High-resolution particle image velocimetry (PIV) is employed to resolve the velocity fields within a Mach 4.9 mechanically distorted turbulent boundary layer (Reθ ≈ 40,000). The goal of this study is to directly observe the mechanisms responsible for the modified turbulent stresses present in mechanically distorted boundary layers. This is achieved by measuring the effects of the mechanical distortions upon the distribution, population, size, orientation, and energy content of the turbulent structures, and how the perturbed state of these structures is manifested within the ensemble-averaged turbulent stresses. The two mechanical distortions under investigation are 1) streamline curvature-induced favorable pressure gradients (Ip = {-0.08; -0.49}), and 2) periodic arrays of diamond roughness elements (k/δ ≈ 0.07). A smooth-wall, flat-plate boundary layer is also included to establish the unperturbed state of the turbulent structures. The response of the mean turbulence statistics is investigated through ensemble-averaged profiles of Reynolds stresses, indicating the respective influences of pressure gradient effects and surface roughness upon the turbulent statistics. The distortion and reorientation of the large-scale coherent motions is quantified through the determination of the integral length scale and local structure angle from two-point correlations. Detection of individual vortices through the swirling strength criterion λci allows the population distribution of the turbulent eddies to be examined, along with the conditionally averaged hairpin structure. The baseline and rough-wall stresses showed good agreement when scaled by the smooth-wall friction velocity. Two-point correlations indicate that the reorientation of the large-scale [i.e. O(δ)] coherent structures, coupled with the modified wall-normal fluctuations, is primarily responsible for the modification of the rough-wall Reynolds stresses. The reduced Reynolds stresses observed in the favorable pressure gradients is partially due to the attenuation of the local flowfield around the near-wall hairpin structures, mitigating the mechanism for “producing” turbulence. The rotational rate of the hairpin vortices, measured through the mean prograde swirling strength, was reduced for the favorable pressure gradient models.

abstract: The central purpose of this work is to investigate the large-scale, coherent structures that exist in turbulent Rayleigh-Bénard convection (RBC) when the domain is large enough for the classical ”wind of turbulence” to break down. The study exclusively focuses on the structures that from when the RBC geometry is a cylinder. A series of visualization studies, Fourier analysis and proper orthogonal decomposition are employed to qualitatively and quantitatively inspect the large-scale structures’ length and time scales, spatial organization, and dynamic properties. The data in this study is generated by direct numerical simulation to resolve all the scales of turbulence in a 6.3 aspect-ratio cylinder at a Rayleigh number of 9.6 × 107 and Prandtl number of 6.7. Single and double point statistics are compared against experiments and several resolution criteria are examined to verify that the simulation has enough spatial and temporal resolution to adequately represent the physical system. Large-scale structures are found to organize as roll-cells aligned along the cell’s side walls, with rays of vorticity pointing toward the core of the cell. Two different large- scale organizations are observed and these patterns are well described spatially and energetically by azimuthal Fourier modes with frequencies of 2 and 3. These Fourier modes are shown to be dominant throughout the entire domain, and are found to be the primary source for radial inhomogeneity by inspection of the energy spectra. The precision with which the azimuthal Fourier modes describe these large-scale structures shows that these structures influence a large range of length scales. Conversely, the smaller scale structures are found to be more sensitive to radial position within the Fourier modes showing a strong dependence on physical length scales. Dynamics in the large-scale structures are observed including a transition in the global pattern followed by a net rotation about the central axis. The transition takes place over 10 eddy-turnover times and the subsequent rotation occurs at a rate of approximately 1.1 degrees per eddy-turnover. These time-scales are of the same order of magnitude as those seen in lower aspect-ratio RBC for similar events and suggests a similarity in dynamic events across different aspect-ratios. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2017

