The long time energy decay of vortices for several different initial flow scenarios is investigated both theoretically and numerically. The theoretical analysis is based on the energy method. Numerical calculations are done by solving the compressible Navier-Stokes equations using a high order stable finite difference method. The simulations verify the theoretical conclusion that vortices decay at a slow rate compared to other types of flows. Several Reynolds numbers and grid sizes in both two and three dimensions are considered.

Previous research has indicated aperiodicity in the positions of tip vortices emitted from a helicopter rotor blade in hover. The objective of the current study is to develop an analysis of the tip vortex aperiodicity in hover and to validate it with measurements on a reduced-scale, 1m diameter, four-bladed rotor. A “vortex ring emitter model” (VREM) was developed to study the statistics of the tip vortices emitted from a rotor blade during hover. In order to better model the rotor wake, a number of independent vortex blobs were used to describe a vortex ring. An empirical model for viscosity was also considered which helped model the core radius growth of the vortex ring with vortex age. A parametric analysis was then performed to obtain a comprehensive qualitative and quantitative convergence study of the time step, viscosity parameter, initial core size, number of rings shed, number of blobs and overlap factor. It was observed that the solution converged rapidly for all the parameters used. The locations of tip vortex cores for vortex ages ranging from 0◦ to 260◦ were measured on the reduced-scale rotor using a stereo PIV system. The blade loading for the reduced scaled rotor was Ct /σ = 0.044 and the blade rotational speed was 1520 RPM, which corresponds to a tip Reynolds number of 248,000. The 95 % confidence region for the position of tip vortex cores exhibited an anisotropic, aperiodic pattern, approximating an ellipse. It was seen that the principal axis of this ellipse appeared to be aligned perpendicular to the slipstream boundary. The analytical model showed good correlation with experimental data in terms of the orientation and extent of the anisotropy. Moreover, an estimate of the total thrust produced and spanwise loading along the rotor blade was also obtained and compared with Blade Element Momentum Theory (BEMT). It was seen that by using more blobs to represent a vortex ring, the solution converged to the BEMT estimate. / text

Turbulence in classical fluids has been the subject of scientific study for centuries, yet there is still no complete general theory of classical turbulence connecting microscopic physics to macroscopic fluid flows, and this remains one of the open problems in physics. In contrast, the phenomenon of quantum turbulence in superfluids has well-defined theoretical descriptions, based on first principles and microscopic physics, and represents a realm of physics that can connect the classical and quantum worlds. Studies of quantum turbulence may thus be viewed as a path for progress on the long-standing problem of turbulence.A dilute-gas Bose-Einstein condensate (BEC) is, in most cases, a superfluid that supports quantized vortices, the primary structural elements of quantum turbulence. BECs are particularly convenient systems for the study of vortices, as standard techniques allow the microscopic structure and dynamics of the vortices to be investigated. Vortices in BECs can be created and manipulated using a variety of techniques, hence BECs are potentially powerful systems for the microscopic study of quantum turbulence.This dissertation focuses on quantized vortices in BECs, specifically experimental and numerical studies of their formation, dynamics, and decay, in an effort to understand the microscopic nature of vortices as elements of quantum turbulence. Four main experiments were performed, and are described in the main chapters of this dissertation, after introductions to vortices, experimental methods, and turbulence are presented. These experiments were aimed at understanding various aspects of how vortices are created and behave in a superfluid system. They involved vortex dipole nucleation in the breakdown of superfluidity, persistent current generation from a turbulent state in the presence of energy dissipation, decay of angular momentum of a BEC due to trapping potential impurities, and exploration of the spontaneous formation of vortices during the BEC phase transition. These experiments represent progress towards enhanced understanding of the formation, dynamics, and decay of vortices in BECs and thus may be foundational to more general studies of quantum turbulence in superfluids.

