible avec un laser conventionnel. Il tire profit des propriétés uniques des modes vortex pour mesurer simultanément la vitesse linéaire et angulaire des particules. Nous finirons cette partie par l'étude d'un autre design de capteur laser possible pour la granulométrie, utilisant d'autres types de modes laser générés dans ce travail
The goal of this PhD thesis is the study, design and the development of highly coherent III-V semiconductor laser sources based on multi-quantum wells (InGaAs/GaAs/AlGaAs) Vertical-External-Cavity-Surface-Emitting-Laser (VeCSEL), operating in the near infra-red (IR), and emitting high order Laguerre-Gauss (LG) and Hermite-Gauss (HG) modes. These modes, usually called ‘complex' or ‘structured' light, have a complex wavefronts, amplitudes and polarizations structures. We especially focus on lasers with modes carrying OAM, and also on sources with controlled photon's spin. These modes are of great interest for the development optical systems in several fields, such as telecommunications, optical tweezers, atom trapping and cooling, and sensing applications. We need to study the light eigenstates in high-finesse laser cavities, we describe these eigenstates with respect to the three axis of the light that define the photon state: longitudinal (frequency), transverse (spatial), and polarization. For each one of these axis, we study the physical ingredients governing mode formation, and develop the theoretical tools required for the calculation of the eigenmodes in non-conventional cavities.In a second step, as the mode selection in a laser involves light-matter interaction, we focus on dynamic study by writing the semi classical Maxwell-Bloch equations for our lasers. These equations allow us to study the role of temporal dynamics in laser mode selection, as well as the path the steady state. We use these theoretical models to explain some none /poorly understood questions, and which lead sometimes to erroneous interpretations in the scientific literature. We see in particular the question of the spontaneous selection of the wavefront handedness in vortex modes. We also address the development and the characterization of a III-V semiconductor based technology that enables us to efficiently select the wanted mode in the eigenbasis. We adopt an approach based on metamaterials integrated on the semiconductor gain structure (1/2- VCSEL) that play the role of a phase and amplitude mask. We use this technology to build a laser cavity that lifts the degeneracy and breaks the symmetry between vortex modes with opposite handedness. These two effects are of paramount importance when one wants to select a vortex mode with a well-defined charge and handedness. In order to control the polarization modes, we study the polarization properties of the optical cavity and the quantum-well based gain medium: the birefringence the dichroism, and the spin-flip time in the quantum wells. We make use of these elements to generate the wanted polarization states: stable linear, and circular carrying an angular momentum controlled via the pump spin. In the end, we present the design and building of a feedback laser sensor (self-mixing) for linear and rotational velocimetry, using a laser source emitting a vortex beam. This sensor shows an example of a measurement inaccessible using conventional laser sources. It takes advantage of the orbital angular momentum of the vortex beam to measure both translational and rotational velocities using the Doppler effect. We end this part by presenting other possible sensor designs for particle sizing, using other exotic modes generated in this work

