Les tourbillons hélicoïdaux générés derrière les rotors sont étudiés. Pour les générer, une méthode basée sur le couplage entre la technique de la ligne active et un solveur des équations de Navier-Stokes (ENS), incompressibles et tridimensionnelles, a été développée. Elle consiste à modéliser la pâle par son équivalent de forces volumiques. Les équations, écrites en coordonnées cylindriques, sont résolues par un schéma de différences finies, écrit en parallèle. La méthode est d'ordre deux en temps et en espace. Le solveur des ENS a été validé par la reproduction des taux de croissance d'un écoulement de jet, instable, trouvés par la théorie d'instabilité linéaire. La comparaison avec des données expérimentales a montré que la méthode prédit bien l'aérodynamique de la pâle. Ensuite, le tourbillon de bout de pâle a été, en particulier, caractérisé. La vorticité et la vitesse azimutale ont été trouvées auto-similaire et la taille du coeur suit asymptotiquement la loi de diffusion linéaire 2D. Un modèle simple du coeur du tourbillon a été proposé. La présence d'une vitesse axiale dans le coeur du tourbillon a été montrée et a été caractérisée en fonction du rapport de vitesse au bout de la pâle. Finalement, une étude de stabilité du tourbillon a été faite en utilisant une vitesse angulaire variable pour perturber l'écoulement. Les taux de croissances des modes les plus instables sont en bon accord avec celui de l'instabilité d'appariement 2D des tourbillons. Trois types de modes ont été identifiés en fonction de la fréquence des perturbations et ont été trouvés similaires aux modes décrits par la théorie et aussi trouvés, précédemment, par l'expérience. / This present work is aimed to study helical vortices encountered in the wakes of rotating elements. For this, the generation of a helical wake of a one-bladed-rotor in a laminar velocity field, is simulated by the actuator line method. This method is a coupling of a Navier-Stokes (NS) solver with the Actuator Line Method where the blade is replaced by the body forces. This method has been implemented in a finite difference code, that we have written in parallel to solve the 3D incompressible NS equations written in cylindrical coordinates. The order of accuracy of the method is two both in time and space. The NS solver was validated comparing growth rates of an unstable jet, found numerically, and those of linear instability theory. A good agreement was found. A good agreement was also found comparing numerical results to analytical formulations and experimental data. It was shown that the method predicts well the blade aerodynamics . Then, the helical tip vortex is characterized for different Reynolds numbers and Tip Speed Ratios. The vorticity and the azimuthal velocity were found self-similar and the vortex core follows asymptotically the linear 2D diffusion law. A simple model for the helical vortex core was proposed. The presence of an axial velocity inside the vortex core was highlighted. Then, a stability study of the helical tip vortex was done using an angular velocity dependent on time to perturb the flow. The largest growth rates were found in good agreement with those of the (2D) pairing instability. Three types of modes were identified based on the perturbation frequency. The results are similar to those found in previous analytical and experimental works.