Phase transitions abound in the physical world, from the subatomic length scales of quark condensation to the decoupling forces in the early universe. In the Bose-Einstein condensation phase transition, a gas of trapped bosonic atoms is cooled to a critical temperature. Below this temperature, a macroscopic number of atoms suddenly starts to occupy a single quantum state; these atoms comprise the Bose-Einstein condensate (BEC). The dynamics of the BEC phase transition are the focus of this dissertation and the experiments described here have provided new information on the details of BEC formation. New theoretical developments are proving to be valuable tools for describing BEC phase transition dynamics and interpreting new experimental results. With their amenability to optical manipulation and probing along with the advent of new microscopic theories, BECs provide an important new avenue for gaining insight into the universal dynamics of phase transitions in general.Spontaneous symmetry breaking in the system's order parameter may be one result of cooling through a phase transition. A potential consequence of this is the spontaneous formation of topological defects, which in a BEC appear as vortices. We experimentally observed and characterized the spontaneous formation of vortices during BEC growth. We attribute vortex creation to coherence length limitations during the initial stages of the phase transition. Parallel to these experimental observations, theory collaborators have used the Stochastic Gross-Pitaevski Equation formalism to simulate the growth of a condensate from a thermal cloud. The experimental and theoretical statistical results of the spontaneous formation of vortex cores during the growth of the condensate are in good quantitative agreement with one another, supporting our understanding of the dynamics of the phase transition. We believe that our results are also qualitatively consistent with the Kibble-Zurek mechanism, a universal model for topological defect formation.Ultimately, our understanding of the dynamics of the BEC phase transition may lead to a broader understanding of phase transitions in general, and provide new insight into the development of coherence in numerous systems.

This thesis examines problems in electron diffraction and related areas of theoretical optics. It begins with a study of the phase of a quantum mechanical wave function and the behaviour of phase vortices and vortex cores. Several rules for vortex core evolution are given and simulated vortex trajectories are studied. These simulations show that in electron microscopy at atomic resolution and in other similar situations, vortices occur in the wave functions very frequently. This means any image processing methods which deal with the wave function phase must permit vortices to occur. In this context a number of methods of phase retrieval are compared and evaluated. The criteria of evaluation are the accuracy of the phase retrieval, its ability to cope with vortices, its numerical stability and its required computational resources. The best method is found to be an iterative algorithm similar in approach to the Gerchberg-Saxton method, but based on a through focal series of images. / Using this phase retrieval method as an essential tool, the thesis continues with a study of inverse problems in electron optics. The first problem considered is that of using a set of images taken to characterise the coherent aberrations present in a general imaging system. This problem occurs in many areas of optics and is studied here with a focus on transmission electron microscopy. A method of using software to simultaneously determine aberrations and subsequently remove them is presented and tested in simulation. This method is found to have a high level of accuracy in aberration determination. The second inverse problem studied in this thesis is the inversion problem in dynamical electron diffraction. This problem is solved for a periodic object, giving an accurate and unique solution for the projected potential in the multiple scattering case. An extension of this solution to objects which are non-periodic in the direction of the incident wave is investigated. Finally a model computation solving the general inversion problem for dynamical diffraction in an aberrated transmission electron microscope is performed, illustrating this and previous material and summing up the advances presented in this work.