Cette thèse a pour objectif l’étude d’un lien effectif potentiel entre la motilité cellulaire, la mécanique cellulaire, et l’activité biochimique de ces mêmes cellules. Ce couplage a été étudié dans divers systèmes biologiques, et aussi bien dans des cultures de cellules qu’à l’intérieur de tissus plus complexes. Notamment, nous avons particulièrement cherché à détecter un couplage électromécanique dans des neurones qui pourrait être impliqué dans la propagation du message nerveux.Pour ce faire, nous avons dû développer deux microscopes optiques à la sensibilité extrême. Ces microscopes se composent de deux parties principales. La première sert à détecter des mouvements axiaux plus petits que la longueur d’onde optique, soit en dessous de 100 nanomètres. La deuxième partie permet la détection d’un signal de fluorescence, offrant la possibilité de suivre l’évolution biochimique de la cellule. Avec ces deux microscopes multimodaux, il est donc possible de suivre de manière simultanée un contraste de motilité, un contraste mécanique, un contraste structurel et un contraste biochimique. Si l’un de ces systèmes est basé sur la tomographie de cohérence optique plein champ et permet de faire de telles mesures en 3-D et en profondeur dans les tissus biologiques, le second ne permet que des mesures dans des cultures de cellules, mais est bien plus robuste au bruit mécanique. Dans ce manuscrit, nous allons essentiellement décrire le développement de ces deux appareils, et préciser les contrastes auxquels ils sont sensibles spécifiquement.Nous développerons également deux des applications principales de ces microscopes que nous avons étudié dans le détail au cours de cette thèse. La première application développe l’intérêt d’un de nos microscopes pour la détection sans marquage des principaux composants cellulaires et structuraux de la cornée et de la rétine. La seconde application tend à détecter et à suivre des ondes électromécaniques dans des neurones de mammifères
This PhD project aims to explore the relationship that might exist between the dynamic motility and mechanical behavior of different biological systems and their biochemical activity. In particular,we were interested in detecting the electromechanical coupling that may happen in active neurons, and may assist in the propagation of the action potential. With this goal in mind, we have developed two highly sensitive optical microscopes that combine one modality that detects sub-wavelength axial displacements using optical phase imaging and another modality that uses a fluorescence path. Therefore, these multimodal microscopes can combine a motility, a mechanical,a structural and a biochemical contrast at the same time. One of this system is based ona multimodal combination of full-field optical coherence tomography (FF-OCT) and allows the observation of such contrast inside thick and scattering biological tissues. The other setup provides a higher displacement sensitivity, but is limited to measurements in cell cultures. In this manuscript, we mainly discuss the development of both systems and describe the various contrastst hey can reveal. Finally, we have largely used our systems to investigate diverse functions of the eye and to look for electromechanical waves in cell cultures. The thorough description of both biological applications is also provided in the manuscript

Negli ultimi anni, la presenza in mare di strutture fondate su pali, come piattaforme petrolifere e turbine eoliche offshore, sta diventando sempre più importante. Per questa ragione, guadagna sempre più importanza l’analisi di possibili criticismi e incertezze nella loro progettazione. L’obiettivo di questa tesi è lo studio dell’idro e della morfodinamica indotta da onde regolari e non su un palo di piccolo diametro attraverso una modellazione fisica e numerica. Questa tesi vuole quindi dare un contributo per la comprensione di tali processi fisici. In particolare, si vogliono fornire degli strumenti che possono risultare utili ad evitare valutazioni errate dei parametri che rientrano nella progettazione di tali strutture. Particolare attenzione è riservata alla valutazione della forza dell’azione ondosa sulla struttura, allo scavo generato alla sua base e al run-up sulla sua superficie. Un modello fisico a fondo rigido è stato realizzato per valutare quale fosse il miglior approccio per la stima della forza dovuta ad onde non lineari. Viene quindi proposta un’alternativa al classico metodo di Morison (1950) per il calcolo della forza totale con valori di velocità e accelerazione orbitale calcolati a partire da una serie temporale della superficie