<p>Dynamic properties of type-II superconductors have been experimentally studied in zero and low magnetic fields using SQUID magnetometry and <i>I–V</i> measurements.</p><p>In zero magnetic field close to the critical temperature, the physical properties of type-II superconductors are dominated by spontaneously created vortices. In three dimensions (3D) such vortices take the form of vortex loops and in two dimensions (2D) as vortex-antivortex pairs.</p><p>The 2D vortex dynamics has been probed using mutual inductance and flux noise measurements on YBa₂Cu₃O₇ (YBCO) and MgB₂ thin films in zero and low magnetic fields. In such measurements, information about vortex correlations is obtained through a temperature dependent characteristic frequency, below (above) which the vortex movements are uncorrelated (correlated). The results obtained in zero magnetic field indicate that sample heterogeneities influence the vortex physics and hinder the divergence of the vortex-antivortex correlation length.</p><p>In low magnetic fields the vortex dynamics is strongly dependent on the applied magnetic field and a power law dependence of the characteristic frequency with respect to the magnetic field is observed. The results indicate that there is a co-existence of thermally and field generated vortices.</p><p>The <i>I–V</i> characteristics of untwinned YBCO single crystals show that only a small broadening of the transition region influences the length scale over which the vortex movements are correlated. The dynamic and static critical exponents therefore exhibit values being larger in magnitude as compared to values predicted by relevant theoretical models. The results also suggest that the copper oxide planes in YBCO decouple slightly below the mean field critical temperature and hence, the system has a crossover from 3D to 2D behaviour as the temperature is increased. </p><p>From temperature dependent DC-magnetisation measurements performed on untwinned YBCO single crystals in weak applied fields, detailed information about the critical current density and the irreversibility line is obtained.</p>

Dynamic properties of type-II superconductors have been experimentally studied in zero and low magnetic fields using SQUID magnetometry and I–V measurements. In zero magnetic field close to the critical temperature, the physical properties of type-II superconductors are dominated by spontaneously created vortices. In three dimensions (3D) such vortices take the form of vortex loops and in two dimensions (2D) as vortex-antivortex pairs. The 2D vortex dynamics has been probed using mutual inductance and flux noise measurements on YBa2Cu3O7 (YBCO) and MgB2 thin films in zero and low magnetic fields. In such measurements, information about vortex correlations is obtained through a temperature dependent characteristic frequency, below (above) which the vortex movements are uncorrelated (correlated). The results obtained in zero magnetic field indicate that sample heterogeneities influence the vortex physics and hinder the divergence of the vortex-antivortex correlation length. In low magnetic fields the vortex dynamics is strongly dependent on the applied magnetic field and a power law dependence of the characteristic frequency with respect to the magnetic field is observed. The results indicate that there is a co-existence of thermally and field generated vortices. The I–V characteristics of untwinned YBCO single crystals show that only a small broadening of the transition region influences the length scale over which the vortex movements are correlated. The dynamic and static critical exponents therefore exhibit values being larger in magnitude as compared to values predicted by relevant theoretical models. The results also suggest that the copper oxide planes in YBCO decouple slightly below the mean field critical temperature and hence, the system has a crossover from 3D to 2D behaviour as the temperature is increased. From temperature dependent DC-magnetisation measurements performed on untwinned YBCO single crystals in weak applied fields, detailed information about the critical current density and the irreversibility line is obtained.

<p>In high-temperature superconductors a large region of the magnetic phase diagram is occupied by a vortex phase that displays a number of exciting phenomena. At low temperatures, vortices form a truly superconducting solid phase which at high temperatures turns into a dissipative vortex liquid. The character of the transition between these two phases depends on the amount and type of disorder present in the system. For weak point disorder the vortex solid-to-liquid transition is a first-order melting. In the presence of strong point disorder the solid is thought to be a vortex-glass and the transition into the liquid is instead of second order. When the disorder is correlated, like twin boundaries or artificially introduced columnar defects, the transition is also second order, but has essentially different properties. In this work, the transition between the solid and liquid phases of the vortex state has been studied by resistive transport measurements in mainly YBa2Cu3O7-[delta](YBCO) single crystals with different types of disorder.