In order to understand water quality in the coastal ocean and its effects on human health, the necessity arises to locate the sources of contaminants and track their transport throughout the ocean. Dynamical systems methods are applied to the study of transport of enterococci as an indicator of microbial concentration in the vicinity of Hobie Beach, an urban, subtropical beach in Miami, FL that is used for recreation and bathing on a daily basis. Previous studies on water quality have shown that Hobie Beach has high microbial levels despite having no known point source. To investigate the cause of these high microbial levels, a combination of measured surface drifter trajectories and numerically simulated flows in the vicinity of Hobie Beach is used. The numerically simulated flows are used to identify Lagrangian Coherent Structures (LCSs), which provide a template for transport in the study area. Surface drifter trajectories are shown to be consistent with the simulated flows and the LCS structure. LCSs are then used to explain the persistent water contamination and unusually high concentrations of microbes in the water off of this beach as compared with its neighboring beaches. From the drifter simulations, as well as field experiments, one can see that passive tracers are trapped in the area along the coastline by LCS. The Lagrangian circulation of Hobie Beach, influenced primarily by tide and land geometry causes a high retention rate of water near the shore, and can be used to explain the elevated levels of enterococci in the water.

The effects of vertical confinement on a neutrally-buoyant turbulent round jet discharging from a circular nozzle into quiescent shallow water were investigated. The focus was on identifying changes in the mean flow, turbulence characteristics, and large vortical structures of a horizontal water jet at different degrees of vertical confinement. The confinement resulted from the proximity of a lower solid wall and an upper free surface. The jet exit Reynolds number for all cases was 22,500. The depth of the water layer was the principal parameter. The axial and lateral confinements were negligible. Three different degrees of vertical confinement were investigated in addition to the free jet case. For the confined cases, the water layer depth was 15, 10 and 5 times the jet exit diameter. The centreline of the jet was located midway between the solid wall and the free surface. Particle image velocimetry (PIV) was used to investigate the flow behaviour. Measurements were taken on two orthogonal planes along the jet axis; one parallel and one perpendicular to the free surface. For each case, measurements were taken at three locations downstream of the jet exit where the effects of vertical confinement were expected to be significant. All image pairs were acquired at a frequency of 1 Hz using a 2048  2048 pixel camera. This rate was slow enough that the velocity fields were uncorrelated. At each location, two thousand image pairs were acquired in order to extract statistical information about the behaviour of the flow. <p>After completing the cross-correlation analysis of the PIV images and filtering outliers using a cellular neural network with a variable threshold, the statistical quantities such as mean velocities, turbulence intensities, Reynolds shear stress, centreline velocity decay, centreline turbulence intensities, and spread rate were obtained. The proper orthogonal decomposition (POD) technique was applied to the PIV data using the method of snapshots to expose vortical structures. The number of modes used for the POD reconstruction was selected to recover ~40% of the turbulent kinetic energy. An automated method was employed to identify the position, size, and strength of the vortices by searching for closed streamlines in the POD reconstructed velocity fields. This step was followed by a statistical study to understand the effect of vertical confinement on the frequency of vortex occurrence, size, strength, rotational sense, and preferred locations.<p>The results showed that the structure of the flow underwent significant changes because of the vertical confinement. The axial velocity profiles in the vertical plane become almost uniform over the entire depth with a mild peak below the centreline of the jet for the shallowest case, while the axial velocity profiles in the horizontal plane are Gaussian but narrower than the free jet profile. The mean vertical and horizontal velocity profiles show that fluid is drawn from the sides of the jet to its centreline and then diverted upward and downward from the jet axis. The decay rate of the mean centreline velocity becomes slower at downstream locations and the jet width becomes narrower in the horizontal mid-plane compared to the free jet case. The mixing efficiency of the fluid in the vertical plane is significantly inhibited by the confinement while there is a slight effect in the horizontal plane. Also, with increasing vertical confinement, the wall jet characteristics become more dominant. Investigation of the coherent structures revealed that at intermediate distances from the exit the population of vortical structures of either rotational sense is almost identical for all vortex sizes. At downstream locations in the vertical plane, this distribution is changed by the vertical confinement which causes a significant increase in the number of small clockwise vortices. In addition, it was observed that, as the confinement increases, the total number of vortical structures decreases and their sizes increase. This is evidence of the pairing process. Moreover, with increasing confinement the circulation decreases as the flow proceeds downstream on the vertical plane with a corresponding increase in the horizontal plane. This behaviour is consistent with the turbulence intensity results.