libera. Tale metodo consiste in una decomposizione spettrale di Fourier del segnale di livello; il contributo di ogni componente, calcolato mediante la teoria di Airy, viene quindi sommato per ottenere un profilo di velocità orizzontale e verticale in ogni istante. I risultati mostrano che questo approccio fornisce una buona stima della forza totale sia in termini di valore massimo che di valutazione della fase ondosa in cui avviene. Al contrario invece, l’applicazione della teoria lineare a tale scopo (che viene utilizzata usualmente nella progettazione) porta ad una sottostima del valore di picco e ad una cattiva rappresentazione dell’andamento della forza nel periodo. Lo scavo alla base del palo è un altro parametro fondamentale nella sua progettazione. Una campagna sperimentale a fondo mobile è stata quindi realizzata studiando l’effetto di onde regolari e non regolari su un fondale sabbioso in cui è stato inserito un cilindro verticale. I risultati di questo studio sono abbastanza in accordo con quelli ottenuti da un precedente la voro di Sumer et al. (1992) sebbene sia mostrato come il processo di scavo inizi in presenza di condizioni idrodinamiche di minore intensità (parametro di Keulegan-Carpenter KC=4) rispetto a quanto presente in letteratura (KC=6). Diverse formule sono proposte per valutare la profondità di scavo in funzione di parametri adimensionali come KC e Ur. Per lo scavo dovuto ad onde irregolari, è stato modificato l’approccio di Ong et al. (2013). Questo metodo dipende dalla funzione di distribuzione cumulata delle altezze di cresta ma, a causa della sua complessità, è stata semplificata per essere resa più adatta a fini progettuali senza però inficiare la bontà dei risultati. Per migliorare la comprensione sul processo di formazione, crescita e distacco dei vortici, sono state svolte misure di tipo PTV che, integrate con le misure di pressione e coi risultati del fondo mobile, hanno permesso di caratterizzare l’intero processo di scavo. Dai risultati si è osservato come le fasi e le posizioni in cui i gradienti di pressione sono massimi corrispondono a quelle in cui è stato osservato distacco dei vortici. Le mappe di scavo ottenute nella campagna a fondo mobile sono state quindi spiegate dall’interpretazione delle mappe di vorticity e del parametro OW. È stato inoltre realizzato un modello numerico con OpenFOAM per ampliare la comprensione del complesso fenomeno tridimensionale riguardante l’interazione onda-struttura. Una nuova condizione al contorno per la generazione ondosa a partire da una serie temporale misurata di superficie libera è stata implementata nel codice. Il campo di velocità viene calcolato con la scomposizione di Fourier sopra descritta. I test della campagna a fondo rigido sono stati simulati allo scopo di ottenere ulteriori informazioni sul distacco dei vortici e per stimare il run-up sulla struttura che è un parametro fondamentale per garantire l’accesso alle strutture in mare. Il confronto con le misure sperimentali di livello, velocità, pressione e forza è eccellente. L’analisi dei massimi valori di run-up è stata realizzata confrontando i risultati con formule presenti in letteratura. In particolare, l’equazione di Hallermeier (1976) è stata adattata per il calcolo del run-up a partire dall’altezza della cresta e i risultati, ottenuti con un numero di campioni significativo, sono molto buoni. Infine, le strutture vorticose sono visualizzate mediante l’uso del Q-criterion. I risultati numerici mostrano come, a volte, un vortice generato nella prima metà di un periodo può rimanere nell’area di influenza del palo. Dopo l’inversione del flusso cambia direzione insieme al flusso e viene finalmente rimosso nel lato del palo opposto rispetto a dove era stato generato. I risultati sono in accordo con quelli della campagna PTV: sia la fase, la dimensione e la posizione dei vortici sono ben rappresentate. Gli obiettivi raggiunti con il modello numerico aumentano la comprensione di tale complesso processo fisico unendo informazioni di diversa natura come i gradienti di pressioni, le strutture vorticose e le mappe di scavo ad esse associate.