</p><p>The vortex-glass transition has been investigated in an extended model for the vortex-liquid resistivity close to the transition that takes into account both the temperature and magnetic field dependence of the transition line. The resistivity of samples with different properties was measured with various contact configurations at several magnetic fields and analyzed within this model. For each sample, attempts were made to scale the transition curves to one curve according to a suitable scaling variable predicted by the model. Good scaling was found in a number of different situations. The influence of increasing anisotropy and angular dependence of the magnetic field in the model were also considered.</p><p>The vortex solid-to-liquid transition was also studied in heavy-ion irradiated YBCO single crystals. The ions create columnar defects in the sample that act as correlated disorder. A magnetic field was applied at a tilt angle with respect to the direction of the columns. At the transition the resistance disappears as a power law with different exponents in the three orthogonal directions considered. This provides evidence for a new type of critical behavior with fully anisotropic critical scaling properties not previously found in any physical system.</p><p>The effect on the vortex solid-to-liquid transition of high magnetic fields applied parallel to the superconducting layers of underdoped YBCO single crystals was also studied. Some novel features were observed: a sharp kink appearing close to Tc at high magnetic fields and a triple dip in the angular dependence of the resistivity close to B||ab in some regions of the phase diagram.</p> / <p>I högtemperatursupraledare består en stor del av det magnetiska fasdiagrammet av en vortexfas som uppvisar ett flertal spännande fenomen. Vid låga temperaturer bildar vortexarna en fast vortexfas utan elektriskt motstånd. Vid högre temperatur övergår denna fas till en dissipativ vortexvätska. Egenskaperna hos denna fasövergång beror på oordningen i form av defekter. Vid svag punktoordning är fasomvandlingen mellan det fasta och flytande vortextillståndet en första ordningens smältövergång. Vid stark punktoordning anses den fasta fasen vara ett vortexglas och övergången till vortexvätskan är istället av andra ordningen. När oordningen är korrelerad, som för tvillinggränser eller artificiellt skapade kolumndefekter, är övergången också av andra ordningen men med väsentligt annorlunda egenskaper. I detta arbete har övergången mellan det fasta och det flytande vortextillståndet studerats med resistiva transportmätningar i framförallt enkristaller av YBa2Cu3O7-[delta] (YBCO) med olika typer av oordning.</p><p>Vortexglasövergången har undersökts i en utvidgad modell för resistansen i vortexvätskan nära fasövergången där hänsyn tas till såväl temperatur- som fältberoendet. Resistansen hos prover med olika egenskaper mättes i varierande magnetfält och i flera kontaktkonfigurationer och analyserades inom denna modell. Övergångskurvorna skalades till en kurva med en skalningsvariabel som givits av modellen. God skalning uppnåddes i flera olika fall. Effekten av ökande anisotropi och vinkelberoendet i modellen undersöktes också.</p><p>Vortexövergången mellan det fasta och det flytande vortextillståndet undersöktes även i enkristaller av YBCO bestrålade med tunga joner. Jonerna skapade kolumndefekter som fungerar som korrelerad oordning. Vinkeln mellan pålagt magnetfält och dessa kolumndefekter varierades. Vid fasövergången avtar resistansen som en potenslag med olika exponenter i de tre undersökta ortogonala riktningarna. Detta ger experimentell belägg för en ny typ av kritiskt beteende med fullständigt anisotropa kritiska skalningsegenskaper.</p><p>Egenskaparna hos på vortexövergången mellan fast och flytande fas vid höga magnetfält parallella med de supraledande lagren hos underdopade YBCO enkristaller undersöktes också. Några nya effekter observerades: en skarp knyck uppstod nära Tc vid höga magnetfält och en tredubbel dipp i den vinkelberoende resistiviteten nära B||ab i några regioner av fasdiagrammet.</p>

Research into advanced wind turbine design has shown that load alleviation strategies like bend-twist coupled blades and coned rotors could reduce costs. However these strategies are based on nonlinear aero-structural dynamics providing additional benefits to components beyond the blades. These innovations will require Multi-disciplinary Design Optimization (MDO) to realize the full benefits. This research expands the MDO capabilities of Horizontal Axis Wind Turbines. The early research explored the numerical stability properties of Blade Element Momentum (BEM) models. Then developed a provincial scale wind farm siting models to help engineers determine the optimal design parameters. The main focus of this research was to incorporate advanced analysis tools into an aero-elastic optimization