Stepped chutes have been used as hydraulic structures for more than 3.5 millennia for different purposes: For example, to dissipate energy, to enhance aeration rate in the flow and to comply with aesthetical functions. They can be found acting as spillways in dams and weirs, as energy dissipators in artificial channels, gutters and rivers, and as aeration enhancers in water treatment plants and fountains. Spillways are used to prevent dam overtopping caused by floodwaters. Their design has changed through the centuries. In ancient times, some civilizations used steps to dissipate energy in open channels and dam over-falls in a similar fashion as natural cascades. However, in the first half of the twentieth century, the use of concrete became popular and the hydraulic jump was introduced as an efficient energy dissipator. In turn, the use of a stepped geometry became obsolete and was replaced with smooth chutes followed by hydraulic jump stilling basins. In recent years, new construction techniques and materials (Roller Compacted Concrete RCC, rip-rap gabions, wire-meshed gabions, etc.) together with the development of new applications (e.g. re-aeration cascades, fish ladders and embankment overtopping protection or secondary spillways) have allowed cheaper construction of stepped chutes, increasing the interest in stepped chute design. During the last three decades, research in the hydraulics of stepped spillways has been very active. However, studies prior to 1993 neglected the effect of free-surface aeration. A number of studies since this time have focused on air-water flows in steep chutes (θ ≈ 50o). But experimental data is still scarce, and the hydraulic performance of stepped cascades with moderate slope is not yet understood. This study details an experimental investigation of physical air-water flow characteristics down a stepped spillway conducted in two laboratory models with moderate slopes: the first model was a 3.15 m long stepped chute with a 15.9o slope comprising two interchangeable-height steps (h = 0.1 m and h = 0.05 m); the second model was a 2.5 m long, stepped channel with a 21.8o slope comprising 10 steps (h = 0.1 m). Different arrangements of turbulence manipulators (vanes) were also placed throughout the chute in the second model. A broad range of discharges within transition and skimming flow regimes was investigated to obtain a reliable representation of the air-water flow properties. Measurements were conducted using single and double tip conductivity probes at multiple span wise locations and at streamwise distances along the cavity between step edges to obtain a complete three-dimensional representation of the flow. Although the present study was conducted for two moderate slope chutes (θ = 15.9º & 21.8o), it is believed that the outcomes are valid for a wider range of chute geometry and flow conditions. The purpose of this study is to improve the understanding of turbulent air-water flows cascading down moderate slope stepped chutes, and gain new understandings of the interactions between aeration rate, flow turbulence and energy dissipation; scale effects are also investigated. The study provides new, original insights into air-water turbulent flows cascading down moderate slope stepped spillways not foreseen in prior studies, thus contributing to improve criterion designs. It also presents an extensive experimental database (available in a CD-ROM attached at the end of this thesis) and a new design criterion that can be used by designers and researchers to improve the operation of stepped chutes with moderate slopes. The present thesis work included a twofold approach. Firstly, the study provided a detailed investigation of the energy dissipative properties of a stepped channel, based upon detailed airwater flow characteristics measurements conducted with sub-millimetric conductivity probes. Secondly, the study focused on the microscopic scale properties of the airwater flow, using the experimental data to quantify the microscopic scale physical processes (e.g. momentum transfer, shear layer development, vertical mixing, airbubbles/ water-droplets break-up and coalescence etc.) that are believed to increase the flow resistance in stepped canals. The study highlighted the tridimensionality of skimming flows and hinted new means of enhancing flow resistance by manipulating turbulence in the stepped chute. Basic dimensional analysis results emphasized that physical modelling of stepped chutes is more sensitive to scale effects than classical smooth-invert chute studies and thus suggested that the extrapolation of results obtained from heavily scaled experimental models should be avoided. The present study also demonstrated that alterations of flow recirculation and fluid exchanges between free-stream and cavity flow affects drastically form losses and in turn the rate of energy dissipation. The introduction of vanes demonstrated simple turbulence manipulation and form drag modification that could lead to more efficient designs in terms of energy rate dissipation without significant structural load on the stepped chute.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xiv, 139 p.; also includes graphics (some col.) Includes bibliographical references (p. 134-139). Available online via OhioLINK's ETD Center