During the last years, the presence of piled structures, such as offshore wind farms or oil platforms, in the marine environment is becoming more important. For this reason, it gains relevance the correct analysis of possible criticisms and uncertainties in the design process. The aim of this thesis is the study of both the hydrodynamics and the morpho-dynamics induced by regular and random waves over a single slender pile by means of laboratory and numerical modelling. Therefore, the objective of the present thesis is to contribute to a better understanding of such physical processes. In particular, it aims to provide some tools that can be useful in the design process, in order to avoid a wrong estimation of the most important parameters and, thus, to ensure a proper design of the piled marine structure and its facilities. Particular attention is paid on the evaluation of the total force due to wave action, on the scour at the base of the pile and on the run-up over its surface. A rigid bed model has been realised to evaluate the best approach for the estimation of the total force over the pile due to nonlinear waves. An alternative method to the classical Morison (1950)'s approach has been proposed for the computation of the total force from the velocity and acceleration of the water particles from a measured water surface elevation time series. Such method consists in a Fourier spectral decomposition of the input free water surface signal; the contribution of each component, computed according to the Airy theory, is summed to obtain the total horizontal and vertical velocity along the vertical profile. The results showed that this approach allowed to give a very good estimate of the total force both in terms of maximum value and of the phase in which it occurs. On the contrary, the application of the linear theory for the calculation of the velocity to be applied in the force calculation (classical Morison approach used in the design process) leads to an underestimation of the peak value and to a wrong representation of the shape of the force. Another primary parameter in the stability of a structure in the marine environment is the scour at the base of the monopile. This experimental campaign is performed by means of a mobile bed model in which a vertical cylinder is placed over a sandy seabed and it is attacked by both regular and random nonlinear waves. The results for regular waves are quite in agreement with the earlier work of Sumer et al. (1992). However, the results of this study reveal that the scour process due to nonlinear regular waves starts for hydrodynamic conditions characterized by a lower intensity Keulegan-Carpenter parameter KC=4) in comparison with those reported in the literature for linear waves (KC=6). Different formulas are proposed for its estimation depending on dimensionless parameters (KC, Ur). For random waves, the approach proposed by Ong et al. (2013) for scour evaluation has been modified. This method depends on the cumulative distribution function of the dimensionless crest heights but, because of its complexity, it has been simplified in order to became suitable for design purposes without affecting the quality of the results. To better understand the process of formation, growth and detachment of vortices, PTV measurements are carried out and the results are integrated with those from pressure sensors and from the mobile bed model for the characterization of the whole process of vortex formation and scour generation. The results showed that the wave phases and positions in which the maximum values of the pressure gradients occur, correspond to those in which the detachment of vortices is observed. From the interpretation of the contour maps of the vorticity and of the OW parameter it is possible to explain the scour patterns obtained in the mobile bed campaign. Furthermore, a numerical model has been realised with the tool OpenFOAM that permitted to contribute to the comprehension of the complex 3D physical phenomenon induced by the wave-structure interaction. A new wave generation boundary condition for the generation of a measured water surface elevation time series has been added to the numerical code. The corresponding velocity field in this BC has been computed with the Fourier decomposition method mentioned above. The nonlinear waves of the rigid bed experimental campaign are here simulated for the better comprehension of the vortex formation process and for the estimation of wave run-up which is very important for the design of the access facility of the marine structures. Excellent results are obtained in comparison with experimental data of force, pressure, velocity and water elevation. The analysis of the maximum values of run-up is performed and the results are compared with some formula available in the literature. An adaptation of the equation of Hallermeier (1976) that compute the run-up depending on the crest height, is proposed and the results, obtained with a significant number of samples, are very good. Finally, the visualization of the three-dimensional vortical structures by means of the Q-criterion has been performed. The numerical results showed that, in some instances, a vortex generated during the first half of the period can remain in the area of influence of the pile. After the reversal of the flow, it changes the direction according to the stream until it is finally removed on the opposite side of the pile with respect to where it was generated. The results are in agreement with those of the PTV campaign: both the phase, size and position of vortices are well represented. The achievements obtained with the numerical model are able to improve the understanding of the complex physical processes by linking the different results, such as the pressure gradients, vortical structures and the associated scour patterns.