framework. To adequately explore advanced designs with optimization, a new set of medium fidelity analysis tools is required. These tools need to resolve more of the physics than conventional tools like (BEM) models and linear beams, while being faster than high fidelity techniques like grid based computational fluid dynamics and shell and brick based finite element models. Nonlinear beam models based on Geometrically Exact Beam Theory (GEBT) and Variational Asymptotic Beam Section Analysis (VABS) can resolve the effects of flexible structures with anisotropic material properties. Lagrangian Vortex Dynamics (LVD) can resolve the aerodynamic effects of novel blade curvature. Initially this research focused on the structural optimization capabilities. First, it developed adjoint-based gradients for the coupled GEBT and VABS analysis. Second, it developed a composite lay-up parameterization scheme based on manufacturing processes. The most significant challenge was obtaining aero-elastic optimization solutions in the presence of erroneous gradients. The errors are due to poor convergence properties of conventional LVD. This thesis presents a new LVD formulation based on the Finite Element Method (FEM) that defines an objective convergence metric and analytic gradients. By adopting the same formulation used in structural models, this aerodynamic model can be solved simultaneously in aero-structural simulations. The FEM-based LVD model is affected by singularities, but there are strategies to overcome these problems. This research successfully demonstrates the FEM-based LVD model in aero-elastic design optimization. / Graduate / 0548 / pilot.mm@gmail.com

In high-temperature superconductors a large region of the magnetic phase diagram is occupied by a vortex phase that displays a number of exciting phenomena. At low temperatures, vortices form a truly superconducting solid phase which at high temperatures turns into a dissipative vortex liquid. The character of the transition between these two phases depends on the amount and type of disorder present in the system. For weak point disorder the vortex solid-to-liquid transition is a first-order melting. In the presence of strong point disorder the solid is thought to be a vortex-glass and the transition into the liquid is instead of second order. When the disorder is correlated, like twin boundaries or artificially introduced columnar defects, the transition is also second order, but has essentially different properties. In this work, the transition between the solid and liquid phases of the vortex state has been studied by resistive transport measurements in mainly YBa2Cu3O7-[delta](YBCO) single crystals with different types of disorder. The vortex-glass transition has been investigated in an extended model for the vortex-liquid resistivity close to the transition that takes into account both the temperature and magnetic field dependence of the transition line. The resistivity of samples with different properties was measured with various contact configurations at several magnetic fields and analyzed within this model. For each sample, attempts were made to scale the transition curves to one curve according to a suitable scaling variable predicted by the model. Good scaling was found in a number of different situations. The influence of increasing anisotropy and angular dependence of the magnetic field in the model were also considered. The vortex solid-to-liquid transition was also studied in heavy-ion irradiated YBCO single crystals. The ions create columnar defects in the sample that act as correlated disorder. A magnetic field was applied at a tilt angle with respect to the direction of the columns. At the transition the resistance disappears as a power law with different exponents in the three orthogonal directions considered. This provides evidence for a new type of critical behavior with fully anisotropic critical scaling properties not previously found in any physical system. The effect on the vortex solid-to-liquid transition of high magnetic fields applied parallel to the superconducting layers of underdoped YBCO single crystals was also studied. Some novel features were observed: a sharp kink appearing close to Tc at high magnetic fields and a triple dip in the angular dependence of the resistivity close to B||ab in some regions of the phase diagram. / I högtemperatursupraledare består en stor del av det magnetiska fasdiagrammet av en vortexfas som uppvisar ett flertal spännande fenomen. Vid låga temperaturer bildar vortexarna en fast vortexfas utan elektriskt motstånd. Vid högre temperatur övergår denna fas till en dissipativ vortexvätska. Egenskaperna hos denna fasövergång beror på oordningen i form av defekter. Vid svag punktoordning är fasomvandlingen mellan det fasta och flytande vortextillståndet en första ordningens smältövergång. Vid stark punktoordning anses den fasta fasen vara ett vortexglas och övergången till vortexvätskan är istället av andra ordningen. När oordningen är korrelerad, som för tvillinggränser eller artificiellt skapade