A ocorrência de vibrações induzidas pelo escoamento em estruturas hidráulicas é um fenômeno altamente indesejável, pois pode causar uma série de problemas de funcionamento, manutenção e em alguns casos pode ocasionar até mesmo o colapso da estrutura em questão. Apesar disso, esse aspecto ainda é considerado como um elemento secundário de projeto. O estudo numérico desse fenômeno ainda é extremamente complexo, fazendo-se necessário o uso de modelos em escala reduzida das estruturas reais para a estimativa do comportamento dinâmico dessas estruturas. A modelagem do comportamento dinâmico de estruturas submetidas ao escoamento de água é denominada de modelagem hidroelástica. Para a aplicação correta da modelagem hidroelástica é fundamental um entendimento profundo sobre os aspectos básicos dos fenômenos hidráulicos e mecânicos atuantes na estrutura. O presente trabalho concentrou-se na investigação experimental de alguns aspectos básicos do fenômeno de vibrações induzidas por vórtices em estruturas cilíndricas, com o objetivo de ampliar a base de conhecimento existente sobre esse fenômeno e, dessa forma, contribuir para o aperfeiçoamento das técnicas de modelagem hidroelástica. Vale ressaltar que existem outros mecanismos de instabilidade causadores de vibrações, além do desprendimento de vórtices, que não foram abordados nesta dissertação. Os aspectos básicos abordados neste trabalho foram os seguintes: • Razão de Aspecto L/D – razão entre o comprimento do cilindro exposto ao escoamento e seu diâmetro; • Parâmetro de massa-amortecimento (m*+CA)ζ − parâmetro adimensional formado pelo produto entre a massa da estrutura e seu amortecimento ζ. Para a investigação experimental foram ensaiados cilindros rígidos elasticamente montados e pivotados na base, submetidos ao escoamento permanente de água em canal aberto, com dois graus de liberdade para oscilar. Apesar da liberdade para oscilar em duas direções, o presente trabalho concentrou-se apenas nas vibrações transversais à direção do escoamento. Os cilindros empregados possuem diferentes diâmetros, diferentes massas e dois tipos de molas para a fixação elástica. A variação desses parâmetros resultou em comportamentos oscilatórios diferentes, caracterizados através da medição das acelerações no topo do cilindro, que posteriormente foram convertidos em valores de deslocamento no topo do cilindro. O comportamento oscilatório dos cilindros foi descrito através de curvas de amplitudes adimensionais A/D, ou seja, amplitude de oscilação dividida pelo diâmetro do cilindro, e curvasde freqüência adimensional fd/fna, ou seja, freqüência de oscilação dominante (fd) dividida pela freqüência natural da estrutura na água (fna). Como principais resultados dessa investigação experimental pode-se ressaltar os seguintes pontos: • O parâmetro (m*+CA)ζ não influencia de maneira significativa o comportamento oscilatório do sistema em termos de freqüência adimensional (fd/fna); • Demonstrou-se a influência da razão de aspecto sobre as amplitudes máximas de oscilação, em conjunto com o uso do parâmetro (m*+CA)ζ. As amplitudes máximas de oscilação sofreram redução com o aumento da razão de aspecto dos cilindros, para valores de L/D entre 6 e 20. O comportamento das amplitudes máximas de oscilação com relação ao parâmetro (m*+CA)ζ apresentou um comportamento mais complexo, dependendo da razão de aspecto ensaiada; • Alguns ensaios colocam em dúvida a validade do uso do parâmetro (m*+CA)ζ para representar de forma combinada as variações do amortecimento estrutural e razão de massa, pelo menos para a configuração experimental adotada e valores de (m*+CA)ζ < 0,074. / The occurrence of flow-induced vibrations in hydraulic structures is a highly undesirable phenomenon, because it can cause a series of operational and maintenance problems, and in some cases it can cause even the collapse of the structure. In spite of that, that aspect is still considered as a secondary element of project. The numeric study of that phenomenon is still extremely complex, being done necessary the use of models in reduced scale of the real structures for the estimate of the dynamic behavior of those structures. The modeling of the dynamic behavior of structures submitted to the flow of