Quasi two-dimensional turbulent flows, like mesoscale oceanic and large-scale atmospheric flows, create finite-time coherent structures, compact fluid masses that resist mixing for finite-time despite the turbulent nature of the ambient flow. These coherent structures significantly affect the mixing and transport of fluid elements. In return, the transport of passive scalars like heat, humidity, salinity, chemical concentration, nutrients and even algae has a substantial impact on countless geophysical phenomena. Thus, in order to understand these effects reliable methods for coherent structure detection and the identification of their boundaries are necessary. Here, in this thesis, we present two contributions in this regard. First, we present improvements of the transfer operator approach, an established stochastic approach for the detection of almost-invariant and coherent sets. The approach approximates the transport properties of a complicated flow by a linear transfer operator and aims to partition a given domain in multiple sets such that the inter-set mass transport is minimized. The improvements include the introduction of mixing boundary conditions in stationary and time-dependent flows. By modifying the transfer operator we couple the filaments that surround the coherent and jointly rotating fluid volume such that effectively only two non-communicating sets remain: the coherent eddy core and the ambient flow. This significantly stabilizes the inference of coherent eddy cores and makes the use of popular but error-prone clustering techniques unnecessary. In addition, we discuss the identification of temporally consistent areas of increased coherence. Instead of coherent structures that are defined by advected non-filamenting masses, the concept describes consistent and moving patches of reduced mixing whose mass can change over time. This permits the decoupling of the coherence time scale from the time window under consideration. Both modifications are used to study the transport properties of eight selected Baltic Sea eddies. Secondly, we introduce the MSCS-search, a new algorithm for the inference of finite-time coherent volumes that is solely based upon the concept of convexity. Persistent convexity is a sufficient condition for coherence in two-dimensional flows if coherent structures are understood as non-filamenting volumes. However, convexity has never been considered as condition of coherence, even though some methods use it, for practical reasons, as an explicit constraint. The approach identifies the largest structure inside a given volume that remains star-convex with respect to a given reference trajectory within a given time window. We test the approach thoroughly and our results show that the approach yields good and reliable estimations of coherent structures in all test cases. Moreover, since the results depend explicitly on the considered time window, the results are intuitive and enable the identification and study of filaments. The novel approach is then used to re-evaluate transport processes in the data set of Baltic eddies.:1 Introduction 2 Theoretical Background 2.1 Methods 2.1.1 Okubo-Weiss criterion 2.1.2 Finite-Time Lyapunov Exponents 2.1.3 Lagrangian Descriptors and Lagrangian averaged vorticity deviation 2.2 Models 2.2.1 Euler equation 2.2.2 Stationary Gaussian Blob Model 2.2.3 Periodically Perturbed Gaussian Blob Model 2.2.4 Bickley-Jet 3 Transfer Operator Approach I: State of the Art 3.1 Frobenius-Perron Operator 3.2 Markov-Chains 3.3 Laplacian matrices 3.4 Finding Almost-Invariant Sets 3.5 Finding Coherent Sets 3.5.1 Coherent pairs as tuples 3.5.2 Coherent pairs as triples 3.6 Spectral Clustering 3.7 Critique and Discussion 4 Transfer Operator Approach II: Mixing Boundary Conditions in Stationary Flows 4.1 Overview 4.2 Estimation of Transfer Probability Matrices P 4.3 Mixing Boundary Conditions 4.4 Thresholding 4.5 Results 4.5.1 Robustness with respect to parameters 4.5.2 Comparison and alternatives 4.5.3 Handling of false positives 4.5.4 Periodically perturbed flow 4.6 Closing Remark 5 Transfer operator approach III: Analysis of Oceanic Transport 5.1 Mixing Boundary Conditions: Time-Dependent Flows 5.1.1 Method 5.1.2 Results 5.2 Temporal consistency 5.2.1 Method 5.2.2 Results 5.3 Treatment of Coastal Effects 5.4 Application to Baltic velocity fields 5.4.1 Method 5.4.2 Results 5.5 Closing Remark 6 Prototypes of Coherent Sets: Star-Convex Structures 6.1 Mathematical Considerations 6.2 MSCS-Algorithm 6.3 Extracting star-convex sub-volumes 6.4 Results 6.4.1 Stationary Gaussian blob model 6.4.2 Bickley-Jet 6.4.3 Two dimensional inviscid flow 6.4.4 Real data sets 6.5 Closing Remark 7 Conclusion and Outlook