The effects of vertical confinement on a neutrally-buoyant turbulent round jet discharging from a circular nozzle into quiescent shallow water were investigated. The focus was on identifying changes in the mean flow, turbulence characteristics, and large vortical structures of a horizontal water jet at different degrees of vertical confinement. The confinement resulted from the proximity of a lower solid wall and an upper free surface. The jet exit Reynolds number for all cases was 22,500. The depth of the water layer was the principal parameter. The axial and lateral confinements were negligible. Three different degrees of vertical confinement were investigated in addition to the free jet case. For the confined cases, the water layer depth was 15, 10 and 5 times the jet exit diameter. The centreline of the jet was located midway between the solid wall and the free surface. Particle image velocimetry (PIV) was used to investigate the flow behaviour. Measurements were taken on two orthogonal planes along the jet axis; one parallel and one perpendicular to the free surface. For each case, measurements were taken at three locations downstream of the jet exit where the effects of vertical confinement were expected to be significant. All image pairs were acquired at a frequency of 1 Hz using a 2048  2048 pixel camera. This rate was slow enough that the velocity fields were uncorrelated. At each location, two thousand image pairs were acquired in order to extract statistical information about the behaviour of the flow. <p>After completing the cross-correlation analysis of the PIV images and filtering outliers using a cellular neural network with a variable threshold, the statistical quantities such as mean velocities, turbulence intensities, Reynolds shear stress, centreline velocity decay, centreline turbulence intensities, and spread rate were obtained. The proper orthogonal decomposition (POD) technique was applied to the PIV data using the method of snapshots to expose vortical structures. The number of modes used for the POD reconstruction was selected to recover ~40% of the turbulent kinetic energy. An automated method was employed to identify the position, size, and strength of the vortices by searching for closed streamlines in the POD reconstructed velocity fields. This step was followed by a statistical study to understand the effect of vertical confinement on the frequency of vortex occurrence, size, strength, rotational sense, and preferred locations.<p>The results showed that the structure of the flow underwent significant changes because of the vertical confinement. The axial velocity profiles in the vertical plane become almost uniform over the entire depth with a mild peak below the centreline of the jet for the shallowest case, while the axial velocity profiles in the horizontal plane are Gaussian but narrower than the free jet profile. The mean vertical and horizontal velocity profiles show that fluid is drawn from the sides of the jet to its centreline and then diverted upward and downward from the jet axis. The decay rate of the mean centreline velocity becomes slower at downstream locations and the jet width becomes narrower in the horizontal mid-plane compared to the free jet case. The mixing efficiency of the fluid in the vertical plane is significantly inhibited by the confinement while there is a slight effect in the horizontal plane. Also, with increasing vertical confinement, the wall jet characteristics become more dominant. Investigation of the coherent structures revealed that at intermediate distances from the exit the population of vortical structures of either rotational sense is almost identical for all vortex sizes. At downstream locations in the vertical plane, this distribution is changed by the vertical confinement which causes a significant increase in the number of small clockwise vortices. In addition, it was observed that, as the confinement increases, the total number of vortical structures decreases and their sizes increase. This is evidence of the pairing process. Moreover, with increasing confinement the circulation decreases as the flow proceeds downstream on the vertical plane with a corresponding increase in the horizontal plane. This behaviour is consistent with the turbulence intensity results.

Further understanding the small scale coherent structures which occur in high Reynolds number turbulence would be of enormous benefit. Therefore, the aim of the current project was to make well resolved three-dimensional flow measurements of the mixing flow between counter rotating impellers, using Tomographic Particle Image Velocimetry (TPIV).TPIV software was developed, with a novel approach permitting a significant reduction in processing time, and a series of numerical accuracy studies contributing to the fundamental understanding of this new technique. Basic flow characterisation determined the local isotropy, homogeneity and expected Reynolds number scaling. A favourable comparison between planar PIV and TPIV increased confidence in the latter, which was used to assess the dynamics and topology of the dissipation scale structures. In support of previous investigations similar topology, strain rate alignment, scale-invariance, and clustering behaviours are demonstrated. Correlated high enstrophy and dissipation regions occur in the periphery of larger structures, resulting in intermittency. Geometry characterisation indicates a predominance of tube-like structures, which are observed to form from larger ribbon-like structures through unsteady breakdown and vortex roll-up. Significant correlation between intermittent fields of dissipation and enstrophy describe the fine scales effects. These relationships should pave the way for more accurate models, capable of relating small scales and large scales during the prediction of dynamically important quantities.

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.