water is denominated hydroelastic modeling. For the correct application of the hydroelastic modeling it is fundamental a deep understanding on the basic aspects of the hydraulic and mechanical phenomena active in the structure. The present work concentrated on the experimental investigation of some basic aspects of the phenomenon of vortex-induced vibrations in cylindrical structures, with the objective of enlarging the base of existent knowledge on that phenomenon and, in that way, to contribute for the improvement of the hydroelastic modeling techniques.It is worth to emphasize that there are other mechanisms of instability responsible for the vibrations, besides vortex-shedding, they were not approached in this dissertation. The basic aspects approached in this work were the following ones: • Aspect ratio L/D - ratio of the submerged cylinder length to its diameter; • Mass-damping parameter (m*+CA)ζ − dimensionless parameter formed by the product between the mass of the structure and its structural damping ζ. For the experimental investigation, pivoted rigid cylinders were elastically mounted, submitted to steady flow of water in an open channel, with two degrees of freedom to oscillate. The present work concentrated in the study of the vibrations perpendicular to the flow direction. The employed cylinders possess different diameters, different masses and two types of springs for the elastic fixation. The variation of those parameters resulted in different oscillatory behaviors, characterized through the measurement of the accelerations in the top of the cylinder, that later were converted in displacement values in the top of the cylinder. The oscillatory behavior of the cylinders was described through curves of dimensionless amplitudes A/D, in other words, oscilation amplitude divided by the diameter of the cylinder, and curves of dimensionless frequency fd/fna, in other words, oscillating dominant frequency (fd) divided by the natural frequency of the structure in the water (fna). As main results of that experimental investigation the following points can be emphasized: • The parameter (m*+CA)ζ does not influence in a significant way the oscillatory behavior of the system in terms of dimensionless frequency (fd/fna); • The influence of the aspect ratio was demonstrated on the dimensionless amplitude of oscillation, together with the use of the parameter (m*+CA)ζ. The maximum amplitudes of oscillation suffered reduction with the increase of the aspect ratio of the cylinders, for values of L/D between 6 and 20. The behavior of the maximum dimensionless amplitudes of oscillation regarding the parameter (m*+CA)ζ presented a more complex behavior, depending on the aspect ratio; • Some results put in doubt the validity of the use of the parameter (m*+CA)ζ to combine the variations of the structural damping and mass ratio, at least for the experimental configuration adopted and values of (m*+CA)ζ < 0.074.

xiii, 129 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / Surface plasmon polaritons (SPPs) are collective electron excitations with attendant electromagnetic fields which propagate on a metal-dielectric interface. They behave, in many ways, as model two-dimensional electromagnetic waves. However, because the evanescent field of the SPPs extends a short distance outside the interface, a near-field probe can modify the wave propagation. We use this behavior to study both SPP scattering within the plane of the interface and also the transition to free-space propagation out of the plane. We have, in particular, studied the multiple scattering of SPPs excited on rough silver films. Our laboratory possesses apertureless near-field scanning optical microscopes (A-NSOMs), the probes of which can act as an in-plane scatterer of SPPs. Subsequent momentum-conserving decays of the SPPs generate an expanding hollow cone of light to which information about the direction and phase of the SPPs on the surface is transferred. A focus of our studies has been SPP multiple scattering when one of the scatterers (the tip) can move. This problem is very closely related to a similar problem in mesoscopic electronic transport, involving "universal conductance fluctuations". It is also related to various radar-detection, microwave communications and medical imaging problems. In parallel with actual experimental measurements, we have also conducted extensive Monte Carlo simulations of the scattering. Multiple scattering leads to the appearance and detection of "speckle" in the far field. A speckle field, however, is more properly considered in terms of its embedded optical vortices and so we have used holographic techniques to study these. We have demonstrated that vortices can be manipulated, created and destroyed by movement of the STM probe tip. Optical vortices are an example of the effect of "geometric" or "topological" phase in physics and as such link the trajectory of a parameter in one space to the phase observed in another. In our case, the trajectory of the A-NSOM tip parallel to the sample surface plane generates topological phase in the far field, manifestations of which are vortices. / Committee in charge: Stephen Kevan, Chairperson, Physics; Stephen Gregory, Advisor, Physics; Michael Raymer, Member, Physics; David Strom, Member, Physics; Mark Lonergan, Outside Member, Chemistry