Es ist bekannt, dass quasi-zweidimensionale turbulente Strömungen, wie etwa Strömungen an der Meeresoberfläche oder großskalige Atmosphärenbewegungen, kohärente Strukturen ausbilden, kompakte Volumina, welche einer Mischung mit dem umgebenden Material für endliche Zeit widerstehen, obwohl die Strömung als solche turbulent ist. Diese Strukturen haben einen signifikanten Einfluss auf den Transport von Fluidelementen. Der Transport von passiven skalaren Größen, wie etwa Wärme, Feuchtigkeit, Salzgehalt, Nährstoffgehalt, jegliche Konzentration che- mischer Stoffe und sogar Algendichte hat wiederum einen Effekt auf unzählige geophysikalische Phänomene. Um diese Phänomene im Detail zu verstehen, sind zuverlässige Methoden für die Detektion von kohärenten Strukturen und die Identifikation ihrer Grenzen notwendig. In der vorliegenden Arbeit präsentieren wir zwei Beiträge zur Lösung dieses Problems. Als erstes präsentieren wir Verbesserungen der Transferoperatormethode. Diese etablierte Methode zur Identifikation von fast-invarianten und kohärenten Mengen approximiert die Transporteigenschaften eines Flusses mithilfe eines linearen Transferoperators, mit dem Ziel, das betrachtete Gebiet in Bereiche zu unterteilen, welche den Materialaustausch zwischen den Bereichen minimieren. Die Verbesserungen beinhalten die Einführung von mischenden Randbedingungen in stationären und nicht-stationären Flüssen. Dabei wird der Transferoperator so modifiziert, dass Filamente, welche die kohärente Struktur umgeben, gekoppelt werden, was zur Folge hat, dass effektiv nur zwei nicht kommunizierende Strukturen übrig bleiben: die kohärente Struktur und das sie umgebende Volumen. Dies führt zu einer signifikant erhöhten Stabilität der Methode ohne auf die sonst üblichen aber fehleranfälligen clustering-Techniken zurückgreifen zu müssen. Des Weiteren diskutieren wir die Identifikation von zeitlich konsistenten Regionen erhöhter Kohärenz. Anstatt von kohärenten Strukturen als bewegliche nicht filamentierende Massen zu sprechen, beschreibt dieses Konzept kohärente Strukturen als konsistente sich bewegende Regionen reduzierten Mischverhaltens deren beteiligte Masse zeitlich veränderlich ist. Dies erlaubt die Entkopplung der Kohärenzzeitskala vom betrachteten Zeitfenster. Im Anschluss verwenden wir beide Modifikationen, um die Transporteigenschaften von acht ausgewählten Ostseewirbeln zu untersuchen. Als zweiten Beitrag stellen wir den MSCS-Algorithmus vor, eine neue Methode zur Identifikation von kohärenten Strukturen, welche einzig und allein auf dem Prinzip von Konvexität basiert. Versteht man kohärente Strukturen als nicht filamentierende Massen, ist persistente Konvexität eine hinreichende Bedingung für Kohärenz. Konvexität wurde bisher noch nie als Grundlage für Kohärenz untersucht, obwohl sie aus praktischen Gründen in einigen Methoden bereits als einschränkende Bedingung verwendet wird. Die Methode identifiziert die größte Struktur innerhalb eines gegebenen Volumens, welches während eines gegebenen Zeitraums stern-konvex bezüglich einer gegebenen Referenztrajektor bleibt. Alle studierten Testszenarien zeigen, dass der Ansatz gute und zuverlässige Ergebnisse liefert. Diese Ergebnisse hängen darüber hinaus direkt von den Eingangsparametern ab, was die Interpretation der Ergebnisse stark erleichtert und zusätzlich die Untersuchung von Filamentbildung erlaubt. Die neue Methode wird verwendet um den kohärenten Transport in den bereits untersuchten Ostseewirbeln zu reevaluieren.:1 Introduction 2 Theoretical Background 2.1 Methods 2.1.1 Okubo-Weiss criterion 2.1.2 Finite-Time Lyapunov Exponents 2.1.3 Lagrangian Descriptors and Lagrangian averaged vorticity deviation 2.2 Models 2.2.1 Euler equation 2.2.2 Stationary Gaussian Blob Model 2.2.3 Periodically Perturbed Gaussian Blob Model 2.2.4 Bickley-Jet 3 Transfer Operator Approach I: State of the Art 3.1 Frobenius-Perron Operator 3.2 