Turbulent structures are known to be important physical processes in gravel-bed rivers. A number of limitations exist that prohibit the advancement and prediction of turbulence structures for optimization of civil infrastructure, biological habitats and sediment transport in gravel-bed rivers. This includes measurement limitations that prohibit characterization of size and strength of turbulent structures in the riverine environment for different case studies as well as traditional numerical modeling limitations that prohibit modeling and prediction of turbulent structure for heterogeneous beds under high Reynolds number flows using the Navier-Stokes equations. While these limitations exist, researchers have developed various theories for the structure of turbulence in boundary layer flows including large eddies in gravel-bed rivers. While these theories have varied in details and applicable conditions, a common hypothesis has been a structural organization in the fluid which links eddies formed at the wall to coherent turbulent structures such as large eddies which may be observed vertically across the entire flow depth in an open channel. Recently physics has also seen the advancement of topological fluid mechanical ideas concerned with the study of vortex structures, braids, links and knots in velocity vector fields. In the present study the structural organization hypothesis is investigated with topological fluid mechanics and experimental results which are used to derive a vortex model for gravel-bed flows. Velocity field measurements in gravel-bed flow conditions in the laboratory were used to characterize temporal and spatial structures which may be attributed to vortex motions and reconnection phenomena. Turbulent velocity time series data were measured with ADV and decomposed using statistical decompositions to measure turbulent length scales. PIV was used to measure spatial velocity vector fields which were decomposed with filtering techniques for flow visualization. Under the specific conditions of a turbulent burst the fluid domain is organized as a braided flow of vortices connected by prime knot patterns of thin-cored flux tubes embedded on an abstract vortex surface itself having topology of a Klein bottle. This model explains observed streamline patterns in the vicinity of a strong turbulent burst in a gravel-bed river as a coherent structure in the turbulent velocity field.

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.

Questões ambientais estão no centro das discussões nas últimas décadas. A poluição atmosférica, causada pela expansão pós-revolução industrial fez surgir a necessidade de aprender a descrever, usando modelos matemáticos, esse fenômeno. Com esse conhecimento pode-se propor soluções que mitiguem a poluição e os danos colaterais causados ao ambiente. A dispersão de poluentes modelada por soluções analíticas, a partir das equações de advecção-difusão oferecem um conhecimento sobre cada componente que constrói a equação, característica inexistente em outras abordagens, como a numérica. Entretanto ela era incapaz de descrever propriedades que se referem à turbulência, as estruturas coerentes, causadas por componentes não-lineares suprimidas por construção das equações governantes do modelo. Este trabalho estudou uma forma de recuperar características associadas à turbulência através de uma componente fundamental em estruturas coerentes, a fase. Essa é incluída no modelo que passa a descrever manifestações da turbulência em processos de dispersão através de flutuações de pequena escala na concentração da solução do modelo sesquilinear, que é determinístico-estocástico. No decorrer do trabalho há um estudo através de variações de parâmetros para compreender os efeitos da fase no modelo. Ele também foi aplicado ao experimento de Copenhagen e a dois cenários reais com a intenção de compreender o modelo frente à variáveis micrometeorológicas assim como aprimorá-lo para simular a dispersão de poluentes oriundos de fontes de forma realística. / Environmental issues have been at the center of discussions in the last few decades. Atmospheric pollution, caused by post-industrial revolution, has increased the necessity to describe, using mathematical models, this phenomenon. With this knowledge is possible to propose solutions mitigating the pollution and collateral damages caused in the environment. The pollutant dispersion modeled by analytical solutions, from advection-diffusion equations, offers a knowledge about each component that constructs the equation, a characteristic that does not exist in other approaches, such as numerical. However it was unable to describe properties that refer to turbulence, coherent structures, caused by nonlinear components suppressed by constructing the model governing equations. This work studied a way to recover characteristics associated with turbulence through a fundamental component in coherent structures, the phase. This is included in the model which describes manifestations of turbulence in the dispersion process through the presence of small-scale concentration fluctuations in the sesquilinear model, which is deterministicstochastic. In the course of this work there is a study through variations of parameters to understand the phase effects in the model. It was also applied to Copenhagen experiment and to two real scenarios with the intention of understanding the model regarding micrometeorological variables as well as improving it to simulate the pollutant dispersion from sources in a realistic way.