FROTA, Diego Araujo. Estudo de um sistema supercondutor-ferromagneto: efeitos da aplicação de campo magnético e corrente elétrica. 2016. 72 f. Tese (Doutorado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2016. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2016-04-14T18:02:17Z No. of bitstreams: 1 2016_tese_dafrota.pdf: 22222249 bytes, checksum: 3c4b2e4990667c1280e4839ee1d811ac (MD5) / Approved for entry into archive by Edvander Pires (edvanderpires@gmail.com) on 2016-04-14T18:03:42Z (GMT) No. of bitstreams: 1 2016_tese_dafrota.pdf: 22222249 bytes, checksum: 3c4b2e4990667c1280e4839ee1d811ac (MD5) / Made available in DSpace on 2016-04-14T18:03:42Z (GMT). No. of bitstreams: 1 2016_tese_dafrota.pdf: 22222249 bytes, checksum: 3c4b2e4990667c1280e4839ee1d811ac (MD5) Previous issue date: 2016 / Using advanced Ginzburg-Landau simulations, we study the superconducting state of a thin super- conducting film under a ferromagnetic layer, separated by an insulating oxide, in applied external magnetic field and electric current. The taken uniaxial ferromagnet is organized into a series of parallel domains with alternating polarization of out-of-plane magnetization, sufficiently strong to induce vortex-antivortex pairs in the underlying superconductor in absence of other magnetic field. We show the organization of such vortex-antivortex matter into rich configurations, some of which are not matching the periodicity of the ferromagnetic film. The variety of possible configurations is enhanced by applied homogeneous magnetic field, where additional vortices in the superconductor may lower the energy of the system by either annihilating the present antivortices under negative ferromagnetic domains, or by lowering their own energy after positioning under positive ferromag- netic domains. As a consequence, both the vortex-antivortex reordering in increasing external field and the evolution of the energy of the system are highly nontrivial. Finally, we reveal the very inter- esting effects of applied dc electric current on the vortex-antivortex configurations, since resulting Lorentzian force has opposite direction for vortices and antivortices, while direction of the applied current with respect to ferromagnetic domains is of crucial importance for the interaction of the applied and the Meissner current, as well as the consequent vortex-antivortex dynamics - both of which are reflected in the anisotropic critical current of the system. / A partir da solução numérica das equações de Ginzburg-Landau, estudamos o estado supercondutor de um filme fino supercondutor sob uma camada ferromagnética, separados por um óxido isolante, na presença de campo magnético ou corrente elétrica aplicados. O ferromagneto considerado é organizado em uma série de domínios paralelos com magnetização oposta, perpendicular ao plano do ferromagneto, e suficientemente forte para induzir pares vórtice-antivórtice no supercondutor subjacente, quando na ausência de campo magnético aplicado. Pares vórtice-antivórtice se auto-organizam em um rico conjunto de configurações, algumas das quais não apresentam correspondência com a periodicidade do filme ferromagnético. A variedade das possíveis configurações é aumentada pela aplicação de campo magnético externo, caso em que vórtices adicionais podem diminuir a energia do sistema pela aniquilação dos antivórtices, que estão sob os domínios negativos do ferromagneto, ou diminuindo sua própria energia após se posicionarem sob domínios positivos do ferromagneto. Como consequência, o reodernamento de vórtices-antivórtices bem como a evolução da energia do sistema são não-triviais em função do aumento da intensidade do campo magnético externo. Por fim, revelamos efeitos curiosos da corrente elétrica dc aplicada sobre as configurações de pares vórtice- antivórtice, uma vez que a força de Lorentz resultante tem direção oposta para vórtices e antivórtices, enquanto que a direção da corrente aplicada em relação aos domínios ferromagnéticos é de importância crucial para a interação das correntes e Meissner e aplicada, bem como a dinâmica de vórtice-antivórtice resultante - ambas as quais estão refletidas na anisotropia da corrente crítica do sistema.