Markov-Chains 3.3 Laplacian matrices 3.4 Finding Almost-Invariant Sets 3.5 Finding Coherent Sets 3.5.1 Coherent pairs as tuples 3.5.2 Coherent pairs as triples 3.6 Spectral Clustering 3.7 Critique and Discussion 4 Transfer Operator Approach II: Mixing Boundary Conditions in Stationary Flows 4.1 Overview 4.2 Estimation of Transfer Probability Matrices P 4.3 Mixing Boundary Conditions 4.4 Thresholding 4.5 Results 4.5.1 Robustness with respect to parameters 4.5.2 Comparison and alternatives 4.5.3 Handling of false positives 4.5.4 Periodically perturbed flow 4.6 Closing Remark 5 Transfer operator approach III: Analysis of Oceanic Transport 5.1 Mixing Boundary Conditions: Time-Dependent Flows 5.1.1 Method 5.1.2 Results 5.2 Temporal consistency 5.2.1 Method 5.2.2 Results 5.3 Treatment of Coastal Effects 5.4 Application to Baltic velocity fields 5.4.1 Method 5.4.2 Results 5.5 Closing Remark 6 Prototypes of Coherent Sets: Star-Convex Structures 6.1 Mathematical Considerations 6.2 MSCS-Algorithm 6.3 Extracting star-convex sub-volumes 6.4 Results 6.4.1 Stationary Gaussian blob model 6.4.2 Bickley-Jet 6.4.3 Two dimensional inviscid flow 6.4.4 Real data sets 6.5 Closing Remark 7 Conclusion and Outlook

L’étude des processus physiques d’un système d’upwelling est essentielle pour comprendre sa variabilité actuelle et ses changements passés et futurs. Cette thèse présente une étude interdisciplinaire du système d’upwelling côtier à partir de différentes données acquises par satellite, l’accent étant mis principalement sur le système d’upwelling d’Afrique du Nord-Ouest (NWA). Cette étude interdisciplinaire aborde (1) le problème de l’identification et de l’extraction automatiques du phénomène d’upwelling à partir d’observations satellitaires biologiques et physiques. (2) Une étude statistique de la variation spatio-temporelle de l’upwelling de la NWA tout au long de son extension et de ses différents indices d’upwelling. (3) Une étude des relations non linéaires entre le mélange de surface et l’activité biologique dans les régions d’upwelling. (4) études lagrangiennes de tourbillons cohérents; leurs propriétés physiques et identification automatique. (5) L’étude des transports effectués par les tourbillons lagrangiens de la NWA Upwelling et leur impact sur l’océan
Studying physical processes of an upwelling system is essential to understand its present variability and its past and future changes. This thesis presents an interdisciplinary study of the coastal upwelling system from different satellite acquired data, with the main focus placed on the North West African (NWA) upwelling system. This interdisciplinary study covers (1) the problem of the automatic identification and extraction of the upwelling phenomenon from biological and physical satellite observations. (2) A statistical study of the spatio-temporal variation of the NWA upwelling throughout its extension and different upwelling indices. (3) A Study of the nonlinear relationships between the surface mixing and biological activity in the upwelling regions. (4) Lagrangian studies of coherent eddies; their physical properties and automatic identification. (5) The study of transport made by Lagrangian eddies off the NWA Upwelling and their impact on the open ocean. [...]

In the first part of the thesis, we carried out direct two-dimensional (2D) multipoint measurements of the velocity fields in a turbulent Rayleigh-Benard convection cell to study the properties of small-scale convective turbulence. The local homogeneity and isotropy of the velocity field are tested using a number of criteria and are found to hold to an excellent degree. The properties of velocity circulation Gammar are also studied. The results show that the circulation appears to be more effective to capture the effect of local anisotropy than the velocity field itself. The distribution of Gammar is found to depend on the scale r, reflecting strong intermittency. It is further found that velocity circulation has the same anomalous scaling exponents as the longitudinal and transverse structure functions for low-order moments (p ≲ 5). Whereas, for high-order moments (p ≳ 5), the anomalous scaling exponents for circulation are found to be systematically smaller than the scaling exponents of the longitudinal and transverse structure functions.