kolumndefekter, är övergången också av andra ordningen men med väsentligt annorlunda egenskaper. I detta arbete har övergången mellan det fasta och det flytande vortextillståndet studerats med resistiva transportmätningar i framförallt enkristaller av YBa2Cu3O7-[delta] (YBCO) med olika typer av oordning. Vortexglasövergången har undersökts i en utvidgad modell för resistansen i vortexvätskan nära fasövergången där hänsyn tas till såväl temperatur- som fältberoendet. Resistansen hos prover med olika egenskaper mättes i varierande magnetfält och i flera kontaktkonfigurationer och analyserades inom denna modell. Övergångskurvorna skalades till en kurva med en skalningsvariabel som givits av modellen. God skalning uppnåddes i flera olika fall. Effekten av ökande anisotropi och vinkelberoendet i modellen undersöktes också. Vortexövergången mellan det fasta och det flytande vortextillståndet undersöktes även i enkristaller av YBCO bestrålade med tunga joner. Jonerna skapade kolumndefekter som fungerar som korrelerad oordning. Vinkeln mellan pålagt magnetfält och dessa kolumndefekter varierades. Vid fasövergången avtar resistansen som en potenslag med olika exponenter i de tre undersökta ortogonala riktningarna. Detta ger experimentell belägg för en ny typ av kritiskt beteende med fullständigt anisotropa kritiska skalningsegenskaper. Egenskaparna hos på vortexövergången mellan fast och flytande fas vid höga magnetfält parallella med de supraledande lagren hos underdopade YBCO enkristaller undersöktes också. Några nya effekter observerades: en skarp knyck uppstod nära Tc vid höga magnetfält och en tredubbel dipp i den vinkelberoende resistiviteten nära B||ab i några regioner av fasdiagrammet. / QC 20110125

Un jet heurtant une plaque fendue peut générer, dans certaines configurations, des nuisances sonores. En effet, l’interaction de l’écoulement et de l’obstacle au niveau de la fente, sous certaines conditions, donne naissance à une perturbation remontant l’écoulement et pouvant contrôler son détachement à sa naissance. La perturbation produite par cette boucle de rétroaction optimise le transfert d’énergie du champ aérodynamique du jet vers le champ acoustique rayonné. Afin d’appréhender la dynamique tourbillonnaire, d’analyser les couplages entre cette dernière et les émissions sonores générées et de mieux comprendre les phénomènes responsables de ces nuisances, un dispositif expérimental basé sur de la métrologie laser a été réalisé. Ce système permet, d’une part, la génération de l’écoulement et la maitrise de ses paramètres (confinement, vitesse, forme,…) et d’autre part, la réalisation de plans lasers et de mesures par imagerie de particules (PIV). Ainsi le travail présenté dans ce manuscrit concerne les couplages qui existent entre la dynamique de l’écoulement heurtant une plaque fendue et les champs acoustiques générés. Les mesures de champs cinématiques d’un jet plan heurtant une plaque fendue par Vélocimétrie par Images de Particules (PIV) sont réalisées simultanément avec des mesures de champs acoustiques. Après avoir caractérisé les écoulements étudiés, on présente par des graphes spatio-temporels, les corrélations entre les signaux acoustiques et les vitesses de l’écoulement depuis la sortie du jet jusqu’à son arrivée à la plaque fendue. Ces corrélations sont calculées de deux manières : à partir de signaux bruts dans un premier temps, puis, dans un second temps, avec une méthode de pré-blanchiment (terme anglo-saxon : ‘’pre-whitening’’). Cette méthode vise à mettre en exergue l’existence d’une instabilité globale du jet qui existe dans les signaux analysés. Cette instabilité est importante pour la boucle de rétroaction des sons auto-entretenus, mais quasiment masquée devant les phénomènes principaux dominants (tourbillons primaires) dans le calcul des inter-corrélations. / Self-sustaining sounds related to aero-acoustic coupling occurs in impinging jets when a feedback loop is present between the jet exit and a slotted plate: the downstream-convected coherent structures and upstream-propagating pressure waves generated by the impingement of the coherent structures on the plate are phase locked at the nozzle exit. The upstream-propagating waves excite the thin shear layer near the nozzle lip and result in periodic coherent structures. The period is determined by the convection speed of the coherent structures and the distance between the nozzle and the plate. Simultaneous measurements of the velocity fields and the acoustic waves in a plane jet impinging a slotted plate were performed using time-resolved particle image velocimetry (PIV) and a microphone. A better understanding of the flow physics and the aero-acoustic coupling are obtained thanks to spatio-temporal cross-correlations between the transverse velocity and the acoustic signals. Cross-correlations are calculated using two different methods: classical analysis of the original signals and by developing a pre-whitening technique. The latter method is useful for analyzing small random signals superimposed on a high amplitude pure tone.