In the second part of the thesis, the simultaneous visualization of the temperature and velocity fields was used to study the properties of thermal plumes. Our visualization reveals the process of the morphological evolution between sheetlike and mushroomlike plumes, which were also quantified by the height dependence of plume numbers and of vorticity fluctuations. A direct connection between the heat transport and coherent structures, i.e. thermal plumes, was established, which shows that it is plume number that primarily determines the Nu-Ra scaling relation. Individual plumes were extracted and their statistical and geometric properties were studied. It is found that the log-normal distribution is universal for thermal plumes and the log-normal statistics may be used to model them. In addition, both our quantitative characteristic and direct 3D spatial visualizations indicate that the previously-believed sheetlike plumes should be reconsidered to be only one-dimensional structures.
In the third part of the thesis, the planar laser-induced fluorescence technique was induced to study the 2D passive scalar mixing in high-Schmidt-number buoyancy-driven turbulence. The passive scalar mixing evolution was studied and various geometric properties, such as shape complexity, fractal dimension and local curvature, were used to characterize the isoconcentration contours of the 2D passive scalar fields. It is found that when the flow gets more turbulent the shape of passive scalar packets becomes closer to a circular shape and the passive scalar mixing becomes more isotropic, indicating the increased mixing and stirring of the turbulent flow.
The objective of this thesis is to address the following three key issues in turbulent thermal convection, i.e. turbulent fluctuations in small scales, coherent structures and passive scalar mixing in buoyancy-driven turbulence.
Zhou, Quan = 對流熱湍流中能量級串, 相干結構和標量場混合的实验研究 / 周全.
Adviser: Ke-Qing Xia.
Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3576.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2008.
Includes bibliographical references (leaves 103-117).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts in English and Chinese.
School code: 1307.
Zhou, Quan = Dui liu re tuan liu zhong neng liang ji chuan, xiang gan jie gou he biao liang chang hun he de shi yan yan jiu / Zhou Quan.

This thesis concerns the occurrence of the large-scale bed and plan forms known as alternate bars and meandering, and the internal structures of the flow associated with their formation. The work is to be viewed as an extension of previous work by da Silva (1991), Yalin (1992), and Yalin and da Silva (2001). As a first step in this work, the criteria for occurrence of alternate bars and meandering of Yalin and da Silva (2001) is re-considered in view of additional field and laboratory data from the recent literature and data resulting from two series of experimental runs carried out in two sediment transport flumes. This leads to a number of modifications of the boundary-lines in the related existence-region diagram of Yalin and da Silva. The size of the largest horizontal coherent structures (HCS’s) of an alternate bar inducing flow was then investigated experimentally on the basis of three series of flow velocity measurements. These were carried out in a 21m-long, 1m-wide straight channel, conveying a 4cm-deep flow. The bed consisted of a silica sand having a grain size of 2mm; its surface was flat. The measurements were carried out using a Sontek 2D Micro ADV. The horizontal burst length was found to be between five and seven times the flow width. The effect of the HCS’s on the mean flow was also investigated. A slight internal meandering of the flow caused by the superimposition of burst-sequences on the mean flow was clearly detectable. Finally, with the aid of three new series of measurements in the same channel, an attempt was made to penetrate the dynamics and life-cycle of the HCS’s. For this purpose, quadrant analysis was used; the cross-sectional distribution of relevant statistical turbulence-related parameters was investigated; and cross-correlations of flow velocity along the flow depth and across the channel were performed. The analysis indicates that the HCS’s originate near the channel banks, with the location of ejections and sweeps being anti-symmetrically arranged with regard to the channel centreline, and then evolve so as to occupy the entire depth of the water and the entire width of the channel.
Thesis (Ph.D, Civil Engineering) -- Queen's University, 2010-03-09 10:20:53.596