The present thesis involves the study of introducing passive exit flexibility in a two dimensional starting jet. This is relevant to various biological flows like propulsion of aquatic creatures (jellyfish, squid etc.) and flow in the human heart. In the present study we introduce exit flexibility in two ways. The first method was by hinging rigid plates at the channel exit and the second was by attaching deformable flaps at the exit. In the hinged flaps cases, the experimental arrangement closely approximates the limiting case of a free-to-rotate rigid flap with negligible structural stiffness, damping and flap inertia; these limiting structural properties permitting the largest flap openings. In the deformable flaps cases, the flap’s stiffness (or its flexural rigidity EI) becomes an important parameter. In both cases, the initial condition was such that the flaps were parallel to the channel walls. With this, a piston was pushed in a controlled manner to form the starting jet. Using this arrangement, we start the flow and visualize the flap kinematics and make flow field measurements. A number of parameters were varied which include the piston speed, the flap length and the flap stiffness (in case of the deformable flaps). In the hinged rigid flaps cases, the typical motion of the flaps involves a rapid opening with flow initiation and a subsequent more gradual return to its initial position, which occurs while the piston is still moving. The initial opening of the flaps can be attributed to an excess pressure that develops in the channel when the flow starts, due to the acceleration that has to be imparted to the fluid slug between the flaps. In the case with flaps, additional pairs of vortices are formed because of the motion of the flaps and a complete redistribution of vorticity is observed. The length of the flaps is found to significantly affect flap kinematics when plotted using the conventional time scale L/d. However, with a newly defined time-scale based on the flap length (L/Lf ), we find a good collapse of all the measured flap motions irrespective of flap length and piston velocity for an impulsively started piston motion. The maximum opening angle in all these impulsive velocity program cases, irrespective of the flap length, is found to be close to 15 degrees. Even though the flap kinematics collapses well with L/Lf , there are differences in the distribution of the ejected vorticity even for the same L/Lf . In the deformable flap cases, the initial excess pressure in the flap region causes the flaps to bulge outwards. The size of the bulge grows in size, as well as moves outwards as the flow develops and the flaps open out to reach their maximum opening. Thereafter, the flaps start returning to their initial straight position and remain there as long as the piston is in motion. Once the piston stops, the flaps collapse inwards and the two flap tips touch each other. It was found that the flap’s flexural rigidity played an important role in the kinematics. We define a new time scale (t ) based on the flexural rigidity of the flaps (EI) and the flap length (Lf ). Using this new time scale, we find that the time taken to reach the maximum bulge (t* 0.03) and the time taken to reach the maximum opening (t* 0.1) were approximately similar across various flap stiffness and flap length cases. The motion of the flaps results in the formation of additional pairs of vortices. Interestingly, the total final circulation remains almost the same as that of a rigid exit case, for all the flap stiffness and flap lengths studied. However, the final fluid impulse (after all the fluid had come out of the flap region) was always higher in the flap cases as compared to the rigid exit case because of vorticity redistribution. The rate at which the impulse increases was also higher in most flap cases. The final impulse values were as large as 1.8 times the rigid exit case. Since the time rate of change of impulse is linked with force, the measurements suggest that introduction of flexible flaps at the exit could result in better propulsion performances for a system using starting jets. The work carried out in this thesis has shown that by attaching flexible flaps at the exit of an unsteady starting jet, dramatic changes can be made to the flow field. The coupled kinematics of the flaps with the flow dynamics led to desirable changes in the flow. Although the flaps introduced in this work are idealized and may not represent the kind of flexibility we encounter in biological systems, it gives us a better understanding of the importance of exit flexibility in these kinds of flows.

In this thesis we study a variety of problems in superfluid turbulence, princi-pally in two dimensions. A summary of the main results of our studies is given below; we indicate the Chapters in which we present these. In Chapter 1, we provide an overview of several problems in superfluid turbulence with special emphasis on background material for the problems we study in this thesis. In particular, we give: (a) a brief introduction of fluid turbulence; (b) an overview of superfluidity and the phenomenological two-fluid model; (c) a brief overview of experiments on superfluid turbulence; (d) an introductory accounts of the phenomenological models used in the study of superfluid turbulence. We end with a summary of the problems we study in subsequent Chapters of this thesis. In Chapter 2, we present a systematic, direct numerical simulation of the two-dimensional, Fourier-truncated, Gross-Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters. We find that the time evolution of this system can be classified into four regimes with qualitatively different statistical properties. First, there are transients that depend on the initial conditions. In the second regime, power- law scaling regions, in the energy and the occupation-number spectra, appear and start to develop; the exponents of these power laws and the extents of the scaling regions change with time and depend on the initial condition. In the third regime, the spectra drop rapidly for modes with wave numbers k > kc and partial thermalization takes place for modes with k < kc ; the self-truncation wave number kc(t) depends on the initial conditions and it grows either as a power of t or as log t. Finally, in the fourth regime, complete thermalization is achieved and, if we account for finite-size effects carefully, correlation functions and spectra are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms. Our work is a natural generalization of recent studies of thermalization in the Euler and other hydrodynamical equations; it combines ideas from fluid dynamics and turbulence, on the one hand, and equilibrium and nonequilibrium statistical mechanics on the other. In Chapter 3, we present the first calculation of the mutual-friction coefficients α and α (which are parameters in the Hall-Vinen-Bekharevich-Khalatnikov two-fluid model that we study in chapter 5) as a function of temperature in a homogeneous Bose gas in two-dimensions by using the Galerkin-truncated Gross-Pitaevskii equation, with very special initial conditions, which we obtain by using the advective, real, Ginzburg-Landau equation (ARGLE) and an equilibration procedure that uses a stochastic Ginzburg-Landau equation (SGLE). We also calculate the normal-fluid density as a function of temperature. In Chapter 4, we elucidate the interplay of particles and fields in superfluids, in both simple and turbulent flows. We carry out extensive direct numerical simulations (DNSs) of this interplay for the two-dimensional (2D) Gross-Pitaevskii (GP) equation. We obtain the following results: (1) the motion of a particle can be chaotic even if the superfluid shows no sign of turbulence; (2) vortex motion depends sensitively on particle charateristics; (3) there is an effective, superfluid-mediated, attractive interaction between particles; (4) we introduce a short-range repulsion between particles, with range rSR, and study two- and many-particle collisions; in the case of two-particle, head-on collisions, we find that, at low values of rSR, the particle collisions are inelastic with coefficient of restitution e = 0; and, as we in-crease rSR, e becomes nonzero at a critical point, and finally attains values close to 1; (5) assemblies of particles and vortices show rich, turbulent, spatio-temporal evolution. In Chapter 5, we present results from our direct numerical simulations (DNSs) of the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) two-fluid model in two dimensions. We have designed these DNSs to study the statistical properties of inverse and forward cascades in the HVBK model. We obtain several interesting results that have not been anticipated hitherto: (1) Both normal-fluid and superfluid energy spectra, En(k) and Es(k), respectively, show inverse- and forward-cascade regimes; the former is characterized by a power law Es(k) En(k) kα whose exponent is consistent with α 5/3. (2) The forward-cascade power law depends on (a) the friction coefficient, as in 2D fluid turbulence, and, in addition, on (b) the coefficient B of mutual friction, which couples normal and superfluid compo-nents. (3) As B increases, the normal and superfluid velocities, un and us, re-spectively, get locked to each other, and, therefore, Es(k) En(k), especially in the inverse-cascade regime. (4) We quantify this locking tendency by calculating the probability distribution functions (PDFs) P(cos(θ)) and P(γ), where the angle θ ≡ (un • us)/( |un||us|) and the amplitude ratio γ = |un|/|us |; the former has a peak at cos(θ) = 1; and the latter exhibits a peak at γ = 1 and power-law tails on both sides of this peak. (4) This locking increases as we increase B, but the power-law exponents for the tails of P(γ) are universal, in so far as they do not depend on B, ρn/ρ, and the details of the energy-injection method. (5) We characterize the energy and enstrophy cascades by computing the energy and enstrophy fluxes and the mutual-friction transfer functions for all wave-number scales k. In Chapter 6, we examine the multiscaling of structure functions in three-dimensional superfluid turbulence by using a shell-model for the three-dimensional HVBK equations. Our HVBK shell model is based on the GOY shell model. In particular, we examine the dependence of multiscaling on the normal-fluid fraction and the mutual-friction coefficients. We hope our in silico studies of 2D and 3D superfluid turbulence will stimulate new experimental, numerical, and theoretical studies.

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.